Relationship Between Risk Exposure Volatility Forecasting

Section 1: Foundation of the Study

The goal of a hedge fund manager is to consistently provide superior performance

using dynamic strategies (Almeida et al., 2020). Cui and Kolokolova (2020) and Muteba

Mwaba (2017) attributed superior performance to either manager timing skill, asset

selection ability, or a combination of both. However, Limam et al. (2017), Stafylas and

Andrikopoulos (2020), Cai et al. (2018), and Racicot and Théoret (2018) provided

evidence that hedge fund performance is subject to structural breaks, discrete shifts,

market volatility, and time-varying properties of hedge fund dynamics. Under severe

market conditions, various hedge fund strategies are likely to have different exposures to

changes in market risk factors based on varying volatility regimes (Agarwal et al.,

2018a).

Investment decisions rely on each strategy's risk/reward ratio, which requires

managers to use the appropriate style analyses in the hedge fund market (Stafylas &

Andrikopoulos, 2020). Skilled timing managers deliver excess returns by timing market

liquidity and predicting both market and volatility conditions (Cao et al., 2018a). On the

other hand, selecting managers deliver consistently excessive returns due to their

selecting abilities (Cui & Kolokolova, 2020). However, when managers fail to forecast

sudden shocks, which results in unexpected trends in asset prices, they deliver low

returns. The purpose of this study was not to evaluate the skills of hedge fund managers

directly, but to examine the relationship between risk exposure, volatility forecasting, and

the financial performance of hedge funds.

Background of the Problem

In the last two decades, from 2000 to 2020, hedge funds became popular in

producing absolute returns in varying market conditions. Despite the success of hedge

funds, they remained susceptible to losses during the financial crisis of 2007-2009

(Metzger & Shenai, 2019; Zhang et al., 2021). During the global financial crisis of 2007-

2009, the total number of assets managed by the hedge fund industry declined by

approximately 33% (Billio et al., 2017; Page & Panariello, 2018). The authors attributed

the problem to hedge funds' exposure to new types of market risk factors. Furthermore,

evaluating hedge funds using conventional methodologies may be inadequate (Chevalier

& Darolles, 2019).

Hedge funds use varying investment strategies to produce higher returns than

traditional assets (Cai et al., 2018). Consequently, the returns of hedge funds show

abnormal and dynamic risk characteristics. Some researchers have come up with models

to capture the hedge fund return dynamics (Almeida et al., 2020; Balcilar et al., 2017;

Shin et al., 2018). The authors identified the regime-switching model as the most efficient

model to capture time-varying risk exposure for hedge funds that are conditional on

various market situations. Forecasting volatility captures the asymmetry and changes in

the hedge fund returns characteristics (Limam et al., 2017). Xaba et al. (2017) found that

using Markov regime-switching modeling was more accurate to forecast nonlinear time

series. This study was an attempt to evaluate hedge fund performance relationships with

volatility dynamics and market risk factors to understand market behavior and drivers of

return.

Problem Statement

Poor hedge fund performance can negatively impact the financial performance of

a business organization (Metzger & Shenai, 2019; Zhang et al., 2021). During the global

financial crisis of 2007-2009, the total number of assets managed by the hedge fund

industry declined by approximately 33% (Billio et al., 2017; Page & Panariello, 2018;

Stoforos et al., 2017).). The general business problem is that hedge funds have a negative

effect on company profits in a downturned market. The specific business problem is that

some managers do not understand the relationship between risk exposure, volatility

forecasting, and financial performance of hedge funds.

Purpose Statement

The purpose of this quantitative correlational study was to examine the

relationship between risk exposure, volatility forecasting, and the financial performance

of hedge funds. The independent variables were volatility forecasting, and risk exposure.

The dependent variable was the financial performance of hedge funds. The targeted

population comprised archival data from hedge fund databases in South Africa. The

implication for positive social change includes the potential to provide organizational

leaders who partner with hedge funds the ability to maximize profit by diversifying risk

in volatile market conditions. Using an investment tool to dispel uncertainty in various

market conditions is a financial means to foster a positive change (Sosner & Steblea-

Lora, 2022). Accordingly, through partnerships with foundations and nonprofit

organizations, hedge funds may help organization leaders fund projects in local

communities.

Nature of the Study

Researchers may use quantitative, qualitative or mixed method approaches to

conduct a study (Morgan, 2018; Zoellner & Harris, 2017). A quantitative method of

research was suitable for this study as it is used to identify solutions through statistical

data analysis and provide explanations of predictions and causal relationships (Köhler et

al., 2017). Further, the quantitative method was appropriate for this study because the

purpose was to examine the relationship between variables. A qualitative method is

applicable when a researcher intends to understand the experiences and attitudes of

people in a business or social setting (Mohajan, 2018). A mixed methods approach

includes both quantitative and qualitative methods (Brannen, 2017). Researchers employ

the mixed methods approach to combine the qualitative and quantitative methodologies

when analyzing both textual and numerical data (Brannen, 2017; Williamson et al.,

2020). Therefore, the qualitative portion of a mixed methods approach was not

appropriate for this study.

Researchers may use a correlation design to examine the ability of the variables to

predict an outcome (Zyphur & Pierides, 2020). A correlation design was appropriate for

this study because of its purpose in examining the efficacy of modern portfolio constructs

predicting financial performance of hedge funds. Other designs such as experimental and

quasi-experimental comparative designs are appropriate when researchers seek to

examine how independent variables may influence a dependent variable (Cortina, 2020).

I did not manipulate the variables, and I did not randomize the secondary data during the

collection process. An experimental research design was, therefore, not appropriate for

this study, and the correlation design was most appropriate.

Research Question

Is there a statistical significant relationship between risk exposure, volatility

forecasting, and financial performance of hedge funds?

Hypotheses

H0: There is no statistically significant relationship between risk exposure,

volatility forecasting, and financial performance of hedge funds.

Ha: There is a statistically significant relationship between risk exposure,

volatility forecasting, and financial performance of hedge funds.

Theoretical Framework

Markowitz (1952) developed the modern portfolio theory to explain how to

reduce a portfolio’s risk and increase the expected rate of return when combining

uncorrelated asset classes. Markowitz demonstrated that researchers could use the

variance of the rate of return to calculate a portfolio’s risk. Furthermore, Markowitz

derived the statistical formula for computing the covariance of a portfolio (Shadabfar &

Cheng, 2020). With the covariance formula, Markowitz was able to demonstrate the

importance of diversifying investments to reduce risks effectively.

Diversification is the core concept of the modern portfolio theory, and is also a

concept used to calculate risk (Tan & Trinidad, 2018). Markowitz contended that, over

time, a diversified portfolio reduces volatility more efficiently than one that isn’t

diversified. Based on the analysis, the most prominent tenets of the modern portfolio

theory are (a) an assumption that markets are efficient, and markets use this information

to determine security prices; (b) investors receive higher returns for using high-risk

investments over time; (c) adding high-risk, low-correlation asset classes to a portfolio

can increase the expected rate of return and decrease volatility; and (d) investors can

diversify passive asset class fund portfolios over time to deliver the highest expected rate

of return (Markowitz, 1952). Similarly, Markowitz identified the key constructs of the

modern portfolio theory as (a) volatility forecasting and (b) risk exposure. As applied to

this study, the independent variables (modern portfolio constructs) were measured using

archived data collected from publicly and privately accessible databases to predict the

financial performance of hedge funds. The MPT applies to this study because the goal is

to examine variables that may relate to the financial performance of hedge funds.

Operational Definitions

Capital markets: Capital markets include regulated markets where all-size

capitalized companies can acquire funding for their short and long-term investments,

including core corporations and expansion (Cao et al., 2018a).

Financial bubble: Financial bubble refers to an economic phase characterized by

a sudden rise in asset prices followed by their reduction. Unjustifiable investor behavior

can create a surge in asset prices (Jang & Kang, 2019).

Funds of funds: Funds of funds refers to an investment strategy of owning a

portfolio of other investment funds. A fund of fund invests in other hedge-funds instead

of investing in particular securities (Getmansky et al., 2019).

Hedge fund management and incentive fees: The management fee is usually set at

2% of the total asset, and is paid to the hedge fund manager for asset management. The

incentive or performance fee can be up to 20% of the fund's profit. The incentive fee is to

reward the hedge fund manager for good performance, including taking higher risks

(Ben-David et al., 2020).

Hedge funds: Hedge funds or alternative investments are a collective of private

investment vehicles that allow different investors to combine their money (Getmansky et

al., 2019). The funds are under the management of an investment manager according to

terms and conditions set in the fund prospectus. Hedge funds use dynamic trading

strategies to seek absolute returns, regardless of the market condition (Stafylas et al.,

2018a).

Institutional investor: An institutional investor is an organization that trades

securities in significant quantities or a large sum of money, such as banks, pension funds,

investment advisers, insurance companies, and mutual funds. Institutional investors are

often eligible for preferential treatment and lower commission (Kolokolova et al., 2020).

Regime-switches: Regime-switches are structural changes in the market.

According to the risk environment, the regime represents good and bad or up/down

equity market conditions (Stafylas et al., 2017).

Assumptions, Limitations, and Delimitations

Assumptions

Assumptions, which are statements, issues, ideas, or positions the researcher

accepts without verification during a study, are an accepted part of the research process

(AbuRaya & Gomaa, 2020; Foss & Hallberg, 2017). In this study, there were three

assumptions. The first assumption was that the sample represents the population I

inferred. The second assumption was that the data were accurate and performed the

measurements. Finally, the third assumption is that the hedge fund return data included

all the necessary elements before assigning value for the quality.

Limitations

Researchers confront some limitations when performing a research study.

Limitations are potential weaknesses of a study out of the researcher's control (Harari &

Lee, 2021). Limitations usually relate to the study's design and methodologies, such as

bias or specific statistical models (Ross & Bibler Zaidi, 2019). The first limitation is

associated with the generalizability of study findings due to a specific time sampling

period (Greener, 2018). Because hedge funds report voluntarily to commercial databases,

hedge fund data can have biases (Joenväärä et al., 2021b). The two biases that have

significant impact on hedge fund data include survivorship bias and backfill bias

(Hutchinson et al., 2021). The second limitation arises from the bias inherent in archival

data. Some biases that may exist in databases can also influence hedge fund empirical

research (Aragon & Nanda, 2017). The sample in this study was subject to the bias of

missing time series data (Kiss et al., 2017). In addition, hedge fund returns are subject to

delisting bias because managers can choose when and which funds to disclose to the data

vendor (Aragon & Nanda, 2017). The final limitation is the generalization of the study

findings to the hedge fund industry.

Delimitations

Delimitations are actions taken by the researcher to determine the study's scope or

boundaries (Theofanidis & Fountouki, 2018). Unlike assumptions and limitations,

delimitations are under the researcher’s control. This doctoral study's first delimitation

was the research problem's scope, which includes the theoretical perspectives and

variables of interest. The second delimitation was the restriction of the specific study

period, as the sample time frame puts restrictions on the examined study results. The third

delimitation relates to the restriction to a geographical area in South Africa. Thus, the

conclusion might infer only to hedge funds based in South Africa.

Significance of the Study

Contribution to Business Practice

Hedge fund managers and individual investors stand to benefit from this study.

Hedge fund managers may benefit from a better understanding of effective methods to

reduce portfolio risks by diversifying assets to maximize the expected rates of return

(Stafylas et al., 2017). Also, individual investors such as retirees could have a better

understanding of their invested funds (Stafylas et al., 2017). Furthermore, business

owners could use volatility forecasting as a risk management tool to price derivatives and

hedge risks (Gaetano, 2018). In addition, the results of the study might positively impact

the financial professionals' ability to predict the market volatility (Xaba et al., 2017).

Thus, a better assessment of the impact varying economic conditions or business phases

have on the risk dynamics of the strategies.

Implications for Social Change

The implication for positive social change includes the potential to provide

organizational leaders who partner with hedge funds the ability to maximize profit by

diversifying risk in volatile market conditions. The ability to use an investment tool to

dispel uncertainty in various market conditions is a financial means to foster positive

change (Sosner & Steblea-Lora, 2022). Well-informed investors make profitable

decisions that could generate advantages for the societies and organizations to which they

contribute. Accordingly, through partnerships, hedge funds can help leaders of

foundations and nonprofit organizational fund projects in local communities.

A Review of the Professional and Academic Literature

The purpose of this quantitative study was to investigate the relationship between

risk exposure, volatility forecasting, and financial performance. The literature review was

an essential component of the research study as it provides an extensive analysis of the

subject area, defines the theoretical framework, and substantiates the research problem

(Snyder, 2019). Investigating how hedge funds can be used as potential alternative

investments for investors, as well as comprehension of hedge fund performance and

fund-specific characteristics were part of the professional and academic literature review.

Search Strategy

I used the peer-reviewed articles and journals found in Walden University's

library databases to conduct the academic literature search. The databases included

Business Source Complete, Sage, ProQuest, ScienceDirect, ABI/INFORM, Dissertations,

Directory of Open Access Journals, Google Scholar, and Emerald Management Journals.

The keywords used included industry-specific terms such as hedge funds, mutual funds

forecasting volatility, volatility, equity markets, modern portfolio management, efficient

market hypothesis, risk exposure in the market, regime-switching models, hedge funds

risk management, performance persistence, liquidity, hedge funds characteristics, hedge

fund managers, behavioral finance, value investing, beta, time-varying risk, Hedge funds

in South Africa, and performance evaluation.

Table 1

Summary of Literature Review Resources

Reference type

> 5 Years

< 5 Years

Total

Peer-reviewed Journals

191

228

Nonpeer-reviewed Journals

Dissertations

Books

Government or Corporate Sites

Total

203

243

The literature review content included 243 sources, one website, three books, and

one dissertation. Out of the total cited sources, 228 (94%) journals were peer-reviewed,

and 203 (84%) of the sources were current within 5 years of my expected graduation

date. The literature review structure begins with the background discussion of the

theoretical framework grounding the study, including the models describing the

theoretical link between risk and return. The seminal literature is grounded on modern

portfolio theory (MPT) by Markowitz (1952) as the theoretical framework to investigate

the relationship between risk exposure, volatility forecasting, and financial performance

of hedge funds. During the research, I identified additional models to extend the MPT

and to discuss the key themes (Bedoui et al., 2020).

The second part of the section covers the following supporting and contrasting

theories: (a) value investing theory (Graham et al., 1934) and (b) behavioral finance

theory (Tversky & Kahneman, 1974). The central part of the literature review covers the

critical analysis and synthesis of the sources on each study variable: (a) volatility

forecasting, (b) risk exposure, and (c) the financial performance of hedge funds. The

literature review chapter will conclude with a summary of critical contents and an

overview of primary objectives.

Modern Portfolio Theory

This study is grounded in the modern portfolio theory (MPT). I used the MPT for

this purpose because it supports the principle of diversification, which is a risk

management technique for investors and fund managers (Arize et al., 2019). Harry

Markowitz is the founder of the modern portfolio theory, which is an influential

economic theory to engage in finance and investment practices (Markowitz, 1952).

Markowitz proposed two principles for portfolio construction and optimization via MPT:

(a) the mean-variance model or risk-return model, and (b) the efficient frontier. The

mean-variance model focuses on an asset's risk and return elements (Moulya et al., 2019).

In this model, the investors allot weights to each asset or risky securities to create a

portfolio in a vector format. Oliinyk and Kozmenko (2019) recommended that investors

construct portfolios by allotting optimal weights on the risky assets to minimize the risk

of the expected return. Bender et al. (2019) compared alternative weighting schemes for

constructing portfolios. The authors recommended constructing portfolios of factors

based on average variance values because they describe details comprehensively due to

the explicit use of input factors.

Investors gain the expected return of an asset by accepting the variance of an

asset's returns or risk (Schadler & Steurer, 2019). Simultaneously, by diversifying

securities in a portfolio, an investor can reduce the expected return variance. Thus, an

investor who aspires to reduce the volatility of portfolios' total returns may seek funds

with lower returns and, therefore, lower risk. Xin Rui et al. (2018) examined the

relationship between risk in financial investment and the expected return. The research

findings correspond to those found by Zhu et al., (2020), noting a significant positive

relationship between risk and return during up markets.

According to MPT, an investor can use each asset's mean return and the mean-

variance of that asset to determine both (a) the expected return and (b) the expected

variance of a portfolio, respectively. Also, the investor can determine the covariance

between assets by using the correlating coefficient between the returns of the assets in the

portfolio (Markowitz, 1952). The mean-variance model postulates that the assets'

historical returns influence future returns (Sui et al., 2020). The variables are obtainable

from archival data in the market. The investor can calculate the proportion of each asset

to allocate in the portfolio using weights. The expected return of the portfolio as follows:

E(Rport) = wa ERa + wb ERb + …, where table 2 describes all terms.

Table 2

Term Description for Expected Return for Portfolio using MPT

Term

Description

E(Rport)

Expected return on the portfolio

Individually weighted of asset a in the portfolio

ERa

Expected return on the asset a

Individually weighted of asset b in the portfolio

ERb

Expected return on the asset b

Note. From “Portfolio Selection” by H. Markowitz, 1952, Journal of Finance, 7(1), p. 77.

(https://doi.org/10.1111/j.1540-6261.1952.tb01525.x)

The MPT postulates that investors are risk-averse or risk-neutral, and thus try to

maximize the trade-off between risk and expected return in investment decisions (Guo et

al., 2019). Thus, investors and fund managers can create an investment portfolio

representing the investor's perceptions and requirements, ultimately leading to a

collection of efficient portfolios known as the efficient frontier (Siswanah, 2020).

Furthermore, each level of expected return on the efficient frontier has minimum

volatility, and each volatility level has the maximum expected return. The MPT showed

that the return rate variance is an appropriate measure of portfolio risk under certain

assumptions (Gruszka & Szwabinski, 2020). The variance formula indicates the

importance of diversifying investments to reduce the total risk of a portfolio. Thus, MPT

allows investors to minimize risk and maximize their wealth.

