Presentation slides

Finance applications of big data and

predictive analytics: risk & return

FINM4100

Analytics in Accounting,

Finance and Economics

Week 10

Lesson Learning Outcomes

1 Define risk and return

2 Explore different ways of measuring risk and return

3 Investigate factors influencing risk and return

4 Performing portfolio analytics and optimisation

Why Build Models?

“Just because you

have more data

doesn’t mean that

you’re going to make

better decisions.”

Models encapsulate

patterns that exist in

data, helping us make

sense of them.Christina Zhu Assistant Professor of Accounting Wharton School of the University of Pennsylvania

Software for today

1. Google Colab

• Either

A. watch the teacher demonstrate analytics and accounting in python OR

B. you can run the python scripts yourself in Google Colab

• If you want to run the code provided, make sure you have access (signed in) to Google Colab https://colab.research.google.com

2. Exploratory

A. watch the teacher demonstrate analytics and accounting in Exploratory OR

B. run each step yourself online (access is explained on the next slide)

The risk return relationship is one of

the most fundamental relationships in

all of finance

• Return is a measure of the amount

earned by owning an asset

• Risk is a measure of the variability of

that return

To earn more return, an asset owner

must be prepared to accept more risk

The Risk Return Relationship

Photo by Parker Johnson on Unsplash

All investments carry risk, some more than others.

Risk & Return

Cash is generally low

risk. Suitable for investors

who have a short-term

investment outlook or low

tolerance for risk.

Shares are the most

volatile asset class, but

historically over long

periods of time have

achieved on average the

highest returns.

Risk and return in Australia

Risk and Return for Australian Shares & Bonds from 1974 to 2009

High return, high risk

Medium return, medium risk

Low return, low risk

Average

return

Std

14.34% 21.89%

10.14% 7.66%

9.73% 4.33%

How do we measure risk and return?

Return is a

measure of the

earnings made on

an asset

Risk is a measure

of the variability in

earnings made on

an asset

Dollar terms ($)

Percentage terms

(%)

Standard deviation

Coefficient of

variation

Beta

Dollar terms ($)

Percentage terms

(%)

• Let’s review the measures of standard deviation and

coefficient of variation

• We saw Beta in week 8

Glossary 1: Variance and Standard

deviation as measures of variability

• Measures the squared difference of a data set relative to its mean.

Variance

• Measures the spread of a data set relative to its mean.

Standard deviation

Recall from STAM4000 that

Hence, standard deviation is used a

measure of financial risk

Formulas for the variance &

standard deviation

N = population size

n = sample size

𝜇 = population mean (average)

ҧ𝑥 = sample mean (average)

Population Sample

Variance 𝜎2= σ x−𝜇 2

𝑁

𝑠2= σ x− ҧ𝑥 2

(n−1)

Standard deviation σ = 𝜎2 s = 𝑠2

11

Use 𝑠2 and s, respectively, as we have a sample.

First, we need ҧ𝑥 = σ 𝑥

𝑛 =

6.9−4.8+2.3+2.2+0.6

6 = 1.68%

𝑠2= σ 𝑥− ҧ𝑥 2

(𝑛−1) so we have

Example of STDEV of returns for the

S&P 500

Month Return

October 2021 6.9%

September 2021 -4.8%

August 2021 2.9%

July 2021 2.3%

June 2021 2.2%

May 2021 0.6%

Returns for S&P 500, May 2021-October 2021

𝑠2= 6.9−1.68 2+ −4.8 −1.68 2+ 2.9−1.68 2+ 2.3−1.68 2+ 2.2−1.68 2+ 0.6−1.68 2

(6 −1) =14.5

Standard deviation, s = 14.5 = 3.8%

https://www.businessinsider.com.au/what-is-standard-deviation

Standard deviation measures the variability of possible

outcomes and therefore quantifies uncertainty and risk

%150

Melbourne

investment

( = 2%)

Sydney investment

( = 3%)

Which investment is riskier – Melbourne or

Sydney?

Quantifying uncertainty and risk

• To measure the relationship between average return and

(risk) volatility simultaneously, we use the Coefficient of

Variation (CV):

CV = 𝜎

𝜇 =

Standard Deviation

Annualised Return

• Thus, CV can be used as a measure of asset quality.

• Note that single measures rarely provide the entire picture

but this is a start.

Glossary 2: Coefficient of variation

Activity 1: Can you identify the

least/most risky assets?

Investment Risk & Return

RISK

RETURN

Other risk factors and return

Interest Dividend Capital

Gains

Housing

Bubble

Stock Market

Downturn

Geopolitical

Risk

Social Unrest Inflation

Erosion

Liquidity

Risk

Activity 2: Risk and Return • Watch the video on risk and return at

https://www.youtube.com/watch?v=4KGvoy_Ke9Y

• From the video and previous slides, answer the following

Q1. Return and risk are measures of what ?

Q2. What is standard deviation used to measure ?

Q3. Are bonds riskier than shares or visa versa?

Q4. What measure maximises return for the same risk?

What is a Portfolio?