Managers aim to select an optimal portfolio along the efficient frontier to meet the

investor's profile and utility function (Zavera, 2017). In this case, Zavera applied the

MPT to evaluate the performance and risk of portfolios in the Romanian stock market,

using historical data from 2010 to 2015 of the gas sectors, energy sector, and food sector

to create three securities. From these, Zavera (2017) determined the efficient frontier and

the portfolio's minimum variance. The study findings were negative returns because of

the inadequate sample size for the study. Also, this lack of information makes it difficult

to make decisions for the investor. Besides the diversification component, the MPT has

an inherent strategy of low asset classes' low correlation (Arize et al., 2019). Assets can

lower volatility when in an uncorrelated combination. Bessler et al. (2017) found that a

broader diversification by adding government bonds enhances portfolio optimization

benefits. Also, Oliinyk and Kozmenko (2019) showed that portfolio diversification grants

higher returns for a given risk for the minimum-variance portfolio; the variability in

returns is due to variability in allocation in estimating weights.

Investors and fund managers desire better downside risk protection. Lin and Wu

(2018) found that risk-adjusted returns, volatility, diversification, correlation, and

downside protection allow investors to search for tools to customize portfolios and

improve performance. Wu et al. (2020) recommended a differential evolution algorithm

to dissipate financial and portfolio risks under certain conditions. However, Bessler et al.

(2017) suggested incorporating alternative asset classes, such as commodities and hedge

funds, to improve the risk-free rate. Simonian and Wu (2019) applied the regression

method to replicate hedge fund strategies to build portfolios for hedging risks and

increase returns. The term hedge fund is an alternative investment that aims to increase

risk-adjusted performance or absolute returns (Getmansky et al., 2019).

Markowitz (1952) found that risk could not be diversified entirely away from an

investment. Each investment has two main types of risk: (a) systematic risks, beta β, and

(b) unsystematic risks. Systematic risks are part of a security's risk that originate from

external factors affecting the whole market; systematic risks cannot be diversified away

(Xin Rui et al., 2018). Examples of such factors are interest rates, inflation, liquidity,

equity, credit, wars, fiscal, monetary policies, and pandemics. Avkiran (2018) found the

systematic risk to be related to macroeconomic shifts associated with the market

conditions.

Unsystematic risks refer to specific risks part of a security risk caused by factors

unique to a firm (Xin Rui et al., 2018). According to Puspitaningtyas (2017), this risk can

diversify away because it originates from internal factors (microeconomic). Sources of

specific risks include company management, credit rating, lawsuits, marketing strategies,

strikes, and other related issues unique to the company. In summary, a portfolio's

systematic risk of assets is correlated to market factors, while unsystematic risks are not

correlated.

Assumptions and Limitations of MPT

Markowitz (1952) based the model on the following assumptions (a) Investors are

rational and risk-averse, which may not apply to all investors. Stork et al. (2020) found

evidence contrasting the theories that assume rational expectations and support the

bounded rationality theory of behavioral heterogeneity. Alternatively, Taffler et al.

(2017) found that the prospect theory asserts that investment decisions stem from various

behavioral biases that encourage the investors from rationality (b) Markets are efficient.

All information is available to all investors. However, behavioral theories attest that the

market is inefficient because of frequent anomalies (Filbeck et al., 2017). Also,

Senarathne (2019) pointed out that bounded rational theory explains that not all market

participants have access to all information to make possible decisions, (c) Identifies an

asset's return with a normal distribution. However, the real world’s correlation between

asset returns is not constant (Xin Rui et al., 2018). (d) The mean-variance model

presumes that the assets' expected return stems from the mean of the assets' historical

returns. Jones (2017) argues that the archival method ignores risk factors that impact

assets' returns.

Capital Asset Pricing Model (CAPM)

The CAPM is a continuation of the MPT that attempts to assess the price of risk

of assets. Sharpe (1964) and Lintner (1965) introduced the CAPM to model the

relationship between risk and expected return for equities. The CAPM is a simplified and

more practical extension of Markowitz's MPT and is applicable to assess the relationship

between risk and return rate. The model bases its theory on the two aspects of risk,

systematic and unsystematic (Fernando, 2018). As discussed, the MPT shows that

diversification cannot eliminate systematic risk. The model also allows an investor to

evaluate a portfolio's expected return, given the risk β. (Puspitaningtyas, 2017). Hence,

the CAPM evolved to determine the systematic risks in a portfolio.

Sharpe (1992) built the CAPM on the basis of fundamental assumptions about the

capital market and investors' operation: First, all investors have identical expectations,

and all information is freely available to all market participants simultaneously.

Secondly, investors are rational and seek to maximize their utility, and high expected

returns at a lower risk. Third, all investors can borrow or lend any money at a risk-free

rate of return. Fourth, there is a linear relationship between the expected return rate of an

asset and its risk. The fifth assumption is that transactions are exempt from any fees or

tax costs. The sixth assumption is that markets are efficient; investors do not affect prices

and have the same odds for the expected return. Most of these assumptions have a

drawback for unrealistic reflection of the actual market. Sharpe (1992) formulated the

CAPM based on the principle that an asset's return rate equals risk plus the risk-free rate.

The following formula represents the CAPM is as follows:

E(Ra) = Rf + βa (ERm - Rf ), where table 3 describes all terms

Table 3

Term Description for CAPM Equation

Term

Description

E(Ra)

Expected return on asset a

Risk-free rate return of an asset (10-year government bond-yield)

E(Rm)

Expected return of market, m or Index

βa

Systematic risk (beta) of asset a

Note. From “Capital asset prices: A theory of market equilibrium under conditions of risk” by W. F. Sharpe, 1964,

Journal of Finance, 19(3), p. 432. (https://doi.org/10.2307/2977928)

The beta (β) coefficient measures an asset's relative sensitivity to market

movements: the asset's risk exposure. Black and Scholes (1973) studied price movements

in stock portfolios relative to the Stock Exchange between 1931 and 1965. From these

Black and Scholes (1973) confirmed the linear relationship between the returns of their

stock portfolios and their betas. However, Fama and French (1993) found that the

difference in betas over time did not justify stocks' performance in the portfolio. The

equation for expected returns represents the relationship between an asset's risk and

return, named the Security Market Line (SML). The efficient frontier graph rearranges to

illustrate the performance of individual assets. In the SML equation, the coefficient of

beta, βa, is as follows:

βa = cov(a* m) / ρ2m , where table 4 describes all terms

Table 4

Term Description for Beta in the SML Equation

Term

Description

βa

Systematic risk (beta) for asset a

cov(a* m)

Covariance between asset a, and market m or index.

ρ2m

Variance on returns on the market m or index

Note. From “Capital asset prices: A theory of market equilibrium under conditions of risk” by W. F. Sharpe, 1964,

Journal of Finance, 19(3), p. 439. (https://doi.org/10.2307/2977928)

For the average asset, beta is equal to or greater than 1; then, it contributes higher

than average risk to the portfolio (Bolander et al., 2017). If the beta is less than zero, the

securities will perform well when the market does poorly and vice versa

(Puspitaningtyas, 2017). Thus, the CAPM model can help investors determine the sources

of common equity risk factors in a portfolio. Unlike traditional funds, hedge funds

evaluate relative and absolute returns performance. The relative return requires the fund

manager to compare performance to other investment instruments such as other funds,

hedge funds, and indexes (Zhang et al., 2021). Also, performance comparison requires a

time frame.

On the other hand, absolute returns or risk-adjusted returns require a performance

comparison to the other hedge fund strategies (Hwang et al., 2017). Hentati-Kaffel and de

Peretti (2015) conducted a nonparametric study to examine the randomness and

persistence of hedge funds' relative returns. In this case, Hentati-Kaffel and de Peretti

used Hedge Fund Research (HFR) data, from January 2000 to December 2012, and the

S&P500 as a benchmark. The study concluded that about 80% of the absolute returns

were random, and the event-driven and relative value strategies present clustering in

relative return. The study confirms that hedge funds' relative returns vary with a

benchmark.

Beta β represents a fund's systematic risks, α, alpha represents the non-systematic

return generated by an asset (Puspitaningtyas, 2017). Furthermore, the unsystematic risk

does not relate to market factors. However, the alpha coefficient is related to the hedge

fund manager's skills and critical quantitative skills when allocating assets to hedge fund

managers (Frydenberg et al., 2017). Consequently, the most efficient hedge fund strategy

will yield a risk-adjusted return with systematic risk factors. Jensen (1968) highlighted

the importance of a better understanding portfolio risks when analyzing alpha. The

Jensen equation is as follows:

E(Ra) = αa + Rf +βa (ERm - Rf ) - Ɛa where table 5 describes all terms

Table 5

Term Description for Jensen Equation

Term

Description

E(Ra)

Expected return of asset a

αa

Risk adjusted return of an asset a, or performance measure

Risk-free rate return of an asset (3-month government bond-yield)

βa

Systematic risk (beta) of asset a

Ɛa

Error term. For asset a, idiosyncratic term will be zero

Note. From “The performance of mutual funds in the period.” by M. C. Jensen, 1968, Journal of Finance, 23(2), p. 393.

(https://doi.org/10.1111/j.1540-6261.1968.tb00815.x)

Jensen's equation above shows a method to evaluate the risk-adjusted return of a

portfolio. Jiang et al. (2022) confirmed by remarking that a manager's alpha is a

testament to time the market effectively. Still, it is more complex to evaluate hedge fund

returns than for classical funds. Unlike mutual funds, a hedge fund manager emphasizes

evaluating absolute returns (Swartz & Emami-Langroodi, 2018). According to Almeida

et al. (2020), managers generate relative returns required by comparing returns to a

benchmark over a set time. On the other hand, to generate absolute returns, the manager

compares them to other strategies. A hedge fund strategy's primary goal is to perform a

risk-adjusted return uncorrelated with systematic risk factors (Puspitaningtyas, 2017).

The CAPM model assumes that the variance in asset returns is linear, depending on the

market's risk factors. However, the drawback of using the CAPM to assess hedge fund

returns relative to risk is that hedge fund returns do not have a normal distribution.

Arbitrage Pricing Theory (APT).

The APT is a different approach to the CAPM to evaluate asset prices. Ross

(1976) adapted a multifactor model to mitigate the limitations presented by the CAPM.

The APT is based on a linear process like the CAPM but with fewer assumptions. The

main difference is that although the CAPM is not a complicated model, it is not easy to

verify empirically. The underlying assumption essential for the CAPM on the natural

economic conditions makes it challenging to study the impact of the capital market on an

investor's decision or performance (Yildiz & Erzurumlu, 2018). The APT specifies

several risk factors and expands the definition of systematic investment risk (Frydenberg

et al., 2017). The authors found that some of the factors could be statistical or

fundamental. Roll and Ross (1980) identified the three underlying assumptions of the

APT as follows: (a) prices of securities, governed by multiple factors, which have

categories such as macroeconomic or specific risk factors, (b) diversification erases the

unsystematic risk (specific risk) in a portfolio. Lastly, if a portfolio is well-diversified,

investors will have no arbitrage opportunity. The APT incorporates all the assumptions in

the following equation:

E(Ra) = Rf + β1 F1 + β2 F2 + . βn Fn + Ɛa, where table 6 describes all terms

Table 6

Term Description for Expected Return of an Asset using the APT

Term

Description

E(Ra)

Expected return of asset a

Risk-free rate return of an asset (3-month government bond-yield)

βn Fn

Price relationship between risk premium and (n beta factors)

Risk premium related to the nth risk factor

Ɛa

Error term. For asset a, idiosyncratic term will be zero

Note. From “The performance of mutual funds in the period.” by M. C. Jensen, 1968, Journal of Finance, 23(2), p. 393.

(https://doi.org/10.1111/j.1540-6261.1968.tb00815.x)

The APT extends the CAPM, and identifies the risk factors (Fernando, 2018).

Thus, the APT users apply the model to determine the relevant factors that might affect

the asset's returns. Roll and Ross (1980) concluded that the important factors would

include: (a) the variation in inflation, (b) variation in risk premiums and market risk, (c)

change in the amount of industrial production, and (d) change in interest rates.

Ultimately, the CAPM and APT are similar, as they aim to estimate the expected returns

of assets or portfolios.

Several studies investigated methods to derive risk exposures from hedge fund

return data (Hespeler & Loiacono, 2017; Mestre, 2021; Stafylas et al., 2017). Frei and

Hughes (2013) adapted the Posterior Cramer-Rao Bound (PCRB) concept from Sharpe's

(1992) earlier study when analyzing hedge fund portfolios of varying securities within an

asset class. The authors applied the PCRB to several hedge fund models to demonstrate

its efficiency in assessing the achievable accuracy of return-based hedge fund exposure.

The authors claimed that the model is appropriate when a researcher lacks access to

hedge fund data. Also, the authors demonstrated that for a manager to achieve an accurate

exposure estimate, they need to consider the following variables (a) covariance of asset

factor, (b) variance of the idiosyncratic error, and (c) value of fund's exposure.

Frydenberg et al. (2017) used the multifactor quantile regression model to

determine which risk factors affect an asset's various hedge fund strategies. The authors

collected data from the Hedge Fund Research (HFR) database containing statistics for

more than 7,000 funds ranging from April 1, 2003, to March 6, 2009. The authors

modeled nine indexes in the study to determine any differences in estimated risk

exposures using quantiles regression compared to the ordinary least squares (OLS)

approach. The analysis revealed that the OLS approach only revealed the risk factors that

contribute to the average return of a hedge fund strategy but failed to account for how the

different risk factors affect tail risk. However, the quantile regression approach

determined the difference in investment styles in each hedge-fund category.

Efficient Market Hypothesis (EMH)

The Efficient Market Hypothesis (EMH) connects to the MPT and is also relevant

to this study. Karp and Van Vuuren (2019) observed that MPT and its precepts evolved

from the EMH. Academic researchers and practitioners use the EMH to study price

movement in the market (Cao et al., 2018b). Fama (1970) described the EMH as a

measure of how the financial markets rapidly process publicly available new information.

Also, Karki (2018) defined the EMH as the Random Walk Theory, demonstrating that

stock price changes fully reflect available information about the firm's value.

Furthermore, the firms are cannot make excess profits from exploiting this information.

Thus, the EMH is a concept of information efficiency and the market's ability to analyze

the data into prices.

Fama (1970) conducted an empirical analysis of the EMH using the fair game

model based on the following assumptions: (a) When market prices fully reflect all

available information, the market is informationally efficient (Cao et al., 2018b), (b)

When market conditions are efficient, only new information creates volatility. However,

stock prices vary with the news, which affects macroeconomic factors (Okonkwo, 2019).

EMH has another assumption, which asserts that investors' reactions, on average, are

appropriately in a normal distribution pattern (Kristoufek & Vosvrda, 2018). On the

contrary, investors, and financial markets are characterized by nonlinear dynamic systems

of interacting agents who rapidly process new information (Mallikariuna & Rao, 2019;

Rehman, 2020). Tiwari et al. (2017) argued that fractals provide a realistic market risk

framework for prices.

In his empirical work, Fama (1970) introduced three market efficiency versions

strong-form, semi-strong, and weak form efficiency. A weak-form efficient market if the

current prices indicate all historical or past information. Prices follow the random walk,

and investors cannot use technical analysis to earn an excess return. Thus, the stock

return is serially uncorrelated, and has a constant mean and normal distribution

(Kristoufek & Vosvrda, 2018). When public and future expectations fully reflect an

efficient market in a semi-strong form, neither technical nor fundamental analysis can

trace a stock's behavior pattern. A condition necessary for abnormal returns is for market

participants to access private information because all publicly available information

shows current prices. The strong-form efficient markets include all information in the

public and private market and reflects in current prices. Thus, all investors can earn

abnormal profits in this form of efficiency. Fama (1970) proposed these three conditions

to attain strong-form market efficiency: (a) no transaction fees, (b) free access to relevant

information, and (c) a similar way of assessing stocks by all investors. However, Fama

(1970) also noted that these conditions do not represent fundamental financial markets.

Furthermore, infringing on these conditions does not necessarily infer inefficiency, but it

is potential aid.

Cao et al. (2018b) and Cao et al. (2018a) studied hedge fund literature and found

that hedge fund trading enhances market efficiency. In comparing the impact of trading

by mutual funds and hedge funds on the stock prices, the studies found that the aggregate

flows to hedge funds correct the market pricing, while mutual funds worsen it. Hwang et

al. (2017) confirmed the positive impact of hedge fund trading on financial markets. The

authors showed that hedge fund returns negatively correlate with market flow changes,

suggesting hedge funds increase market efficiency. Also, Guptha and Rao (2018) report a

positive relationship between hedge fund return shocks and subsequent returns,

suggesting that hedge fund investors have more information than other investors.

Related and Contrasting Theories

To incorporate enough literature into the modern portfolio theory section, I will

discuss two other theories related to and contrasting with the MPT. The two theories

include the behavioral finance theory and the value investment theory. Academic

researchers and practitioners use the value investing theory to evaluate the current

investment price, and the firm’s profit relative to market performance (Zhang, 2019).

Behavioral financial theory can replace the mean-variance portfolio theory, CAPM, asset

CAPM, and other risk models related to expected returns (Mei & Nogales, 2018).

Behavioral Finance Theory

Behavioral finance theory is a contrasting theory to the modern portfolio theory in

this study. Traditional finance theories like the EMH, MPT, or CAPM assume that

investors are rational and maximize utility. However, behavioral economists argue that

emotional and psychological factors shape investors' decision-making processes (Ahmad

et al., 2017). There are two branches of behavioral finance: (a) micro and (b) macro

(Statman, 2017). Micro behavioral finance studies focus on individual investors'

behavior, and macro studies focus on anomalies in the market that behavioral models

may account for (Statman, 2017). Investment decision-making incorporates micro and

macro factors (Ahmad et al., 2017). This review will focus on both branches of

behavioral finance to study investor behavior using the prospect theory components.

The current theories in behavioral finance are the bounded rational theory of

Simon (1955), the prospect theory by Tversky and Kahneman (1974), and the adaptive

theory by Tinbergen (1939). Behavioral finance originates from philosophical and

psychological views, which assumes investor irrationality and inefficient financial

markets (Ahmad et al., 2017). The prospect theory is used to understand the decision

behavior of investors in financial markets (Abdin et al., 2019; Madaan & Singh, 2019).

The primary presumption of the prospect theory is that investors are more risk-averse

than have a desire for potential gains (Abdin et al., 2019). Ahmad et al. (2017)

documented that investor decision-making has two thinking systems, the cognitive and

the biased systems. The cognitive system leads to errors known as cognitive heuristics.

On the other hand, biases in decision-making arise from investor sentiment,

emotion, and mood. Strömbaäck et al. (2017) defined cognitive heuristics decisions as a

simple rule of thumb that explains how investors make decisions and solve problems.

Abdin et al. (2017) divided the cognitive heuristics include the following three factors of

investor behavior:

1. Availability, the tendency for investors to use available information

2. Hindsight, which refers to the investor's behavior to use past events or

experiences to predict future events

3. Representativeness explains how investors use stereotypes when making

decisions

4. Mental accounting, procedure investors, use to direct and measure financial

activities

Abdin et al. (2019) showed that mental accounting has a significant positive effect

on all anomalies. Areiqat et al. (2019) used four behavior biases to study investor

emotional decision-making behavior; overconfidence bias, regret aversion, herd behavior,

and loss aversion.

Herd behavior occurs when investors observe and imitate others' behavior during

market distress (Yu et al., 2018). Also, it occurs when investors herd and ignore their

decisions and follow others. Mertzanis and Allam (2018) found that herding is high

during market anomalies and price bubbles. Chhapra et al. (2018) concluded that herd

bias does not impact investors’ decision-making. However, Madaan and Singh (2019)

found that herd bias strongly influences investors' investment decisions.

Overconfidence is a psychological bias that steers an investor to overestimate

skill, knowledge or perceive the probability of a result occurring (Joo & Durri, 2017). In

behavioral finance, overconfidence leads to excessive trading volume, higher price

volatility, and return variability. Mushinada and Veluri (2018) showed that

overconfidence about comprehending and processing information could make investors

overreact. Abdin et al. (2017) revealed that overconfidence is a negative predictor that

forecasts the performance of investors during market anomalies. However, Chu et al.

(2017) attested that financial literacy makes confidence in investors suitable for financial

management decisions. Regret aversion bias occurs when investors fear their decisions

will not reward gains (Golman et al., 2017). For example, regret aversion bias may cause

the investor to hold on to losing positions for a long time because of fear of making

wrong decisions. Abdin et al. (2019) showed that regret eversion bias positively affects

fundamental market anomalies. Loss aversion bias occurs when investor perceives

avoiding losses as more critical than gains (Areiqat et al., 2019).

According to Ahmad et al. (2017), individual investors react to behavioral biases

such as herding, overconfidence, and hindsight compared to institutional investors. The

researchers found that mental accounting bias affects institutional investors. Shantha

(2019) suggested that most market participants make emotional reactions and heuristic

decisions. Furthermore, there are two types of market participants: Emotional crowds and

behavioral data investors (BDIs). Emotional crowds react to unfolding events, and BDIs

make decisions based on the analysis of available data. Some studies support heuristics in

rewarding decision-making, and some are against it (Chhapra et al., 2018; Rehan &

Umer, 2017). When an investor must make an investment decision, the investor has to

invest without prior knowledge of the outcome.

The MPT posits that rational investors arbitrage away price distortions caused by

irrational investors (Swartz & Emami-Langroodi, 2018). Hence, rational investors are

more influential in the financial pricing process. However, Economou et al. (2018);

Hudson et al. (2018) argued that emotional crowds control markets' pricing and volatility.

The events that cause crowd reactions may be short-lived, but their effects tend to last

longer (Madaan & Singh, 2019). The price distortions are significant and persistent

enough that the BDIs can use them as an opportunity to build portfolios (Wang et al.,

2018). Subsequently, the behavioral finance theory posits that BDIs have higher returns

than emotional crowds. Hedge fund managers receive management and incentive fees for

excess returns they generate (Mitchell et al., 2019). The fees lead to hedge fund

managers' return-chasing behavior due to fund return volatility and investor behavior.

Also, fewer regulatory restraints increase hedge fund managers' risk-taking behavior and

the perception of skilled investors (Chhapra et al., 2018).

Value Investment Theory

Graham et al. (1934) presented in the seminal book publication on value investing

and security analysis. Value investing involves identifying and purchasing underpriced

securities in the market through fundamental analysis to profit (Kok et al., 2017). An

example includes public stocks that trade at discounted prices, with low price-to-earnings

(P/E) or price-to-book (P/B) ratios. Graham et al.’s (1934) seminal work classified

investing into two distinct categories: (a) growth investing and (b) value investing.

Growth investing refers to a company's value, including estimating the stock value

(Graham et al., 1934).

By re-examining the modern portfolio theory from the value investing

perspective, investor behavior is not rational decision-makers (Graham et al., 1934).

Also, value investors prefer avoiding risk and not trading risk for return. However, this

practice contrasts with one of the modern portfolio theory tenets: risk relates to return

(Xin Rui et al., 2018). The value investing theory is suitable for the long term, whereas

the MPT tends to be short-term oriented (Gimeno et al., 2020). For example, using

variance or standard deviation as risk is a short-term strategy. Also, the MPT aligns with

the tenets of efficient market hypotheses and asset pricing models. In value investing,

publicly available information from value investors generates consistent long-term

returns. Cao et al. (2018a) documented that using the information to construct portfolios

resulted in higher than market returns without high risks. Thus, making the efficient

market hypotheses obsolete.

Furthermore, value investors do not follow the MPT strategy of diversifying to

reduce risk (Gimeno et al., 2020). The authors documented that diversification in value

investing is not widespread because of the stock screening process. The stocks with low

price-to-earnings ratios yield high dividends and are subject to high tax rate fees (Ghaeli,

2017). Again, this goes against the MPT, which assumes no tax charges. To evaluate the

performance using value investing, Sondakh (2019) used listed financial service firms on

the Indonesia stock exchange from 2015 to 2018. Sondakh (2019) analyzed the effect of

dividend policies, liquidity, profitability, and firm size on firm value. The study results

show that liquidity and firm size have a significantly positive effect on firm value,

dividend policies have significantly negative effect, while profitability has no effect.

Sondakh (2019) suggested that investors consider the ratio of dividend, liquidity,

profitability, and firm size policies when investing in a firm they pick.

Sahoo (2017) showed that value stocks outperform when markets are down or up,

good or bad, and when the news is good or bad, without high risk. An explanation could

be investor bias of irrational behavior by overestimating, optimistic, and overreacting

(Chhapra et al., 2018). Another issue the authors found is that the undervalued securities

prices in a downturned market could be inaccurate as the market continues to drop.

Risk Exposure Variable

Hedge funds are a component of the financial system and the hedge fund industry.

The hedge fund strategies include using derivatives, non-traditional assets, and engaging

in long/short positions in any financial instrument (Agarwal et al., 2017a; Gao et al.,

2018a). However, such flexible practices expose hedge fund strategies to risk factors,

including complex risk exposures that vary according to style and market environment

(Stafylas et al., 2017). It is helpful for managers and investors to know current risk

exposures to estimate a portfolio, gain insight into a manager's skill, and replicate

strategies. Hedge fund managers vary the exposure of assets to changes in

macroeconomic conditions and fluctuating market conditions (Agarwal et al., 2018a).

The researchers suggest that hedge fund managers vary the portfolio exposure timely by

predicting the fluctuating macroeconomic variables.

Statistical Characteristics of Hedge Funds Return

The principal purpose of hedge funds is to make absolute returns at lower risk

levels unaffected by varying financial markets (Shin et al., 2018). Unlike traditional

investment funds, hedge funds are subject to few regulatory requirements, which allows

for flexible investment strategies (Metzger & Shenai, 2019). For example, hedge fund

managers can combine long/short positions and invest in non-traditional asset classes.

Swartz and Emami-Langroodi (2018) documented that researchers and investors can

classify hedge funds into alternative strategies with specific characteristics, such as style,

asset uses, returns, risk profile, and liquidity. Also, their strategies are grouped into two

key components, to assess hedge fund returns, beta and alpha (Joenväärä et al., 2021b;

Stafylas et al., 2018a). Beta (β) measures the volatility of the returns generated from the

exposure to various asset classes (Frydenberg et al., 2017). In contrast, alpha (γ) shows

the return generated by the manager's skill. Kapil and Gupta (2019) used this concept to

classify the investment strategies of hedge funds to determine performance.

Market Neutrality

Market-neutral hedge funds aim to generate uncorrelated returns to market returns

and return volatility (Joenväärä et al., 2021b). Also, the study's findings concluded that

hedge funds correlate less with traditional assets than mutual funds with market indices.

Joenväärä et al. (2021b) documented two types of hedge fund strategies; (a) Strategies

that have a low correlation to the market and (b) Strategies that correlate with the market

or specific index movement. Patton (2009) proposed to classify market neutrality into

four concepts to create a method to measure non-neutrality:

Mean Neutrality. Establishes that a fund's expected return is neutral or

negatively related to the downturned market. This neutral environment ignores the

relationship between the fund and the market when it generates positive returns (Patton,

2009). This test can apply to test market neutrality controlling for hedge fund exposure to

other sources of risk.

Variance Neutrality. Variance neutrality is another form of neutrality, where the

risk of funds is neutral to market risk. The test is applicable where the variance is the

measurement of risk. Agarwal et al. (2017a) applied the variance neutrality test to

examine the influence of uncertainty on hedge fund returns by aggregate volatility.

Value-at-Risk Neutrality. The (VaR) provides an environment where the market

return does not affect a portfolio. Crego and Galvez (2018) applied the value-at-risk

(VaR) neutrality test to investigate the dependence of hedge funds’ returns on the market

portfolio. The study results concluded that the VaR for market-neutral hedge funds

increases when market returns are more negative than positive. Also, the correlation

between market-neutral funds and the stock market varies with the economic state.

Tail Neutrality. Tail risk is the possibility of significant losses in portfolio

returns (Agarwal et al., 2017b). Therefore, investors are tail risk-averse, and there is a

positive relationship between expected return and tail risk (Mhalla et al., 2020). Shin et

al. (2017) conducted a bootstrap analysis to determine that the tail risk timing ability was

because of managerial skill. The authors used a sample of 6147 equity-oriented hedge

funds from 1996-2012 to investigate managers' time market tail risk by adjusting their

portfolios' market exposure to changes to market tail risk. The study's analysis showed

that a manager's tail risk timing skill persists over time, indicating managerial skill.

Non-Linearity

The dynamic use of long and short hedge fund positions produces a nonlinear

relationship between the returns and market returns (Fung & Hsieh, 1997a, 2001, &

2004). The studies' results confirmed other studies that hedge funds have nonlinear

returns (Cai et al., 2018; Huang et al., 2018). Also, the nonlinear exposures vary over

time, according to market conditions. Several studies recommend incorporating a

nonlinear relationship between hedge funds and market returns when analyzing the risk-

return characteristics of hedge funds (Hambuckers et al., 2018; Stafylas et al., 2018a).

Agarwal and Naik (2004) used buy-and-hold and option-based risk factors to

identify various hedge fund strategies' linear and nonlinear risks. The authors performed

an analysis at the index level and individual level. The characterization of nonlinear risk-

return relationships found that hedge funds show significant exposure to Fama and

French's (1993) three-factor model and Cahart's (1997) momentum factor. Fung and

Hsieh (2001), Mitchell and Pulvino (2001) tested neutrality on individual hedge fund

strategies and extracted systematic risk factors. The authors used the Asset Based Style

(ABS) approach, where the market index time can hold a more extended position to allow

trend-following strategies.

A comparable study by Fung et al. (2002) used the ABS method to extract the

well-known sources of risk associated with fixed-income hedge funds. The authors

identified the ABS factors and could associate them with most fixed-income hedge funds.

The findings had enormous implications for asset allocation and identifying the

significant risks. Thus, in selecting the best variation of strategies that can increase alpha.

Baker et al. (2017) applied multivariate regression to identify the factors of high-moment

risks. Evidence from the study factors relating to leverage, incentives, and strategy is

statistically significant in explaining all moments.

Skewness and Kurtosis

Skewness and kurtosis are characteristics of hedge fund returns, known as high-

moment risks (Amin & Kat, 2003). Skewness measures the deviation symmetry of the

hedge fund return distribution, and kurtosis measures the amount of extreme hedge fund

performance (Knif et al., 2020). Also, a positive skewness implies higher expected

returns and more minor losses. The Sharpe ratio assumes that hedge fund returns have a

normal distribution (Sharpe, 1992). However, hedge fund returns mostly have negative

skewness and high kurtosis because of the dynamic nature and nonlinear distribution

(Stoforos et al., 2017). Therefore, the Sharpe ratio is unsuitable as a performance measure

for hedge funds. Kapil and Gupta (2019) examined monthly hedge funds' returns to

account for the performance of various strategies. The author found that return

distribution mostly deviates from the mean and is skewed negatively with excess positive

kurtosis. The author could infer that the skewness and kurtosis occur because of the

strategies' dynamic nature and the bias from data collection from hedge fund indexes.

Fang and Almeida (2018) recommend including higher moments when modeling

hedge fund returns. The arguments for incorporating higher moments are that hedge fund

returns do not have a normal distribution and investors' choice for high positive skewness

and low kurtosis. The study’s evidence shows that most hedge funds outperform the

market index during the study period, based on the Sharpe ratio performance method.

However, the results were different by underperforming the market index with the

inclusion of skewness and kurtosis funds. Thus, the author suggests the inclusion of

skewness and kurtosis when analyzing hedge fund returns.

Hedge Funds Classification

When analyzing hedge funds, a broader system of classifying them is to group

them into a two-step process (Stafylas et al., 2018b): (1) Assessing the fund's exposure to

fluctuating market conditions and (2) Evaluating an aspect of exposure on the funds'

risk/return characteristics. The technique leads to the emergence of three broad hedge

fund categories: (a) event-driven funds, (b) non-directional funds, and (c) directional

funds.

Event-Driven Funds

Strategies in the event-driven or arbitrage funds category aim to profit by focusing

on investing in opportunities occurring in exceptional situations or events (Falkowski et

al., 2020). The uncertainty of an event provides an opportunity to benefit by allocating

funds to the issue's asset at the moment. The strategies in this category include distressed

securities, merger arbitrage, risk arbitrage, and event-driven. Gao et al. (2018b) prove

that hedge fund managers with more skills at exploiting rare disaster events can deliver

superior expected fund performance with limited risk. Also, the funds are less exposed to

disaster risk, and the managers possess skills in managing leverage and timing extreme

market conditions.

Non-Directional Funds

Non-directional or equity funds strategies aim to eliminate risk exposures to the

financial market movements by low correlation with the market (Fang & Almeida, 2018;

Joenväärä et al., 2021b). Also, non-directional strategies are independent of any market

trends and increase returns by exploiting market inefficiencies and arbitrage

opportunities. The category strategies include fixed-income, market-neutral, convertible

arbitrage, and multi-strategy (Frydenberg et al., 2017).

Directional Funds

The market-directional hedge funds display a high correlation with the market and

seek high returns. Also, they use high leverage and adopt strategies that represent bets on

the direction of markets (Frydenberg et al., 2017). Examples of market directional

category strategies include global/macro, long-short equity, emerging markets, short bias,

and managed futures (Frydenberg et al., 2017). Hong et al. (2018) used the multifactor

model to examine hedge fund strategies during varying market conditions. From the

study Hong et al. (2018) discovered that the multi-strategy, global macro and managed

futures were the few strategies that could generate considerable alpha in a downturned

market.

Data Evaluation

It is common for researchers to classify hedge funds in terms of their investment

styles. Some researchers, such as Kapil and Gupta (2019); Gerhard and Rupert (2017),

used a classification scheme created by database vendors. Other authors like Almeida et

al. (2020) and Newton et al. (2021) used hedge fund indices provided by the database

providers, ignoring the indices' representation's limitations. Most researchers use more

than one database to mitigate bias because of hedge fund managers' voluntary inclusion,

such as Metzger and Shenai (2019); Hespeler and Loiacono (2017).

The Hedge Fund Industry in South Africa (SA)

South Africa’s hedge fund sector is still in its infancy compared to its global

counterpart. The first hedge fund began in 1995 and grew to 1.4 billion Rands by 2002

(HedgeNews Africa, 2021). Also, the lending market facilitated short selling in the

1990s, and by 2013, assets under management were part of the strategies. Muteba

Mwamba (2017) identified the causes of growth in the hedge fund industry in South

Africa as individuals seeking high investment returns in alternative investments and

academics pursuing research on hedge funds' performance workings. Before 2012, hedge

funds in SA were subject to few regulatory requirements until the National Treasury and

Financial Services Board (FSB) proposed a regulatory framework for hedge funds

(CISCA, 2015). In 2015, the Collective Investment Scheme Control Act (CISCA)

effectively published new hedge fund regulations (CISCA, 2015). Hedge fund managers

had to register their management companies and portfolios within twelve months. Also,

managers had to comply with investor protection per the regulations. South Africa is one

of the few countries that enacted a comprehensive regulation for hedge fund instruments.

The regulation aims to protect investors better, manage systemic risk spillovers, improve

transparency, and oversee the financial market's progress (Bouamara et al., 2017).

However, this contrasts with the sentiment that light regulations give hedge funds the

advantage of engaging in flexible investments relative to traditional funds.

Macroeconomic Factors in SA

The economic and productivity growth has been declining in South Africa since

2015 (Kreuser & Newman, 2018). However, this study focuses on the economic factors

that may impact the stock market return, volatility, inflation rate, and the short-term

interest rate. Ten sectors make up the JSE. The sectors include basic materials,

industrials, consumer goods, health care, consumer services, oil and gas,

telecommunications, financials, technology, and utilities (Szczygielski et al., 2020).

According to Szczygielski et al. (2020), the performance of each sector varies according

to the macroeconomic factor that impacts it. The macroeconomic conditions affecting

stock market factors include the Gross Domestic Product (GDP), inflation, and interest

rates (Szczygielski et al., 2020). Interest rates are part of external and part of domestic

microeconomic factors (Madaree, 2018). Mitra (2017) used dynamic cointegration to

investigate the relationship between the effective exchange rate and the total stock

transactions in South Africa between 1979 and 2014. The results revealed a significant

positive correlation between the exchange rate and the total value of stock transactions in

South Africa.

Jeelani et al. (2019) used the ordinary least squares technique to examine the

structural changes in microeconomic variables such as GDP, interest rate, and exchange

rates. The findings revealed that major economic events impacted the microeconomic

variables. A low GDP harms investors, businesses, productivity, and uncertainty (Ceruttia

et al., 2017). Understanding the macroeconomic factors of South Africa's market is

necessary to proxy systematic influences for performing studies that model

macroeconomic factors (French, 2017).

Hedge Fund Style Analysis

Style analysis is a component in hedge fund literature that focuses on risk

exposure. The analysis examines dynamic hedge fund strategies' exposure to various

systemic risk factors (Hespeler & Loiacono, 2017). Also, the risks vary since they can

engage in short/long positions in any financial instrument and use high leverage. Fung

and Hsieh (2004) found that investing flexibility and the ability to leverage positions are

salient features that enhance hedge fund returns but potentially add to market volatility.

In hedge fund literature, the risk exposure analysis is in three phases. The first is the

classical linear model, which assumes a constant variance, such as the CAPM (Sharpe,

1964) and the APT (Ross, 1976) derived from modern portfolio theory. The CAPM only

accounts for the market risk. Fama and French (1993) extend the CAPM by introducing

the three-factor model by adding two factors based on size (SMB) and value (HML-high

minus low bond value ratio).

Carhart (1997) extends the 3-factor model by introducing momentum (MOM) to a

four-factor model. The momentum of a stock is the tendency for its trend. The beta

represents the exposure to the risk factor (systematic risk). However, the focus of the

study is more on the economic association of the exposure. The second phase adapts to

the Asset-Based Style Factors (ABS-Factors). It incorporates location factors that proxies

for buy-and-hold strategies on equity, bond, and commodity markets to control nonlinear

risk exposures of hedge funds (Agarwal & Naik, 2004; Bali et al., 2014). However, the

ABC factor model does not account for hedge funds' dynamic property or the market risk

factor's regime volatility.

The next phase is the addition of models that account for dynamic economic risk

factors. Fung et al. (2008) employed the breakpoint analysis to examine the structural

breaks in hedge fund risk exposures from September 1998 to March 2000. The study's

findings revealed significant structural breaks in hedge fund risk during the study period.

The authors confirmed that the structural breaks were associated with the long-term

capital crisis in 1998 and the internet bubble in 2000. Bollen and Whaley (2009)

introduced the changepoint regression models to examine the time-varying risk exposures

of hedge funds. The study results showed that excluding time-varying risk exposures of

hedge funds leads to inaccurate risk and return estimates. Siegmann and Stefanova (2017)

discovered optimal change-points in the relationship between beta and liquidity during

market turmoil or structural change.

Racicot and Théoret (2019) used the regime-switching model to study hedge

funds' risk exposures to traditional asset class factors in different regimes. The study

findings confirmed that hedge funds face nonlinear, option-like risks. Racicot and

Théoret (2019) used the regime-switching process to show that higher moment risk is

conditional to volatility. Another study by Zheng and Osmer (2018) employed the

Markov regime-switching model to investigate the dynamic effect of aggregate stock

market sentiment on various hedge fund strategies' performance. The researchers

examined the effect of investor sentiment on the relationship between investor sentiment

during pessimistic periods. The study analysis found that investor sentiment affects hedge

fund performance during optimistic periods. Furthermore, the relative-event hedge fund

strategies responded to the shocks.

The remaining part of the analysis of the most significant risk exposures

underlying the hedge fund styles: Directional funds or equity hedge strategy take

long/short positions. Literature like from Billio et al. (2018); Stafylas et al. (2017).

evaluate the following group of factors using the model: (a) Equity factors, (b) Volatility

factors, (c) Interest rate and credit risk factors, (d) Fama and French (1993) factors, (e)

Commodity factors, (f) Currency factors, and (g) Emerging markets factors. The studies

found that funds present exposures to various macro conditions. The analysis in the study

section aims to track the behavior using the macroeconomic models.

Volatility Forecasting Variable

In financial markets, volatility refers to the changeable variance of asset returns.

Bhowmik and Wang (2020) described volatility as the statistical measure of the standard

deviation of dispersion around the mean. A unique trait of volatility is that it is not

observable, making financial analysts eager to determine the approximate conditional

variance (Bhowmik & Wang, 2020). Other researchers define volatility as a measure to

which asset prices variate randomly as a time series component (Emenogu et al., 2020;

Schreder, 2018). Thus, volatility mainly describes the rate and magnitude of changes in

prices.

The frequent fluctuation of the broad capital market may cause uncertainty and

impact investors' confidence about the value of assets (Maqsood et al., 2017). The

authors also suggested that the public and investors believe the volatility is the cause of

the market-wide movements, especially the down market movement. However, the

down-market movements do not always relate to a specific news event. Manyang et al.

(2017) showed that risk-averse and neutral investors generally pull back from the market

during high price fluctuation market movements, thereby distorting the capital market.

Market volatility is unavoidable in the financial system, and modeling, volatility,

forecasting, and correlations are fundamentally crucial for all market participants

(Schreder, 2018). Studies focusing on volatility have been increasing in importance

because it contributes to liquidity to the financial system (Agarwal et al., 2017a, 2019;

Lee & Nguyen, 2017). The primary motivators to conduct volatility forecasts are the

prominent role of volatility as a risk management tool and portfolio management.

Volatility makes investors more risk-averse because of uncertainty (Rupande et

al., 2019). Forecasting volatility can help risk-averse investors make decisions (Ahmad et

al., 2017). For example, a high volatility investment could present a possible opportunity

for a risk-tolerant investor with higher risk and possible significant profits (Markowitz,

1952). Therefore, knowing or predicting the volatility benefits the investors, especially

those willing to potentially take a high risk to earn high returns. There are two basic

approaches to forecasting volatility. The first approach is a time series or parametric,

extracting information about the variance of future returns from historical volatility

returns (Grable & Heo, 2017). Also, it uses non-constant volatility techniques such as

generalized autoregressive conditional heteroscedasticity (GARCH), ARCH, and

stochastic volatility models, to capture the clustering in volatility over time. The second

approach is non-parametric or implied volatility and extracts the market's expectation

about future volatility from observable option prices using implied volatility indices (Liu

et al., 2021). The implied methods employ techniques such as Black-Scholes, introduced

by Black and Scholes (1973). Furthermore, the model uses high-frequency data on

volatility trading.

Some authors believe that the time series models are superior because they

capture stylized parametric volatility characteristics, including persistence, a prominent

trait of financial volatility (El Jebari, & Hakmaoui, 2017; Emenogu et al., 2020). On the

other hand, others believe the implied volatility approach outranks the time series models

because it cannot accurately forecast high-frequency volatility (Balcilar et al., 2017;

Yang et al., 2019). For this reason, it has led researchers to propose combining both

models for favorable results. Among the challenges a researcher may face in modeling

volatility are the stylized facts or financial market volatility patterns. Financial market

volatility has several characteristics that are acknowledgeable in the literature. For

instance, Baltas and Kosowski (2019) reinforced the existence of volatility clustering and

supported the ARCH behavior of financial time series. Grable and Heo (2017) also found

that volatilities vary across time and asset classes.

Stylized Market Volatility

The financial time series has some established characteristics of financial market

volatility. Most volatility forecasting models incorporate the salient features of the design

(Kaya & Yarbaşi, 2021; Xaba et al., 2017). This section highlights and briefly describes

some of the characteristics relating to this study. The features include asymmetry

(leverage), volatility clustering, fat tail (leptokurtic) distribution, and autocorrelation

(Ardia et al., 2018, 2019). Forecasting volatility includes selecting stylized properties

such as asymmetry, leverage, persistence, and mean reversion (Dai et al., 2020).

Fat Tail or Leptokurtic Distribution. Leptokurtic refers to the return

distribution curve with higher peaks that deviate from the median. Racicot and Théoret

(2018) show that long-term negative increases the downside risk and failure. Skewness

values higher than 3 lead to leptokurtic, and higher kurtosis values lead leptokurtic

(Swartz & Emami-Langroodi, 2018). Hedge fund returns deviate from the median and

left-skewed (negative), and have leptokurtic distribution because of the nonlinear

investment style (Baker et al., 2017). Also, Fang and Almeida (2018) recommend

allowing for skewness and kurtosis to improve the forecasting analysis.

Volatility Clustering. Clustering refers to the fluctuations of uneven financial

asset returns in contrast to even variations (Bhowmik & Wang, 2020). With volatility

clustering, significant price changes can follow another large price change in an

unpredictable direction (Kumar & Biswal, 2019). Volatility clustering and persistence

produce leptokurtic distribution in financial series (Racicot & Théoret, 2018). Also,

volatility clustering implies that present-day volatility shocks may influence the

expectations of future volatilities. Herbert et al. (2018) found the existence of volatility

clustering and asymmetry (leverage effect) in the Nigerian stock market and that the

clustering is persistent. Similarly, Oseifuah and Korkpoe (2019) found that the

Johannesburg Stock Market (JSE) market returns' volatility features include clustering

and leptokurtic.

Volatility Asymmetry. Volatility asymmetry is another essential characteristic in

the financial markets, especially in the equity markets (Racicot & Théoret, 2018).

According to Xie and Wang (2018), volatility asymmetry reacts to declining markets by

rising. The leverage effect if volatility increases because previous day returns are

negative (El Jebari & Hakmaoui, 2017). The leverage effect is the asymmetric reaction to

fluctuating returns of the same size. Bhowmik and Wang (2020) stated that leverage

indicates negative news, and stock falls, leading to rising leverage effect and thus, an

increase of the degree of stock volatility. Zaiane and Jrad (2020) used APARCH to

investigate the dynamic linkages between the exchange rate (US Dollar) and theTunisia

stock market. The APARCH model was appropriate to study persistent long memory and

asymmetry in both markets. The study results showed that volatility shocks could create

sudden changes in the dynamic correlations. Mashamba and Magweva (2019) evidenced

leverage effects in the market in South Africa. Mohohlo and Hall (2018) found that

operational leverage has no impact on the capital structure in South Africa except for the

industrial sector of the economy.

Autocorrelation. When stock returns are uncorrelated or exhibit weak

autocorrelation, they are dependent (El Jebari & Hakmaoui, 2017). Also, high

autocorrelation values indicate long memory of volatility persistence. The slow decay in

autocorrelation in returns is a sign of long memory. Persistency of volatility poses a

direct threat to the prices of assets (Emenogu & Adenomon, 2018). Volatility persistence

goes against the main principle of EMH, which is that stock prices incorporate all

available information making it impossible to forecast the prices. However, the long

memory process implies that the current prices could be predetermined by previous

prices, which results from autocorrelations rates in prices. Also, the autocorrelation rate

takes a long time to decay; thus, the current shock to the volatility would have long-

lasting effects. Amudha and Muthukamu (2018) used GARCH models to estimate the

volatility of the trends within India Stock Exchange from April 2003 to Sept 2015. The

results showed volatility which displays the clustering and persistence of stocks.

Volatility Forecasting Models

An accurate estimate and forecasting of volatility depend on capturing the most

stylized facts (Di Sanzo, 2018; Pan et al., 2017). According to Gaetano (2018), the

variance of a sample data set σ2 can be used to measure the volatility statistically.

Additionally, the volatility can be calculated from several serial observations as follows:

Where μ is the average return, T is the forecasting period, and Rt, is the excess on

hedge fund return. Engle (1982) introduced the Autoregressive Conditional

Heteroskedasticity (ARCH) model when analyzing and forecasting financial volatility

and economic time series data (Engle, 1982). Engle (1982) 's ARCH model is a linear

function aimed to capture volatility clustering. The following formulae represent the

ARCH (q) model:

rt = μ + εt and εt = σt zt

Where rt = return on an asset at time t, μ = average returns, and εt = residual

returns at time t, zt is independent and evenly distributed with N (0,1) with mean zero

and variance of 1. The formula below shows the conditional variance of ARCH as:

The limitations of the model are ω > 0 and α ≥ 0 (for all i = 1, , q) to ensure

is positive. The parameter is the conditional variance (volatility) at time t, is the squared

error at time t-1 from the mean equation, and q represents the number of lags. According

to Engle (1982), the error variance subject to q logs of the squared residual terms is

necessary to determine the volatility clustering. Bollerslev (1986) extended the ARCH to

the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model that

combines the mean equation and the conditional variance. The GARCH model is

specified as follows:

The mean equation: rt = μ + εt

Where rt = return on asset at time t, μ = average returns, εt = residual returns at

time t. The conditional variance is shown below:

Where

denotes to the conditional variance at time t, ω defines the

unconditional variance,

t-i

denotes to the squared residual at time t-1 from the mean

(ARCH) equation, α1 is the first ARCH parameter, β1 is the first GARCH parameter, and

is the last period forecast variance in the GARCH equation. The limitations for the

GARCH model specify α1 ≥ 0 and β1 ≥ 0 must be met for

t-i

to be positive (Nelson,

1991). Researchers could use the total of the two terms to determine the short- term

dynamic volatility time series (Gaetano, 2018). Also, the conditional variance has

persistent attribute, and the parameters add up to 1. The GARCH and GARCH-M models

capture leptokurtosis and volatility clustering attributes in financial time series (Gaetano,

2018). However, GARCH models cannot capture the asymmetry of the financial data; the

symmetric models assume that bad and good news of the same magnitude has the same

effect on the market (Wu & Hou, 2019). Ndei et al. (2019) used GARCH (1,1) to model

the market return from the Nairobi securities exchange in the presence of structural

breaks. The findings from the study revealed that the GARCH (1,1) model could capture

volatility symmetric and asymmetric effects. Al Rahahleh and Kao (2018) found that the

GARCH (1,1) model overestimates the asymmetry during high volatility periods.

The ARCH and GARCH models cannot eliminate excess kurtosis in the return

series and fail to capture skewness (Brooks, 2019). Nelson (1991) introduced asymmetric

GARCH models (EGARCH, TGARCH, and APGARCH) to address the limitations of

the ARCH and GARCH models. The GARCH variant models can capture the asymmetry

of financial returns (Abdennadher & Hallara, 2018). According to Oseifuah and Korkpoe

(2019), EGARCH, TGARCH, and APGARCH models are nonlinear and can model time-

varying volatilities. Nelson (1991) 's EGARCH model extends the GARCH model of

Bollerslev (1986) by accounting for skewness/asymmetric effect or leverage and

persistence of shocks in conditional variance. The following equation shows the

EGARCH model:

Where γ measures the asymmetry, or the leverage, and αi stands for the magnitude

or the symmetric effect. If γi = 0, or the coefficient is 0, the implication is that both

positive and negative shocks of the same magnitude have the same effect on the

volatility. If γi ≠ 0, implies the presence of the effect asymmetry. The leverage effect is

exponential rather than quadratic, forecasting the conditional variance will be positive

(Fernando, 2018). To test for leverage effects in the volatility by the hypothesis that γi >

0, a positive coefficient means positive shocks tend to produce high volatility in the short

term than negative shocks of the same magnitude (Fernando, 2018). The opposite would

apply in the case of γi < 0. Ewing and Malik (2016) studied the presence of volatility

spillover between oil prices and the U.S. stock market using the EGARCH model.

Initially, the results from the study showed no volatility spillover. However, when the

authors added structural breaks, they found volatility spillover between the U.S and

China markets. Though the EGARCH model is applicable to forecast various financial

features, it reacts slowly to market shifts (Emenogu et al., 2020). Also, the dynamics of

risk exposures limit the EGARCH model by not changing regimes, which characterize

hedge fund returns.

The TGARCH model presented by Rabemananjara and Zakoian (1993) and

Glosten et al. (1993) captures both the positive and negative effects of asymmetry. The

TGARCH equation has an artificial variable, d to account for the asymmetry or leverage

effect. The conditional variance is given by:

In this model, if

t-1

≥ 0, then good news, and if

t-1

< 0, bad news, and total

effects are given by (αi + γi) ε2t-1. Also,

t-1

and

t-1

have a differential effect on the

conditional variance. Good news impacts α, while bad news impacts (αi + γi) (Ndei et al.,

2019). The γ parameter represents the asymmetry or leverage. If γ > 0 indicates the

leverage effect is present, the parameter represents the asymmetry or leverage, and bad

news has a more powerful effect on volatility than good news (Saranya & Prasanna,

2018). On the other hand, if γ ≠ 0, the news impact is asymmetric. Ding et al. (1993)

introduced the APARCH model as an extension of the GARCH model. The conditional

variance is shown as follows:

Where δ denotes the asymmetric power term, enhances the model’s flexibility.

The leverage effect parameter γ tests the asymmetry up to order r (Ndei et al., 2019).

Also, the main advantage of APARCH model is its flexibility and that it captures all

features by EGARCH, and TGARCH. The limitations to the model are δ > 0,| γi | ≤ 1 for i

= 1 , r, γi = 0 for all i > r, and r ≤ p.

Hamilton (1989) proposed the Markov Regime-Switching (MRS) as a time series

technique to capture the shifts in the market during a recession. Gray (1996) further

generalized the Markov regime-switching methods to ARCH models. Klaassen (2002)

introduced the MRS GARCH by differentiating two regimes with different volatilities

levels. The Markov regime-switching model makes it possible to analyze time-varying

hedge fund risk exposures to different market regimes that include risk factors (Balcilar

et al., 2017). A simple regime-switching model does not account for market risk factor

regimes. The results identify different regimes with periods of levels of volatilities for

most hedge fund indices. The out-of-sample forecasting shows the accuracy of the MS-

GARCH regime-switching model. Forecast volatility, the hedge fund risk factors are

necessary. The multifactor models are the foundation of the valuation process in asset

management applications (Lambert & Platania, 2020). Following Billio et al. (2012), the

baseline for the analysis is the Fama and French (1996) eight factors: All-World Index

(market proxy), small-large risk (to capture liquidity risk), credit spread (credit risk

proxy), and VIX (volatility proxy) risk factors. The hedge fund strategies will be on the

index list.

In this section, I examined the relationship between the hedge fund performance

and the forecast of the volatility of the hedge fund returns across different volatility

regimes. Furthermore, I will investigate the exposure in hedge funds to a selection of

market risk factors. Camacho et al. (2018) describe the MRS as a technique to capture

discrete shifts and structural breaks. The focus of this section is to examine hedge fund

excess return to adjust for exposure based on market volatility forecasts. I employed two

different models to conduct the analysis. First, I tested the nonlinear TGARCH model to

assess the asymmetric reaction of the performance of hedge funds to a positive and

negative change in volatility. The second model will use the Markov regime-switching

state-dependent volatility timing model (Hamilton, 1989):

If the value

i,St

of state-dependent volatility-timing is negative, it indicates that

the manager has sufficient market volatility timing skills and can adjust the fund's

performance's market exposure before the market volatility level fluctuates. The

conditional error term is , and the state-dependent volatility-

timing is as follows:

According to Billio et al. (2018), the state-dependent market volatility timing

i,St

, is

identified by two conditional regimes as follows:

Rit-1 = α + βSt It + ωμt

According to Camacho et al. (2018), the Markov regime model has the following

parameters:

StStÎ0,1

}

{

( )

, St is Markov chain, n is the number of states, and P is the

transition probability matrix. For n = 2 states, St = {0,1}. Camacho et al. (2018) revealed

that that the Markov chain St is presented by the following transition probability matrix P.

P S1t=S1tS1t-1=S1t-1ù

ë=P

00 P

01 P

Table 7 below has the term description for the parameters.

Table 7

Terms of Description for the Equations

Term

Description

Ri,t + 1

monthly excess return on hedge fund styles at time t + 1

αt

Adjusted performance of hedge fund securities in time interval, t

It+1

Market factor in month t + 1

time interval in months

Average market volatility level

i,St

State-dependent volatility-timing

Zt,

Markov chain proxy for non-linear factors not captured by hedge funds and market risk factors.

Market volatility level at time t + 1

Ɵk,

Linear factor loading of the hedge fund on the k-th risk factor

Fkt +1,

Systematic factor on the k-th factor at time t + 1.(See table 10)

β,

Coefficient of exposure, and varies in various n state regimes H

St,

Regime indicator, Markov chain for n states, total n=2 (state 0, 1,)

σ2

Conditional variance

Actual observed volatility

µt

Average return over T periods

ϵt

Residual term or deviated return value from estimated mean return at time, t.

ω,

Idiosyncratic risk factor

Forecasting Performance Evaluation

This study follows Poon and Granger’s (2003) work to evaluate the adequacy of

the fitted model using the in-sample. For the in-sample, the goodness fit statistics method

is appropriate to evaluate the models such as Akaike Information Criteria (AIC) and the

Bayesian Information Criteria (BIC) (Bayer & Cribari-Neto, 2017). In this study, the

significance of the second regime is not a comparison, but goodness-of-fit is the focus of

this forecasting performance. According to Bayer and Cribari-Neto (2017), different

models are only suitable for various loss functions. To quantify the forecasting

performance of each model, a regression of the volatility forecasts the observed volatility

and derives the coefficient value of (R2).

The out-of-sample analyses comprise a period from January 2020 to December

2020 for twelve months. In this study, I will employ two loss functions to assess the out-

of-sample forecasting performance of the models: Root Mean Square Error (RMSE) and

Mean Absolute Error (MAE). The out-of-sample and in-sample performance from the

TGARCH and MRS models will be measured using the RMSE and MAE loss functions.

If the in-sample output value from RMSE and MAE is greater than the out-of-sample, the

forecast model is adequate (Khattak & Wali, 2017).

Financial Performance of Hedge Funds Variable

There is two strands of performance measures in the literature of hedge fund

performance analysis (Stafylas & Andrikopoulos, 2020): (1) returns-based performance

evaluation and (2) portfolio holdings-based performance evaluation (Stafylas et al.,

2017). The returns-based approach is beta premium. In the returns-based method, the

volatility of the returns relates to the risk exposure to the market (Agarwal et al., 2018a).

The portfolio holdings-based approach generates alpha, designed to evaluate the

manager's skill. A manager can use the return-based performance technique to evaluate

systematic risk exposures of hedge funds (Frydenberg et al., 2017). Hedge fund returns

exhibit nonlinear and option-based strategies, and the analysis focuses on regression

approaches to regress the factors that proxy the strategies (Stafylas et al., 2017). The

portfolio holdings-based performance approach focuses on unsystematic risks, making it

appropriate for evaluating a fund manager's skill. This study includes combining both

approaches to evaluate the variables of the research.

Benchmarking

Unlike mutual funds, where the benchmarks are relative, such as the S&P 500,

hedge funds use indices (Pilbeam & Preston, 2019). Joenväärä et al. (2021a) cautioned on

the importance of selecting the appropriate benchmark and technique because using the

wrong methods could lead to error. Almeida et al. (2020) propose using a set of assets as

benchmarks to evaluate hedge fund performance. The most basic performance

measurement model is Jensen's alpha based on CAPM, where the fund's return is monthly

risk-adjusted (Fama & French, 1993). The CAPM as the market proxy is the only factor

as a benchmark. From here, the CAPM extends to the Fung and Hsieh (2001, 2004)

multi-factor model to capture the abnormal performance of hedge funds, given the many

strategies and risk factors. Also, the Sharpe ratio can assess risk-adjusted performance

(Stafylas et al., 2018a). The Sharpe ratio is equal to the monthly return of the hedge fund

index. The Sharpe ratio is scaled by the fund's return volatility as measured by the

standard deviation. The Sharpe and CAPM models evaluate and rank hedge fund

managers and are subject to criticism because they ignore their characteristics (Agarwal

et al., 2018a). Platanakis and Sutcliffe (2017); Oikonomou et al. (2018) provide robust

and innovative ways to manage the risk inherent in hedge fund returns. Silva et al. (2017)

employed the Black-litterman portfolio model (BL) benchmark to estimate risk and make

forecasts efficiently. The BL model weighs the portfolios to evaluate the returns.

Performance Persistence

Persistence in performance is a sought-after skill by fund managers and investors,

as it is a direct test of the hedge fund manager's skill. However, past studies' conflicting

results have weakened the certainty of performance persistence (Sun et al., 2018).

Literature on hedge fund performance persistence is in three parts: (1) analysis of hedge

fund performance and persistence in up and down markets and sustainability, (2) analysis

of hedge fund market exposure, such as neutral market funds, and (3) hedge funds as

diversification tool (Joenväärä et al., 2018).

The first field compares the performance of hedge funds to mutual funds

(Agarwal et al., 2018b). Proponents of hedge funds argue that the low correlation of

traditional alternative assets' returns makes a better risk-return trade-off (Cao et al.,

2018a; Kolokolova et al., 2020; Stafylas et al., 2018a). Furthermore, this low correlation

is with traditional assets enhanced by the exemption from the Security Exchange Act of

1934. Thus, providing more flexibility with different investment options to generate

persistent returns. Other studies found no evidence of performance persistence for hedge

funds (Barth et al., 2021; Bollen et al., 2021). The authors found that hedge funds

positively correlated with the S & P 500 during bear or down markets.

Some studies found strong evidence of at least short-term performance persistence

for hedge funds (Agarwal et al., 2018a; Joenväärä et al., 2021b). Agarwal et al. (2018a)

combined four hedge fund databases: Eurekahedge, HFR, Lepper TASS, and

Morningstar. The researchers examined the information from the data for persistence in

returns. Evidence from the study showed the short-term persistence of alpha. Other

studies challenged the short-term performance persistence of hedge funds (Cui &

Kolokolova, 2020; Sun et al., 2018). Other studies found that performance persistence

varies based on the market environment and investment strategies (Ilerisoy et al., 2018;

Metzger & Shenai, 2019). While Agarwal et al. (2017b) found more substantial

performance persistence when using monthly, quarterly, or semi-annual returns instead of

annual data.

Liquidity

Another essential feature contributing to hedge fund performance persistence is

illiquidity (Hwang et al., 2017). The authors found evidence of high stock prices resulting

from hedge fund liquidity returns during the financial crisis of 2007-2009. Another study

by Kolokolova et al. (2020) observed unstable corporate bond yields, resulting from

hedge fund liquidity during that period. Ilerisoy et al. (2018) provide evidence of a

relationship between hedge fund performance, market risk, and funding liquidity risk.

The authors show that the funding liquidity risk is an influential factor in hedge fund

performance.

Fee Structure

The hedge fund fee structure includes the annual operational fee of 2% of assets

under management, and an incentive fee of 20% of the returns (Fung et al., 2021). The

researchers observed that higher feed leads to higher performance for the institution, and

the fee structure is a driving feature of liquidity. Kolokolova and Mattes (2018) argued

that higher management fees lead to less aggressive risk styles. Low performance at the

beginning of the year leads to conservative techniques to increase the chance of survival.

Gao et al. (2018a) show that management fee does not motivate managers to pursue

performance as funds grow. The authors conclude that the size of the management fee

exceeds the fund's profit.

Lock-Up and Restrictions

Lock-up and restrictions are policies or a period imposed on investors from

withdrawing funds early (Getmansky et al., 2019). Lock-up and restriction are other

components of illiquidity in hedge fund performance (Getmansky et al., 2019). The lock-

up period is the outflow term of performance, and the inflow restriction is the closure to

new investor periods (Getmansky et al., 2019). Giannetti and Kahraman (2018) found

that hedge funds with excessive share restrictions are more likely to trade against

mispricing equities than unrestricted funds. Aiken et al. (2021) confirmed that hedge fund

performance positively correlates with restraining withdrawal capital.

Leverage

Hedge fund investors employ leverage in the strategies to increase returns and

volatility of any strategy (Getmansky et al., 2019). Leverage involves borrowing money

from banks or brokers to use individual hedge funds or strategy groups (Getmansky et al.,

2019). Other studies suggest that high leverage affects hedge fund returns distribution

(Baker et al., 2017; Molyboga et al., 2017). Baker et al. (2017) confirmed their first

hypothesis that leverage correlates with negative skewness due to asymmetric payoff

from derivatives. The authors also found that, despite controlling for persistence, the

leverage variable predicts the future hedge fund return distribution.

Market Timing

Market conditions may affect the properties of assets and fund managers'

investment strategies, affecting performance persistence. Cai et al. (2018) documented

the market timing ability of hedge funds, especially during down and volatile market

conditions. Agarwal et al.(2018a) investigate hedge funds’ exposure to different financial

and microeconomic risk factors by decomposing alpha, traditional beta return, and exotic

beta return and examining investor flows' sensitivity to return components. Their results

indicate a weak persistence to exposure. Like Crego and Galvez (2018), evidence from

the study shows that market-neutral hedge funds can adjust their strategies according to

the economic state. Finally, Falkowski et al. (2020) examine various hedge fund

strategies' effectiveness during varying market conditions. Findings from the analysis

indicate that the specific strategies were effective in a particular market condition, and

others did well in another environment. Also, others performed well in hybrid conditions.

Performance Measurement Models

Hedge funds use a variety of dynamic trading strategies and use derivatives,

short-selling, and leverage (Gao et al., 2018a; Zheng & Osmer, 2018). The hedge fund

characteristics feature nonlinear returns, exposure to risk factors, and strategies that

change over time (Agarwal et al., 2018a; Falkowski et al., 2020). This thesis aimed to

examine the dynamic features.

Non-Parametric Models

Performance analysis for hedge funds differs from traditional assets because the

returns have a low correlation with market indices (Canepa et al., 2020). Thus, using the

CAPM, or Jensen's (1968) ratio, is inappropriate as a measurement tool for hedge funds.

The CAPM's alpha can be helpful as the market proxy or benchmark for hedge fund

performance. Fama and French's (1993) model extends CAPM's model by using the size

and the book price ratio to develop the three-factor model. The expected return is a linear

combination of various factors and affiliates. Carhart (1997) added momentum to the

Fama-French' (1993) model as a fourth factor to account for trend-following strategies in

the stock market. However, hedge funds are flexible and can choose from various classes

to employ dynamic strategies (Metzger & Shenai, 2019). Fung and Hsieh's (1997b, 2004)

model captures eight standard fund asset classes when analyzing risk factors to explain

the performances. The risk factors include (1) the market index factor (MKT), (2) the size

spread factor (SMB) of Fama and French (1993), (3) the Book-to-market ratio factor

(HMLt) by Fama and French (1993), (4) Book-to-market ratio factor (HMLt ) by Fama

and French (1993), (5) Moment factor (MOMt ) by Cahart (1997), (6) Interest rate and

credit risk factor, (7) MSCI Emerging Markets Equity Index, (MSCIEMt), and (8) Option

risk factor (Agarwal & Naik, 2004).

Parametric Models

Linear asset models cannot account for the dynamic properties of hedge fund

returns. To overcome the limitations of traditional or non-parametric approaches, several

researchers have developed models to account for hedge fund characteristics (Cao et al.,

2018a; Shin et al., 2018). Agarwal et al. (2017b) applied a factor model to investigate

hedge fund index exposure. Mero (2016) created the Markov regime-switching (MRS)

framework to account for macroeconomic indicators. The framework also has an

investment decision-making process. Cai et al. (2018) studied equity-oriented hedge fund

strategies to analyze hedge fund risks relating to nonlinear factor loading. The authors

focused on the dynamic factors that switch from a regular regime or state to two other

regimes with high or low volatility characteristics. This study analysis employs the

Markov regime-switching model from (Hamilton, 1989). In this model, Chen and Liang

(2007) combined the timing measure to Jensen's (1972) model relating to the Sharpe ratio

to allow risk-adjusted performance measurement as follows:

i,t+1∼i.i.d.N0,

( )

Where

Rm,t+1

is the return from the stock market at time t + 1;

m,t+1

is the stock

market volatility level; and

is the timing skill of the manager. Chen and Liang (2007)

proposed the timing term

Rm,t+1

m,t+1

çö

, which is associated with the Sharpe ratio of the

market, which lead to risk adjusted returns.

Hedge Fund Data Bias

Some authors have reported biases in hedge fund data because of managers'

voluntary reporting (Ben-David et al., 2020; Jorion & Schwarz, 2019). Ben-David et al.

(2020) used data from BarclayHedge and TASS to study three return biases from 1994-

1918: survivorship bias, delisting bias, and backfill bias. Survivorship bias occurs when

hedge fund managers exclude liquidated/dead funds. Further, survivorship bias may

cause liquidity bias, resulting in inhomogeneity data (Agarwal et al., 2017b). Ultimately,

the lack of homogeneity of the database construction rules may impact the study's

analysis and findings.

Backfill bias occurs when a hedge fund manager cherry picks surviving funds to

report and drops low-performing funds (Jorion & Schwarz, 2019). The authors cautioned

researchers to mitigate the biases as they may skew study analysis and results. Joenväärä

et al. (2021b) discussed two approaches to address backfill bias. The first approach is the

ad-hoc cut-off, where the researcher excludes the first 12-24 months of funds’ returns.

The second approach is the listing date method, where the researcher removes all data

before the listing date in the database. Jorion and Schwarz (2019) developed an algorithm

to identify backfill listings and amputate them from the central funds to mitigate the

backfill bias. In addition, hedge fund returns are subject to delisting bias (Aragon &

Nanda, 2017). Delisting bias occurs when managers strategically report a selected group

of returns late to vendors, sometimes months after occurrence (Aragon & Nanda, 2017).

Furthermore, the manager may strategically drop the low-performing returns, making it

difficult for researchers to sample the excluded data. Delisting returns become missing

data, causing upward bias in returns. Forsberg et al. (2018) found that managers are more

likely to delist funds that underperform. Forsberg et al. (2018) suggest finding and

amputating the incomplete data to control for delisting bias.

Transition

In Section 1, I justified using a quantitative correlational research study to

examine the relationship between risk exposure, volatility forecasting, and the financial

performance of hedge funds. Section 1 includes the background of the problem,

highlighting the dynamic nature of hedge fund characteristics for managers to adapt to

their trading strategies accordingly. Also included in Section1 is the problem statement

for this study, discussing the general and specific business problem. A discussion on the

purpose statement, assumptions, limitations, delimitations, nature of the study, and the

academic literature review are also part of Section 1. The nature of the study discussion

includes the research method and design. The academic literature review includes the

theoretical framework, analysis, and literature synthesis on the variables.

In Section 2 of this doctoral study, I included a description of my role of as the

researcher, justified the implementation of research methodologies and design to validate

analysis. Also included in Section 2 is a discussion of ethical considerations, participants,

target population, and data collection procedures. The final section, Section 3, includes

pre-data analyzing procedures, findings, application to professional practice, implications

for social change, recommendations for action, and conclusion.

Section 2: The Project

In Section 2, I provided an overview and justification of the chosen research

methodology and design for this study. The section begins with a purpose restatement,

followed by a description of my role as the researcher in the data collection procedure.

This section also includes information about (a) population sampling, (b) data collection,

The section concludes with a transition summary statement.

Purpose Statement

The purpose of this quantitative correlational study was to examine the

relationship between risk exposure, volatility forecasting, and financial performance of

hedge funds. The independent variables were volatility forecasting and risk exposure.

The dependent variable was the financial performance of hedge funds. The targeted

population comprises archival data from hedge fund databases in South Africa. The

implication for positive social change includes the potential to provide organizational

leaders who partner with hedge funds the ability to maximize profit by diversifying risk

in volatile market conditions. Using an investment tool to dispel uncertainty in various

market conditions is a financial means to foster positive change (Tarhani & Ameli, 2016).

Accordingly, through partnerships, hedge funds may help leaders of foundations and

nonprofit organizations fund projects in local communities.

Role of the Researcher

As the researcher in this study, my role included collecting, organizing, analyzing

the secondary data, and interpreting the findings objectively. Using existing data is cost-

effective and convenient if the researcher can analyze the data to address the research

question (Martins et al., 2018). Part of performing my role included collecting secondary

numerical data from website sources. Köhler et al. (2017) confirmed the use of statistical

software in data analysis. I analyzed the data to determine if a relationship existed

between the variables relating to the financial performance of hedge funds. In addition, I

identified the effect of independent variables on the dependent variable in the financial

performance of hedge funds. Finally, I used statistical analysis to make valid inferences

and conclusions.

In a qualitative research study, the researcher is the primary data collection

instrument because the researcher gathers the data through interviews, observations, and

focus groups (Mason-Bish, 2019). In this study, I was not the data collection instrument

because I used secondary data to perform the study data analysis. My role was to comply

with the ethical principles and guidelines in the Belmont Report. The Belmont Report of

1979 provides an ethical framework that includes respect, beneficence, and justice as

virtues researchers must follow when working with participants (U.S. Department of

Health and Human Services, 2016). During this research, I did not use human participants

and the ethical concerns identified in the Belmont Report did not apply.

My role as a quantitative researcher was to remain objective from my interests,

bias, and experiences when interpreting and presenting the study results. Furthermore, the

quantitative researcher is to practice ethical conduct and avoid influence by any

organization to maintain the integrity of the research (Edwards, 2020). In this study, there

were no boundary issues because I did not have any association with the industry or topic

of study. Also, I did not associate with hedge fund managers in this profession. In

addition, as the researcher, I did not provide investment advice on hedge funds related to

this study. Ultimately, my role as a researcher was to uphold the highest ethical standards

throughout the research process.

Participants

For this doctoral study, there were no human participants. Data for this study

came from secondary sources relating to South Africa-based hedge funds. The data

included historical monthly returns for hedge fund indices from the online database. The

choice to use monthly returns was because hedge fund managers’ report performance

monthly to hedge fund databases (Shin et al., 2017). The retrieved data assisted in

addressing the research question. Other data for this study included the financial

information from Bloomberg as used in the performance evaluation variable.

For a quantitative correlational study, secondary data is an acceptable strategy

(Queirós et al., 2017). Queirós et al. (2017) explained that using archival data is both

more cost and time effective when compared to using primary data. Martins et al. (2018)

highlighted the advantages of using secondary data, which include providing easier

access to international data that would have been costly and time-consuming. In addition,

by using secondary data, the researcher can access a large volume of historical data to

conduct several statistical analyses (Cave & Stumm, 2021). The absence of human

participants limits the risks identified in the 1976 Belmont Report and compliance

requirements; however, I followed the report's guidance when in contact with humans

during of the study.

Research Method and Design

Research Method

Research methodology is a technique that researchers use to collect, analyze, and

interpret information to reach conclusions (Scholtz et al., 2020). Research methods can

be quantitative, qualitative, or mixed method (Morgan, 2018; Zoellner & Harris, 2017).

The researcher selects any one of the methods to conduct a study and address the research

question (Williamson et al., 2020). The quantitative research method is an objective and

systematic process of using numeric data to measure a phenomenon and produce findings

(Ghauri et al., 2020). Researchers use the quantitative approach to examine the

relationships between variables by statistically analyzing numerical data to make

inferences (Köhler et al., 2017). Köhler et al. (2017) explained that the statistical

inferences are generalizable to the larger population to answer the research question. I

used the quantitative method for this study because I sought to examine the relationship

between the variables.

The focus of researchers using qualitative method is to explore a phenomenon

using non-numerical data (Nowell et al., 2017; Williamson et al., 2020). The qualitative

research method is appropriate for understanding a social or human problem from

multiple perspectives (Mohajan, 2018). Similarly, researchers use the mixed study

approach to combine the qualitative and quantitative methodologies to analyze textual

and numerical data (Brannen, 2017). Neither the mixed method nor the qualitative

method were appropriate for this study because I did not explore people's experiences or

attitudes. Therefore, the qualitative method and the qualitative portion of a mixed-method

approach were not appropriate for this study, and the quantitative was the logical choice.

Research Design

Quantitative researchers can use correlational, experimental, or quasi-

experimental designs to conduct research (Podsakoff & Podsakoff, 2019). Researchers

use the correlational design to measure the strength of the relationship between two

variables (Zyphur & Pierides, 2020). Researchers also use the correlational design to

identify an association between variables (Yang et al., 2021). The correlational design

was applicable for this study because the objective was to assess the relationship between

independent variables (risk exposure and volatility forecasting) and a dependent variable

(financial performance).

The causal-comparative design appeared to be an option for this study, but it was

not suitable. Researchers use causal-comparative design to compare groups in order to

explain existing differences between them on the same variable of interest (Gøtzsche-

Astrup, 2018). Gøtzsche-Astrup (2018) explained that researchers use causal-comparative

design to show that a relationship exists between variables and the consequences of

differences that already exist between two groups. In this quantitative correlational

design, I did not seek to understand the differences between groups; rather, I examined

the relationship within a group. Furthermore, causal-comparative design allows the

researcher to make inferences about causation and the correlational design does not.

The experimental designs involve manipulating variables to assess the cause-and-

effect relationship between them (Podsakoff & Podsakoff, 2019). Researchers conduct

the experimental design to determine the ideal values of variables that support the cause-

and-effect relationship rather than an association between variables (Cortina, 2020).

Furthermore, researchers using the true-experimental design assign variables to a group

or manipulate an independent variable. In a quasi-experimental design, the researcher

does not assign the variables randomly, and instead, uses a control group (Yang et al.,

2021). However, in correlational studies, there is no manipulation of variables (Yang et

al., 2021). Therefore, the experimental design was not suitable to address the research

question for this study.

Population and Sampling

Population

A population refers to the summation of elements that the researcher wants to

generate for the results (Hickey & Sollmann, 2018). The general population of this study

encompasses all the asset classes under management in the hedge fund industry. The

target population of this doctoral study includes monthly returns of hedge funds in South

Africa between July 2007 to December 2020 from databases. The data also include the

annual performance of the Johannesburg Stock Exchange (JSE) All Share Index (ALSI)

as the market proxy to measure the surplus return of each hedge fund, along with the

Morgan Stanley Capital International Index (MSCI) performance over the same period

for robust analysis of risk exposure analysis.

Population Alignment with Research Question

The target population for this quantitative correlational study aligned with the

research question with the variables of risk exposure, volatility forecasting, and financial

performance. I regressed the monthly returns over the study period to determine the

financial performance (dependent variable). Also, running the style analysis on the

monthly returns allowed me to examine the hedge fund strategies' exposures relative to

risk factors during the study period (independent variable). Finally, I used the indices

from monthly returns to explain the hedge fund volatility and forecasting (independent

variable). A sampling approach is essential for researchers when exploring datasets,

including determining the appropriate sample size (Trafimow & Myüz, 2019).

Sampling

The two methods of collecting samples include probabilistic and nonprobabilistic

sampling (Sharma, 2017). I used the probabilistic sampling strategy in selecting a sample

of South Africa hedge fund data from databases. I did not use the nonprobabilistic

sampling technique because it does not allow to make inferences about the population

(West, 2017). Quantitative researchers use probabilistic sampling approach to generalize

the findings from the sample to the study population (Sharma, 2017). The probabilistic

sampling strategy was appropriate because the goal was to draw inferences of the entire

population of hedge funds based upon the study sample. However, some there are some

disadvantages for using the probabilistic sampling technique which include being tedious

and time consuming, especially when the sample size is large (Schuster et al., 2022;

West, 2017).

A simple random sampling was the suitable probabilistic sampling method for

this study. The simple random sampling strategy allows every member of the population

an equal chance of selection (Muneer et al., 2017). The sample comprised of time series

data between July 2007 and December 2020. The data yielded 150 observations of

monthly returns of hedge fund indices. The sample comprised of both live and dead funds

from HedgeNews Africa database. In this study, survivorship bias in the sample may

affect the study findings by inflating the performance (Gao et al., 2018a). Furthermore,

potential survivorship bias may produce false conclusions about the relationship between

volatility and performance. To mitigate survivorship bias, the dataset comprised post-

1994 data, consisting of dead and live funds (Barth et al., 2021; Jiang et al., 2022;

Joenväärä et al., 2021a). In addition, backfill bias in the sample may create upward biased

time-series returns for macro funds (Joenväärä et al., 2018; Jorion & Schwarz, 2019).

Backfill bias could also lead to incorrect relationship findings between hedge fund

performance, systematic risks, and volatility. Following the approach by Barth et al.

(2021), Forsberg et al. (2018), Gao et al. (2018b), and Jiang et al. (2022), to address

backfill bias, I eliminated the first 24 month return observations of each fund.

The reason for selecting the simple random sampling technique is because it

enables the use of historical data. The advantage of using the simple random sampling

technique is that it enables the researcher to reduce possible selection bias and minimize

the potential for findings with skewness (Mahalua et al., 2019). Mahalua et al. (2019)

also suggested that researchers use the probabilistic simple random technique when they

require minimal knowledge of the target population. Furthermore, the probabilistic

simple random technique could make a strong representation of the target population.

Another advantage of using the probabilistic simple random technique is that selecting an

individual member in the sample does not affect other members in the sample (Ali &

Shukla, 2020). The sampling choice aligned with the sample in this study because the

data comprised of a monthly return time series. However, the simple random technique

has a potential weakness of requiring a large sample to attain a representative population

(Serdar et al., 2021).

G* Power is the statistical software package researchers use to perform a priori

sample size analysis (Faul et al., 2009). I used the G*Power Version 3.1 to determine the

appropriate sample size for this study. A priori power analysis with the assumptions of

medium effect size (f2 = .15), type I error (α = .05), and two predictor variables. The

priori analysis indicates a minimum size of 68 sample observations to attain the power of

0.8 (Fig. 1). Increasing the power to 0.99 leads to 146 sample observations (see Table 8).

Figure 1

Relationship between effect size and the sample size at power 0.8 for F-Tests Linear

Multiple Regression

Also see the minimum sample size for a different range of powers and effect

sizes, shown in the table below.

Table 8

Minimum Sample Size for Selected Powers and Effect Size

Power

Effective Size

0.8

0.85

0.95

0.99

Small (0.02)

485

550

776

1073

Medium (0.15)

107

146

Large (0.35)

A sample size between 68 and 146 observations was acceptable for this study.

The sample of 146 observations yields a study period of 12years, between July 2007 and

December 2019. Therefore, the sample of 150 observations ranging between July 2007

and December 2020 was the appropriate size for this study.

Ethical Research

Researchers have an ethical responsibility to conduct research with integrity,

regardless of the research methodology (Zyphur & Pierides, 2017). I obtained the IRB

approval from Walden University before collecting and analyzing data, with the licence

number 02-03-22-0552772. I obtained secondary data from public and private electronic

data sources. The ethical protocols in the Belmont Report (U.S. Department of Health,

2016) apply to human research subjects (Friesen et al., 2017). The Belmont Report of

1979 provides an ethical framework that includes respect, beneficence, and justice that

researchers must follow when working with participants (U.S. Department of Health,

2016). I did not use human subjects in this study.

Consequently, the consent documents include (a) informing participants about the

study purpose, (b) possible risks in the study, (c) potential benefits, (d) voluntary

participation, and (e) the process for withdrawal from the study. I maintained

confidentiality by limiting access to the data and securely storing and protecting data in

electronic folders with a password. Finally, I will delete the data five years after the

study’s publication.

Data Collection Instruments

I did not use a data collection instrument in this study. The data originate from

secondary sources. Martins et al. (2018) described secondary data as information from

existing sources. Quantitative researchers may use secondary data for statistical analysis

(Queirós et al., 2017). Theofanidis and Fountouki (2018) also reported that researchers

set boundaries for the research by establishing delimitations for a framework for

recording and analyzing the information. This study involved scaling each variable based

on measurement techniques researchers used to measure variables in previous studies.

The data for this study included monthly time series from the online HedgeNews Africa

(HNA) database from July 2007 to December 2020 (HNA, 2021). The HNA database

provides the most timely, accurate, and independent source of information covering

alternative investment space across the emerging African continent and the South African

hedge fund industry (HNA, 2021). I converted the hedge fund return rates from South

African Rand terms (ZAR) to U.S Dollars (USD) for all strategies for analysis.

Other secondary data sources were the Bloomberg database using the Bloomberg

terminal, I-Net Bridge, and the South African Reserve Bank (SARB). Bloomberg is

among the most global providers of timely, accurate, and high-quality financial news and

information to more than 300,000 trading desks (Guidotti, 2019). Beyond information,

the Bloomberg terminal system allows market participants to monitor and analyze real-

time financial market data for informed decisions. I-Net Bridge is a South African

financial services company that provides electronic economic data, financial market data,

and market intelligence (I-Net Bridge, 2021). The SARB provides high-quality

economic, policy-relevant, and financial statistics that present a holistic view of the South

African equities market (SARB, 2021).

The purpose of this study was to examine the relationship between risk exposure,

volatility forecasting, and the financial performance of hedge funds. The datasets

incorporated the variables, and I utilized them to determine the relationship between the

three variables. Risk exposure is one of the variables in this study. Several studies applied

the style analysis to investigate the risk exposure of funds to gain insight into the impact

of factors on performance (Billio et al., 2018; Hespeler & Loiacono, 2017; Stafylas &

Andrikopoulos, 2020). The style analysis includes a regression process between fund

returns against risk factors (Frydenberg et al., 2017). The HNA database provided the

source for monthly hedge fund returns. Using the Bloomberg terminal, I sourced the JSE

(ALSI) returns and the Morgan Stanley Capital International (MSCI) index from the

Bloomberg database for the study period. I also sourced sample data for risk factors from

I-Net Bridge. The beta coefficient represents a standard measure of a fund's exposure to

movements in the market's return (Frydenberg et al., 2017). If the market beta coefficient

value is zero and an asset contains a beta coefficient of zero, it indicates no correlation

with the market index (Mestre, 2021). Also, a positive beta of the asset shows that the

asset follows the market movements and has higher risk exposure. Several researchers

used the beta coefficient to measure risk exposure in various areas of financial studies

(Agarwal et al., 2018a; Gerhard & Rupert, 2017; Hwang et al., 2017; Yurteri Kösedağli

et al., 2021).

Volatility forecasting is the second independent variable in this study. Previous

research indicates that volatility forecasting in financial instruments demonstrates a direct

association with performance (Gaetano, 2018; Limam et al., 2017). In this study, I used

an autoregressive model to perform volatility forecasting. Autoregressive Conditional

Heteroskedasticity models (ARCH) are statistical techniques that suggest the subsequent

period volatility is conditional on the current period volatility, including the time-varying

nature of volatility (Ndei et al., 2019). Researchers may use ARCH and its variant of

family models to forecast volatility in time-series data with a non-linear model without

assuming constant variance (Mashamba & Magweva, 2019). The HNA database served

as the source for the hedge fund returns for the study period. I sourced the returns on the

JSE (ALSI), MSCI index, South African Volatility Index (SAVI), and MSCI Emerging

Market Stock Index from the Bloomberg database for the study period using the

Bloomberg terminal. In addition, I sourced the exogenous factors from I-Net Bridge and

SARB. The asset return volatility measures how much the returns move around their

mean (Greaves, 2018). Some volatility measures include standard deviation, beta, R-

squared, and alpha (Ardia et al., 2018). Previous researchers have supported the standard

deviation or variance as a measurement of uncertainty or risk (Ardia et al., 2018;

Gaetano, 2018; Greaves, 2018; Siddiqui & Roy, 2019). The standard deviation has

advantages because extreme values do not affect how it functions (Greaves, 2018).

Furthermore, it indicates its magnitude by the cluster level or shocks, and it is more

precise and reliable than the other measurements. I used the Root Mean Square Error

(RMSE) to assess the accuracy of the forecasting performance of the models. The RMSE

compares the out-of-sample of forecast performance of the models. The forecasting

model with the lowest value of RMSE is the most accurate (Al Rahahleh & Kao, 2018).

The financial performance of hedge funds represents the dependent variable in

this study. Like the independent variables, I retrieved secondary data from HNA,

Bloomberg database, I-Net Bridge, and SARB. Alpha represents the measurement of

funds' performance (Kapil & Gupta, 2019). Also, the regression intercept of several

market factors on the hedge fund excess returns to measure the performance. Risk-

adjusted performance measures include the Sharpe, Sortino, omega, and Calmar ratios

(Newton et al., 2021). The Sharpe ratio is inappropriate to measure hedge funds'

performance because it assumes that returns produce a normal distribution (Metzger &

Shenai, 2019). The Sortino, omega, and Calmar ratios use volatility as risk, making them

unsuitable for measuring hedge fund performance (Kapil & Gupta, 2019). This study

included evaluating the hedge fund performance measure by augmenting the Capital

Asset Pricing Model (CAPM) of the Sharpe ratio by factoring in the changing state of the

economy, systematic risk factors, and market timing component. Previous researchers

have supported the time-varying factor approach to evaluate alpha (Bouamara et al.,

2017; Chen & Kawaguchi, 2018; Metzger & Shenai, 2019; Newton et al., 2021)

In this study, the measurement scale for the dependent variable, the financial

performance of hedge funds, is the ratio scale. The basis for financial performance of

hedge funds is the time series returns from assets measured as ratio scale. Also, the

measurement for the independent variable, the volatility forecasting variable was ratio

scale. The second independent variable, the risk exposure variable, was an ordinal scale

with eleven sub-variables: (a) market index (ALSI), (b) size spread factor (SMB), (c)

book-to-market factor (HML), (d) moment factor (MOM), (e) equity markets index

(MSCI), (f) emerging markets equity index (MSCIEM), (g) option risk factor (SAVI), (h)

10- year government bond (10-Yr-bond), (i) 3- month T-Bill (j) metal commodities (k)

exchange rate risk (US/ZAR). Content validity, criterion-related validity, and construct

validity did not apply in this study because I did not use instruments.

Data Collection Technique

The research question of this quantitative correlational study is as follows: Is there

a statistically significant relationship between risk exposure, volatility forecasting, and

the financial performance of hedge funds? The data collection method for this study

involved sourcing data from secondary sources. I collected secondary data for this study

from websites linking to HNA, Bloomberg terminal, SARB, and I-NET Bridge databases

between 2007 and 2020. Yerpude and Singhal (2017) revealed that collecting data using

automated real-time systems increases the accuracy of forecasting output. The SARB

distributes data through an online terminal which allows users to download data (SARB,

2021). The data terminal allows users to download time series data and easily export it to

excel. Significantly, the system provides the researcher with a time series code and uses

keywords to search (SARB, 2021).

The Bloomberg terminal includes an online tutorial and data acquisition

instructions (Guidotti, 2019). In addition, a researcher can transfer data from the

Bloomberg terminal to other software programs like Excel and SPSS for sorting and

analysis. I-NET service provides a workstation for users to access electronic data and

support operating the terminal (I-Net Bridge, 2021). Furthermore, the electronic terminal

incorporates a web application and a data feed system with analytic tools. Finally, the

HNA database provides an online terminal for users to download and transfer data to

various programs, like the Excel spreadsheet (HedgeNews Africa, 2021).

After obtaining the IRB's approval, I extracted the data through the electronic

terminals from the databases for the study period between 2007 and 2020. The first step

was to ensure that sources comprised the relevant data to answer the research question

(Olabode et al., 2018). I used the variables in this study to filter the data from respective

database terminals. The study variables include risk exposure, volatility forecasting, and

the financial performance of hedge funds. The data from sources aligned with variables

as presented in Table 9.

Table 9

Systematic Risks Data, Sources, for Risk Exposure Variables

Factors (Data)

Source

Monthly returns net-of-all-fees, relating to the hedge fund strategy indices

HNA

Equity factors:

1. Market (MKT) JSE (ALSI)

Bloomberg

2. Morgan Stanley Capital International (MSCI) index

Bloomberg

3. MSCI Emerging Markets Equity Index, (MSCIEMt)

Bloomberg

4. Size factor (SMBt) by Fama and French (1993)

I-NET

5.Book-to-market ratio factor (HMLt) by Fama and French (1993)

I-NET

6. Moment factor (MOMt) by Cahart (1997)

I-NET

Option risk factor (Agarwal and Naik (2004):

7. South African Volatility Index (SAVI)-implied volatility

I-NET

Interest rate and credit risk factor:

8. ZAR 10-year South Africa government yields

SARB

Exchange rate factor:

9. Fluctuations in the Rand-Dollar exchange rate (USDt)

Bloomberg

Commodity factor:

10. World metal prices (METt)

I-NET

Spread:

11. Spread: the difference between market return and the 3-month treasury

bill (risk-free rate, rf)

SARB

The second step included:(a) downloading the data onto an Excel spreadsheet, (b)

organizing the data for all variables, and (d) importing the data into SPSS for statistical

analysis. Weston et al. (2019) recommended that secondary researchers document the

data using code, including precise instructions, before the statistical analysis. Arslan

(2019) also proposed code-creating tools such as the codebook package. Tools like the

codebook help secondary researchers with reliability procedures, missing patterns,

storage, plot data, and web interface. Further, the auto code tool includes meta-data, such

as variable names and labels (Arslan, 2019).

Retrieving secondary data from electronic databases has both advantages and

disadvantages for this study. Olabode et al. (2018) stated that collecting electronic data

allows unrestricted access to broad international samples at a limited cost. According to

Yerpude and Singhal (2017), automated secondary data collection is more appropriate for

time series forecasting. Furthermore, the web interface and storage systems grant

researchers unlimited access to data and transfer it to statistical software for analysis

(Arslan, 2019). There is some drawback to employing secondary data. Pernollet et al.

(2017) opined that preparation errors in archival data might affect the study results'

reliability. Because of the voluntary nature of reporting, there is a possibility of missing

or incomplete data in hedge fund databases (Aragon & Nanda, 2017). The missing data

set might exclude the researcher's vital information to address the research question

(Weston et al., 2019). Furthermore, missing or incomplete data may generate bias,

affecting the relationship between the variables (Olabode et al., 2018). Cheng et al.

(2017) suggested that pilot studies are significant steps to evaluate the possible threats to

the validity of empirical research. Fink et al. (2021) pointed out that the primary purpose

of a pilot study is to assess the measurement characteristics of the instruments. However,

a pilot study was not appropriate for this study because of the use of secondary data.

Data Analysis

The research question of this study is as follows: Is there a statistically significant

relationship between risk exposure, volatility forecasting, and the financial performance

of hedge funds? The independent variables are risk exposure and volatility forecasting.

The dependent variable is the financial performance of hedge funds. This study involved

answering the research question by testing the following hypotheses:

H0: There is no statistically significant relationship between risk exposure,

volatility forecasting, and financial performance of hedge funds.

Ha: There is a statistically significant relationship between risk exposure,

volatility forecasting, and financial performance of hedge funds.

I used the multiple regression model to analyze the data in this study. Multiple

regression is a statistical technique that allows researchers to examine relationships

between one dependent variable and several independent variables (Green & Salkind,

2017). According to Jelusic (2017), the multiple regression method is valuable in

quantifying the degree of association between variables. The multiple regression analysis

is appropriate for this study because the research question is about a predictive

relationship between one dependent variable and two independent variables. While I

opted to use the multiple regression approach, I did consider using other techniques like

the Analysis of Variance (ANOVA) and logistic regression.

The ANOVA is a statistical technique that researchers can use to measure the

statistical mean difference between samples (Green & Salkind, 2017). Furthermore,

Green and Salkind (2017) also noted that the ANOVA test applies when the dependent

variable is continuous while the independent variables are categorical. The focus of this

study was not to examine the mean and group differences between samples. Moreover,

the independent variables are not categorical. Therefore, the ANOVA test was not

applicable to this study. Another option was logistic regression. Logistic regression

analysis is another statistical technique that researchers use to examine the relationship

between a dichotomous, binary dependent variable and independent explanatory variables

(Bergtold et al., 2018). Given that the focus of this study did not predict the binary

dependent variable, this made the logistic regression approach unsuitable for this study.

Quantitative researchers use data cleaning and screening procedures to refine raw

data to a suitable format for statistical analysis (Kiss et al., 2017). Data cleaning refers to

the process data analysts use to edit invalid data from the dataset (Bashir & Wei, 2018).

Kiss et al. (2017) also recommend performing data cleaning methods to improve the

quality to minimize the possibility of false positives in the study results. At the same

time, screening involves detecting the anomaly in the dataset (Arslan, 2019). Data

screening starts with establishing the raw data characteristics (Wang & Wang, 2020).

Arslan (2019) suggested performing data screening to ensure that data are ready for

analysis. Furthermore, the quality of acceptable analysis is subjective to the initial phase

of data screening. Data cleaning and screening include standardization, coding, and

reporting (Arslan, 2019). The data cleaning and screening procedures suitable for this

study include scanning, coding, identifying missing values, validation, and implementing

treatment techniques.

Missing data is inevitable in secondary datasets (Coertjens et al., 2017). Most

databases contain duplicate, incomplete, and missing values (Agbehadji et al., 2018).

This research included employing archival information from hedge fund databases.

Agarwal et al. (2017b) noted that managers' voluntary disclosure of hedge funds provides

the source of missing and incomplete data in hedge fund databases. Furthermore, missing

data are problematic when a researcher intends to examine events' occurrence or

variations of change over time (Bashir & Wei, 2018). There are various methods to

mitigate missing data, including imputation techniques. According to Kiss et al. (2017),

methods to consider addressing missing data include (a) listwise deletion, (b) pairwise

deletion and, (c) Expectation-Maximization (EM). The listwise deletion method excludes

all data cases with missing values (Bashir & Wei, 2018). The listwise deletion approach

involves excluding all data cases with missing values. However, time series data involve

removing the time intervals when there is missing data for specific data. The downside to

the listwise deletion method is that it can cause bias and fragment time series data,

distorting the study results (Agbehadji et al., 2018).

The pairwise deletion approach involves deleting the whole variable with the

missing values and substituting it with the median or unconditional mean (Kiss et al.,

2017). Kiss et al. (2017) also noted that a drawback of the pairwise method could

compromise the power of statistical tests because the estimated data could exhibit bias.

The EM approach reconstructs the missing data by estimating the variance or covariance

(Bashir & Wei, 2018). However, Kiss et al. (2017) argued that the EM approach would

affect time series more under multivariate applications. I adopted the listwise approach

for this study to identify the contaminated data and address missing data.

There are assumptions in any statistical analysis (Plonsky & Ghanbar, 2018).

Bergtold et al. (2018) reported that the assumptions associated with using multiple

regression are as follows: (a) multicollinearity, (b) linearity, (c) outliers, (d) normality, (e)

homoscedasticity and (f) independence of residuals. Multicollinearity occurs when two

independent variables are highly correlated, as high as 0.8 to 0.9 (Green & Salkind,

2017). The violation of the multicollinearity assumption in a study may inflate the

variances of the parameter estimates, which may result in questionable p-values (Plonsky

& Ghanbar, 2018). Consequently, incorrect conclusions about relationships between the

independent and dependent variables. Theoretically, it would be challenging to determine

which highly correlated predictor variable is related to the hedge fund's performance. I

examined a bivariate correlation matrix of the predictor variables from the SPSS software

output. A correlation coefficient less than 0.8 is acceptable (Hirk et al., 2019).

Linearity assumes a linear relationship between independent and dependent

variables (Josephat & Ame, 2018). To check for linearity, I visually inspect the

scatterplot of the relationship between the variables using SPSS. A straight line indicates

that the assumption is present. Outliers represent observations or scores whose values

highly differ from the data set under study (Ernst & Albers, 2017). Yuen and Ortiz (2017)

stated that outliers could arise from various sources, like incorrect recording observations

of data. To locate outliers, I visually inspected the scatterplot, histograms, box plot, or

frequency distributions using the SPSS software. Another method to locate outliers

includes converting data to z-scores (Ernst & Albers, 2017). One solution is removing the

outliers from data analysis (Green & Salkind, 2017). However, dropping the data or

outliers may cause bias in the study results (Yuen & Ortiz, 2017). Dropping outliers can

be justified when: (a) they are out-of-range, and misentered data and (b) missing.

Normality assumes that the distribution of residuals is normal (Hirk et al., 2019). Some of

the tests for normality include the following: (a) observing the normal probability-

probability plot (Q-Q), (b) histogram, or (c) a Shapiro-Wilk and Kolmogorov-Snairnov

tests using the SPSS software (Ernst & Albers, 2017).

Homoscedasticity refers to assuming the variability in scores should be constant

across all independent variable levels (Ernst & Albers, 2017). Homoscedasticity

assumption can lead to bias in the findings, and alter the overall analysis, thus weaken the

statistical power (Dattalo, 2018). Ernst and Albers (2017) observed that a weak power

increases the potential occurrence of Type I error. Consequently, Type I error results in

inaccurate F-test results and discrepant conclusions. To assess the presence of

homoscedasticity, a visual inspection of the Normal Probability Plot (P-P) of the

Regression Standardized Residual using the SPSS software (Dattalo, 2018). Also, I

observed the scatterplot from SPSS software. A funnel shape indicates the assumption is

unacceptable, and a random array of dots indicates that the homoscedasticity assumption

is acceptable (Green & Salkind, 2017). Finally, the independence of residuals refers to

the residual difference between each observed and the average predicted value of the

dependent variables (Hirk et al., 2019). Ernst and Albers (2017) suggested using the

Durbin-Watson test to determine autocorrelation for serial correlation between errors.

Thus, I used the same procedure to test for the independence of the residual assumption.

To combat the possible influence of violations of statistical assumptions, I

employed a bootstrapping technique. Researchers use the bootstrapping technique to

address the violation of assumptions (Dattalo, 2018). According to Dattalo (2018), the

bootstrapping technique is equally appropriate as an alternative to statistical inference

without relying on assumptions to quantify the uncertainty. Violating assumptions could

lead to an unreliable and invalid analysis of data (Ernst, & Albers, 2017). Therefore, I

used the bootstrapping technique to address the possible influence of assumption

violations. I employed the Statistical Packages for Social Science (SPSS), version 25, for

this doctoral study to analyze the data. The SPSS software translates numerical and non-

numerical information into data for statistical analysis (Green & Salkind, 2017). The

SPSS software provides specific output parameters for interpretation as follows:

(a) F value, (b) B, (c) R2, (d) β, (e) SE B, (f) Sig (p), and (g) t results.

F value or the F-ratio of the analysis of variance, including the sig p values,

applies to ascertain if the null hypothesis is accepted or rejected (Shyti & Valera, 2018).

A sig p-value less than 0.05 could lead to the rejection of the null hypothesis (Shyti &

Valera, 2018). B refers to the unstandardized coefficient of the predictor variable of the

study (Josephat & Ame, 2018). Researchers use the B value to predict that the magnitude

of a factor of the dependent variable will change by a unit change in the independent

variable, given that all other independent variables stay constant (Josephat & Ame,

2018). β refers to the standardized coefficient of the predictor variable and is the slope of

the regression line that mathematically represents the linear regression equation (Davino

et al., 2020). The β coefficient represents the magnitude of change related to a one-unit

change in each independent variable (Davino et al., 2020). SE B represents the standard

error for the predictor variable's unstandardized coefficient, which indicates the degree of

irregularity in the data (Hirk et al., 2019). The standard error of the estimate refers to the

standard deviation of the error term and is derived by the square root of the mean square

residual (Hirk et al., 2019). R2 is the percentage measure of the variance in the dependent

variable that relates to the independent variable (Josephat & Ame, 2018). The t statistic

measures the distance of a parameter from its notional value and standard error

(Andronov, 2017). Researchers determine the t-statistic when the parameter estimate

value in a regression model differs from the actual parameter estimate and is divided by

the standard error (Andronov, 2017). Sig (p) represents the statistical significance of each

independent variable (Pfeiffer et al., 2017). The p-value is the likelihood that the actual

value associated with the independent variable in the population is zero. A sig p-

value less than 0.05 could lead to the rejection of the null hypothesis (Pfeiffer et al.,

2017).

I used the Markov regime-switching model to compute the risk-adjusted

performance of hedge funds (Hamilton, 1989). In this model, Chen and Liang (2007)

combined the timing measure to Jensen's (1972) model relating to the Sharpe ratio to

allow risk-adjusted performance measurement as follows:

i,t+1∼i.i.d.N0,

( )

(see Table 7 for terms of description)

Study Validity

The two types of study validity are internal and external (Sürücü & Maslakçi,

2020). According to Thomas et al. (2018), internal validity represents the extent to which

the results of a study support a causal relationship between variables. When researchers

use an experimental design, there is a potential risk of internal validity (Rahi, 2017). For

a quantitative correlational study, internal validity does not apply. However, there are

potential threats to statistical conclusion validity.

A researcher could attain statistical conclusion validity by using appropriate

statistics to infer the association between dependent and independent variables (West,

2017). According to Muneer et al. (2017), failing to address threats to statistical

conclusion validity could lead to inaccurate inferences like type I or type II errors. Serdar

et al. (2021) described type I error as the probability of rejecting a true null hypothesis

and type II as the probability of accepting a factually false null hypothesis. Factors that

could affect the statistical conclusion validity include (a) reliability of the instruments, (b)

data assumptions, and (c) sample size (Bergtold et al., 2018). The reliability of

instruments relates to the internal consistency of the instruments of the study. I did not

use an instrument to collect data; I employed secondary data. Therefore, internal

consistency in this study should not be a concern.

When using multiple regression, the data assumptions are normality, linearity,

homoscedasticity, and multicollinearity (Bergtold et al., 2018). According to Josephat

and Ame (2018), the assumption for linearity indicates that the relationship between the

dependent and independent variables is linear. The scatterplot feature on SPSS can help

researchers check for normality, linearity, and homoscedasticity (West, 2017). I visually

examined the scatterplot to determine the linearity of data in this study. According to

Yuen and Ortiz (2017), outliers can impact the results of a regression analysis.

Furthermore, researchers can use a histogram from the SPSS program to locate any

outliers. Data assumptions are the primary threat to the validity of this doctoral study.

Violating the data assumption may lead to Type I or Type II errors (West, 2017). To

mitigate the violation of data assumptions, I ran a bootstrapping technique using SPSS.

The sample size in a quantitative study is essential to assist researchers in

determining the statistical significance between variables (Rahi, 2017). Serdar et al.

(2021) claimed that increasing the sample size would increase the power level,

decreasing the probability of generating type I and II errors. Trafimow (2018) suggested

that researchers use a priori power analysis to determine an adequate sample size.

Thomas et al. (2018) suggested that researchers select an effective size to estimate the

sample size for a specified power (1- β) and significance level (α) at the planning phase

of the research. I performed an a priori power analysis using the G*Power software to

select an adequate sample size of 150 observations in this study. Moreover, I employed a

statistical power of 0.95 at an alpha of 0.5 to minimize the threat to the statistical

conclusion validity.

External validity represents the extent to which the researcher can generalize the

study findings to the broader populations, various settings, and different measurements

(Sürücü & Maslakçi, 2020). Mahalua et al. (2019) explained that a probabilistic sampling

strategy could improve the external validity of a study by increasing the generalizability.

According to Trafimow & Myüz (2019), researchers can overcome threats to external

validity by using an adequate sample size representing the target population. Palazón-Bru

et al. (2017) also noted that a sample that does not represent the target population

adequately could lead to selection bias, which may threaten external validity. Researchers

cannot use a biased sample to generalize findings to a larger population (Mang et al.,

2021). In addition, I used a random sampling technique to select the sample size because

it represents the study population. I used inferential statistical techniques like hypothesis

testing and regression analysis to generalize the study’s population. The study's sample

size comprised hedge funds that invest in South African financial markets. Similar to the

selection process of Kumar and Kumar (2017), the sample included a monthly return time

series of hedge fund indices from July 2007 to December 2020. The results may not

represent the entire global hedge fund industry, threatening validity (Theofanidis &

Fountouki, 2018). Consequently, the findings may include limitations due to the sample

size, characteristics, and period chosen.

Transition and Summary

Section 2 contains narratives on the purpose of the research, my role as a

researcher, the research method, design, and ethical procedures. Furthermore, in Section

2, I discussed sampling techniques, data collection methods and instruments, data

analysis presentation, and the study validity. In Section 3, I presented the study findings,

and discussed the implication for social change and business practices. In addition, I

included recommendations for future research, reflections, and concluding remarks for

the study.

Section 3: Application to Professional Practice and Implications for Change

Introduction

The purpose of this quantitative correlational study was to examine the

relationship between risk exposure, volatility forecasting, and the financial performance

of hedge funds. The independent variables were risk exposure and volatility forecasting.

The dependent variable was the financial performance of hedge funds compared to the

benchmark performance of the Johannesburg stock exchange, ALSI. The model showed

that at F (2, 149) = 238, p < 0.001, R2 = .950, risk exposure and volatility forecasting

significantly predicted the financial performance of hedge funds. Hence, the null

hypothesis was rejected, and the alternative hypothesis was accepted.

Presentation of the Findings

This subsection includes a discussion of assumptions testing, descriptive statistics,

and inferential statistics results, provides a theoretical discussion about the findings, and

concludes with a concise summary. I employed multiple linear regression, with a sample

consisting of 150 monthly observations from July 2007 to December 2020, to address the

relationship between risk exposure, volatility forecasting, and the financial performance

of hedge funds. The employment of bootstrapping with 1,000 samples was applied to

address the violation of the assumptions where appropriate. Hence, bootstrapping of 95%

confidence intervals is presented where applicable.

Test of Assumptions

For the multiple regression, I assessed six assumptions: independence of residuals

(autocorrelation), linearity, normality, stationary, homoscedasticity, multicollinearity,

outliners, and heteroskedasticity. I included all the cleaned samples in the analysis. It is

necessary to meet all assumptions in regression analysis to avoid spurious regressions

(Plonsky & Ghanbar, 2018).

Multicollinearity

Multicollinearity was evaluated by viewing the correlation coefficients between

the predictor variables. All bivariate correlation coefficients between the predictor

variables were small. Therefore, there was no evidence of multicollinearity assumption

violation. Table 11 shows the correlation coefficients.

Table 10

Correlation Coefficients Among Study Variables

Variable

Sub-

Variables

ALSI

SMB

HML

MSCI

SAV

10Y

3mth

COM

US/ZA

Risk

Exposure

ALSI

SMB

0.873

HML

0.630

0.179

MOM

0.141

0.146

0.057

MSCI

0.715

0.671

0.130

0.145

MSCIEM

0.720

0.734

0.201

0.099

0.860

SAVI

0.096

0.110

0.023

0.061

-0.026

-0.096

10Y

0.130

0.274

0.088

0.017

-0.251

-0.307

0.091

3mth

0.094

0.078

0.003

0.026

-0.020

-0.065

0.084

0.047

COM

0.299

0.352

0.008

0.015

0.277

0.443

0.038

0.257

US/ZAR

0.295

0.402

0.165

0.061

-0.596

-0.714

0.144

0.571

0.016

0.401

Volatility

Forecasting

0.021

0.075

0.083

0.076

0.068

0.060

0.011

0.032

0.073

0.044

0.017

Outliers, Normality, Linearity, Homoscedasticity, and Independence of Residuals

I investigated outliers, normality, linearity, homoscedasticity, and independence

of residuals by examining the normality P-P plots, box plots, and the scatterplot of the

standardized residuals from SPSS. The examination indicated there was a violation of

outliers’ assumption. Figure 2 shows the normality P-P plots of the standardized

residuals. The failure of the standardized residuals to lie in a straight line against the

predicted value supports the presence of outliers and the normality assumption violation

(Josephat & Ame, 2018). Figure 3 shows the scatterplot of the standard residuals. The

lack of a clear or systematic pattern in the scatterplot supports the tenability of the

violation of the linearity, homoscedasticity, and independence of residuals assumptions. I

computed 1,000 bootstrapping samples to address any possible influence of assumption

violations and reported 95% confidence intervals, based on the bootstrap samples where

appropriate.

Figure 2

Normality of plot (P-P) of the regression standardized residuals

Figure 3

Scatterplot of the standardized residuals

Descriptive Statistics

The data consists of 150 observations of monthly returns from July 2007 to

December 2020 and eliminated six because of missing data, which resulted in 144

observations. Table 12 presents descriptive statistics of study variables.

Table 11

Means and Standard Deviations for Quantitative Study Variables

Variable

M 95%

Bootstrap CI

SD 95%

Bootstrap CI

Performance

0.123

[-0.02, 0.27]

1.00

[0.80, 1.19]

Volatility Forecasting

0.04

[0.04, 0.04]

0.004

[0.003, 0.005]

Risk Exposure

2.9

[2.05, 3.35]

.28

[.25, .44]

Note: N = 144

Inferential Results

The study involved using the standard multiple linear regression, α = 0.05 (two-

tailed), to examine the efficacy of risk exposure, volatility forecasting, and the financial

performance of hedge funds. The independent variables were risk exposure and volatility

forecasting. The dependent variable was financial performance. The null hypothesis was

that there was no statistically significant relationship between risk exposure, volatility

forecasting, and the financial performance of hedge funds. The alternative hypothesis was

that there is a statistically significant relationship between risk exposure, volatility

forecasting, and the financial performance of hedge funds. The preliminary analysis took

place to assess whether the assumptions of multicollinearity, outliers, normality,

homoscedasticity, and independence of residuals were met. The results of the preliminary

analyses included a violation of outliers, normality, and homoscedasticity assumptions.

However, they did not include any serious violation of the independence of residuals

assumption (see Tests of Assumptions section).

The model as a whole was able to significantly predict hedge funds’ financial

performance at F (2, 149) = 238, p < 0.001, R2 = 0.932. The R2 (0.932) value indicated

that approximately 93% of hedge fund financial performance variations are accounted for

by the linear combination of the predictor variables. Risk exposure and volatility

forecasting were statistically significant in the final model. Table 12 shows the regression

summary of the study. The final regression equation is as follows:

Performance = α + β1(Volatility forecasting) + β3(ALSI) + β4(SMB) + β5(HML) +

β6(MOM) + β7(MSCI) + β8(MSCIEM) + β9(SAVI) + β10(10Yr-Bond) + β11(3month T-

Bill) + β12(Commodities) + β13(US/ZAR) + e

Table 12

Regression Analysis Summary for Predictor Variables

Variable

SE Β

Lower

Bound

Upper

Bound

Volatility

Forecasting

-3.685

4.444

-0.016

-0.829

0.408

-12.466

5.096

Risk Exposure

0.00

.00

ALSI

1.421

1.021

0.136

1.393

0.166

-0.596

3.438

SMB

-0.012

0.055

-0.004

-0.209

0.835

-0.120

0.097

HML

-1.345

0.982

-0.059

-1.369

0.173

-3.285

0.596

MOM

0.013

0.198

0.001

0.068

0.946

-0.378

0.405

MSCI

0.894

0.834

0.090

1.073

0.285

-0.753

2.542

MSCIEM

-0.155

0.823

-0.017

-0.188

0.851

-1.780

1.471

SAVI

0.033

0.167

0.004

0.199

0.842

-0.296

0.363

(table continues)

100

Variable

SE Β

Lower

Bound

Upper

Bound

10Yr-Bond

-0.438

0.493

-0.021

-0.889

0.376

-1.413

0.536

3-mth T-Bill

-8.947

0.950

-0.789

-9.417

<0.001

-10.824

-7.070

COM

-0.496

0.350

-0.030

-1.418

0.158

-1.187

0.195

US/ZAR

-0.061

0.755

-0.003

-0.081

0.936

-1.552

1.430

Note. N= 144; B = unstandardized coefficient; β = standardized coefficient

Volatility Forecasting

The negative slope for volatility forecasting (-3.685) as a predictor of hedge

funds' financial performance indicated a 3.685 decrease in performance for each one-

point increase in volatility forecasting. In other words, hedge funds' financial

performance tends to decrease as volatility forecasting increases. The squared semi-

partial coefficient (sr2) that was an estimate of how much variance in hedge funds'

financial performance was uniquely predictable from volatility forecasting at 0.03,

indicating that 3% of the variance in hedge funds' financial performance is uniquely

accounted for by volatility forecasting when risk exposure is controlled.

Risk Exposure

The categories of risk exposure variable (i.e., ALSI, SMB, HML, MOM, MSCI,

MSCIEM, SAVI, 10Yr-bond, 3mth-bill, Commodities, and SA/ZAR Exchange rate)

helped to determine the occurrence and magnitude of hedge funds financial performance.

The 3-month T-bill rate was the significant predictor of hedge funds' financial

performance at the 1% level, accounting for the highest contribution (B = -8.947).

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Analysis Summary

The purpose of this quantitative correlational study was to examine the

relationship between risk exposure, volatility forecasting, and the financial performance

of hedge funds. I used multiple linear regression to examine the risk exposure and

volatility forecasting ability to predict the value of the financial performance of hedge

funds. Assumptions surrounding multiple regression were assessed with the assessment

results, including violations of outliers, normality, homoscedasticity, and independence

of residual assumptions. The model used in this study, as a whole, was able to

significantly predict the financial performance of hedge funds, F (2, 149) = 238, p <

0.001, R2 = .950. Volatility forecasting and risk exposure provide helpful predictive

information about the financial performance of hedge funds

Theoretical Conversation on Findings

The findings of this study align with the findings of Markowitz (1952). For

example, Stafylas et al. (2017) identified that investors could increase returns by taking

more significant risks. Bedoui et al. (2020) concluded in this research that the MPT was

valid for investigating the standard deviation optimization. Further, Joenväärä et al.

(2021b) identified that hedge funds' returns move in the opposite directions if there is a

positive or negative change in the stock market. The findings from this study extended

and supported Markowitz's (1952) MPT. The premise of MPT is that the expected return

and variances of assets in which a hedge fund manager constructs hedge funds is based

on their customers' risk preferences (Moulya et al., 2019).

102

The findings of this study indicated no significant relationship between volatility

forecasting and the financial performance of hedge funds. The model used in this study,

as a whole, was able to significantly predict the financial performance of hedge

funds, F (2, 149) = 238, p < 0.001, R2 = .950. The negative slope of volatility forecasting

(-0.016) as a predictor of hedge funds' financial performance indicated a 0.016 decrease

in volatility forecasting for a unit’s increase in performance. The findings of this study

supported the findings of Abdennadher and Hallara (2018), who showed that the shifts

explained changes in the return volatilities of equity hedge funds returns.

The findings of this study indicated varying relationships between risk exposure

categories and the financial performance of hedge funds. In this study, the 3-month T-bill

rate had a significant relationship with the financial performance of hedge funds at 1%

from 2007 to 2020. The negative slope of the 3-month T-bill variable (-0.789) as a

predictor of financial performance of hedge funds indicated there was 0.678. The market

index (ALSI) did not contribute significantly to the model (B = 1.421) and had the

highest slope β = 0.136, indicating the highest hedge fund exposure in the analysis.

Frydenberg et al. (2017) findings indicated that the momentum effect (MOM) and market

index (NYSE) were significant at the level of 1% during the recession period. However,

MOM was also significant during the whole period of study, from 1994 to 2015.

Frydenberg et al. (2017) confirmed that hedge fund managers vary the risk exposure of

assets to changing market conditions, indicating managers’ skills.

Similarly, Agarwal et al. (2018a) show that hedge fund managers vary the

portfolio exposure timely by predicting the fluctuating macroeconomic variables. The

103

outcome of this study contrasted with a study conducted by Gerhard and Rupert (2017).

Gerhard and Rupert (2017) examined the relationship between commodity, equity

indices, and hedge fund performance, reporting that MSCIEM and the market index

(S&P 500) were highly significant during the analysis period from 1990 to 2010.

Applications to Professional Practice

The financial performance of hedge fund attracts market participants seeking

higher returns in various market conditions (Schreder, 2018; Shin et al., 2017). One of the

sources of the superior performance of hedge fund managers is skills in market timing

and volatility to adapt the funds' market exposure (Cui & Kolokolova, 2020; Muteba

Mwaba, 2017). The study's findings may be of practical significance to investors and

fund managers because: (a) I based the study design on the decision-making to assess

investment risk, and (b) I highlighted the movement of underlying macroeconomic

variables that correlate with hedge fund performance.

Market participants should account for risks when making investment decisions

(Stafylas & Andrikopoulos, 2020). The results of this study highlight the necessity of risk

dynamics assessment. Simultaneously, timing the market and predicting future levels of

volatility allows the managers to adapt the funds' risk exposure for higher performance or

reduce losses (Cao et al., 2018a). Furthermore, the research findings may provide

essential information to assist investors or managers in determining the impact of varying

economic conditions on the risk dynamics of the hedge fund strategies.

104

Implications for Social Change

The implication of the study results could serve two potential purposes. The first

is that leaders of investment corporations may: (a) factor in the importance of market

pricing when making investment decisions and (b) ensure that superior performance

relates to knowledge of market risks and volatility. Thus, the right timing of investments

could increase a firm's profits and resources to drive social change. Firms that create

profits or increase value have a competitive edge, which allows them to invest in socio-

economic projects that drive change (Sosner & Steblea-Lora, 2022). The implications for

a positive social change of this study include the potential to improve communities by

providing more jobs for local people.

Another implication for a positive social change includes the potential to provide

corporate leaders with a better understanding of factors that drive the financial

performance of hedge funds. The possibility exists to improve the tools for managers to

maximize financial performance by timing market returns and predicting levels of

volatility. The social change implication includes the potential to improve relationships

between leaders, fund managers of the corporation, investors, and shareholders.

Recommendations for Action

The results of this study are consistent with other research on hedge fund

performance (Kapil & Gupta, 2019; Metzger & Shenai, 2019; Zhang et al., 2021). The

performance of hedge funds is an indicator of the manager’s skill (Shin et al., 2017).

Also, the findings from this study supported the validity of MPT, and I recommend that

managers use MPT as a basis for portfolio management strategies. I found a significant

105

relationship between risk exposure, volatility forecasting, and performance. Based on the

findings on these variables, my recommendation for hedge fund managers includes the

risk exposure to maximize financial performance. Risk exposure refers to using

systematic risk factors of hedge funds to evaluate financial performance. I recommend

hedge fund managers allocate strategies by adjusting the funds’ performance market

exposure.

The study results are relevant to fund managers and scholars. The results may

help fund managers make investment decisions or portfolio selections under varying

market conditions. Finally, scholars may use the findings as a foundation for further

research or comparison to other areas of hedge fund literature or models. I intend to

publish the results of this study in the Pro-Quest dissertation database and other scholarly

journals so other scholars, practitioners, and business professionals can have access.

Furthermore, I intend to present the findings to stakeholders via conferences, seminars,

and training workshops.

Recommendations for Further Research

In this study, I examined the relationship between risk exposure, volatility

forecasting, and the financial performance of hedge funds. This study has some

limitations; therefore, recommendations for future studies are necessary. The

performance variable focuses on hedge fund returns in South Africa from 2007 to 2020.

Recommendations for future researchers include expanding to other markets or regions.

Furthermore, I would recommend further research on using different techniques to

analyze performance and increasing the number of years for data analysis. The findings

106

of this study could improve business practices by providing managers with insight into

asset selectivity.

Reflections

In concluding this study, my goal was to gain insight into market risk exposure of

hedge funds, volatility, and the effect on performance. There were few surprises during

the process, especially during the data collection phase. Unfortunately, unlike mutual

funds, accessing hedge fund data from databases is extremely expensive. I had to acquire

the necessary funds to purchase the data. After purchasing, there is a waiting period for a

background check before downloading. In addition, for several weeks, I reviewed the

fields that contained the data required for analysis. Though, this task was a grueling, the

process yielded an effective source for the study.

Conclusion

The primary purpose of the quantitative correlational study was to examine hedge

funds as a potential source of investment profits for individual and corporate investors

without loss. The aim was to determine if a statistically significant relationship exists

between risk exposure, volatility forecasting, and the financial performance of hedge

funds. I examined the relationship between the variables using a multiple regression

model, and a sample consisting of 144 observations of 86 managed funds.

The findings revealed a significant relationship between variables because the p-

values were less than the alpha of 0.05. Consequently, I rejected the null hypothesis; H0:

There is no statistically significant relationship between risk exposure, volatility

forecasting, and financial performance of hedge funds for the period 2007 and 2020.

107

According to the findings, investors and managers may use risk exposure and volatility as

indicators of future hedge fund performance

108

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