• A portfolio is a collection of materials, e.g. career related materials, investments, art work

• In assessment 3 you will create a portfolio of analytics methods

• In a risk return context, a portfolio contains financial investments

https://clarke.edu/academics/careers-internships/student-checklist/resume-writing-and-portfolios/what-is-a-

portfolio/

This Photo by Unknown Author is licensed

under CC BY-NC-ND

This Photo by Unknown Author is licensed under CC BY-

SA-NC

This Photo by Unknown Author is licensed under CC BY-NC-ND

Risk and diversification for an

investment portfolio

In the same way that particular measures apply

to single stocks, they can also be applied to a

portfolio

• Standard deviation captures uncertainty

• Coefficient of variation standardises risk

• Beta measures systematic risk

Diversification refers to correlation reducing

portfolio standard deviation. Hence we seek to

have some uncorrelated (or imperfectly

correlated) investments.Photo by Michel Porro on Unsplash

• Sharpe ratio is a measure of risk-adjusted return of a financial portfolio.

• The formula is 𝑆 = 𝜇−𝑟𝑓

𝜎 , where

• 𝜇 is the average return of the asset

• 𝑟𝑓 is the return on the risk free asset

• 𝜎 is the standard deviation of returns for the asset

• Sharpe ratio will change depending on the composition of your portfolio

• A ratio of 3.0 or higher is considered excellent

• A ratio under 1.0 is considered sub-optimal

• Sharpe ratio can be compared with Coeff. of Var. to make an

assessment on asset quality and performance.

Glossary 3: Sharpe Ratio

Activity 3: Quick Quiz

Q1. What mathematical methods are commonly used to measure risk ?

Q2. Consider

Investment A and Investment B

• Portfolio return: 20% Portfolio return: 30%

• Risk free rate: 10% Risk free rate: 10%

• Standard Deviation: 5 Standard Deviation: 40

If the Sharpe ratios are (A) 2.0 and (B) 5.0, Confirm this from the formula and interpret these outcomes.

Q3. Is diversification useful in a portfolio or do you just need more investments?

Glossary 4: Skewness and Kurtosis

• Skewness and Kurtosis which you may have encountered in STAM4000

are also measures of risk for investments

“Skewness is a measure of symmetry, or the lack of it.

T h is

P h o to

b y U

n k n o w

n A

u th

o r is

lic e n

s e d u

n d e r C

C B

Y -S

A

This Photo by Unknown Author is licensed under CC BY-SA

Kurtosis is a measure of whether the data

are heavy-tailed or light-tailed relative to a

normal distribution. ”

Activity 4: Portfolio calculations

• Make sure you are signed up with Google Colab or watch the demo

• We start with a portfolio of four stocks (Google, Amazon, MacDonalds, The Walt Disney Company) and then start adding Australian stocks to see how the measures of risk change.

• Expected return, volatility, Sharpe ratio, skewness and kurtosis are calculated each time.

• The script is here

https://colab.research.google.com/drive/1T7sS1KLo_WcwyLKnKBmZtaso6 cBsSzSQ?usp=sharing

• All you need to do is run each block of code and attempt to interpret the results with your teacher

Glossary 5: Annualised return • The annualized return equates to what you would earn if the annual

return was compounded over a period of time.

• It is the geometric average of an investment’s earnings in a year

This Photo by Unknown Author is licensed under

CC BY-SA-NC

• There are various analytics methods for portfolio optimisation

• In broad terms, we seek to find the minimum (volatility) variance

portfolio for a given selection of investments, i.e. perform mean-

variance optimisation.

• Requirements and conditions for mean-variance optimisation:

Portfolio optimisation

Minimise

Portfolio

Covariance

Define Acceptable

Portfolio Return

Fully Allocate

Budgeted Capital

Set Capital

Allocation

Constraints

For example, consider a four security portfolio.

• BHP Billiton, QBE Insurance, Telstra and Westpac Banking Corporation

Question: In what proportions should these investments be held such

that the risk (volatility), measured using standard deviation, is minimised

for a given level of return?

That is, how do we make a minimum variance portfolio?

Portfolio Optimisation contd…

Portfolio 1: Equal allocation…

Mean = 23.96% | Standard Deviation = 16.24%

Portfolio 2: Financials heavy…

Mean = 12.49% | Standard Deviation = 21.76%

Portfolio 3: Me heavy…

Mean = 11.73% | Standard Deviation = 19.67%

Attempts to create a min var

portfolio

Portfolio Efficient Frontier

• Efficient Frontier method: An optimisation method which takes into

account volatility and Sharpe ratio

• The idea of an efficient frontier comes from Modern Portfolio theory

• The frontier is a curve representing a set of portfolios which provide the

greatest returns for each level of risk

This Photo by Unknown Author

is licensed under CC BY-SA-

NC

• Using the Efficient Frontier, the portfolio can be optimised for

– minimum volatility

– maximum Sharpe ratio

– minimum volatility for a given target return

– maximum Sharpe ratio for a given target volatility

• We have found a python script which uses the Efficient Frontier method

• This allows us to compute and visualise optimised portfolios

Portfolio Efficient Frontier

This Photo by Unknown Author is

licensed under CC BY-ND

Activity 5: Efficient Frontier

• Make sure you are signed up with Google Colab or watch the demo

• The script is here

https://colab.research.google.com/drive/1FiwNZKvvVLLWEpHRX1plnLjS

zam7kwmb?usp=sharing

• Discuss the results of the different optimisation criteria with your

teacher

• Example output next page

https://finquant.readthedocs.io/en/latest/examples.html This Photo by Unknown Author is

licensed under CC BY

Of the portfolios that comprise the efficient frontier, there is one portfolio

that had the lowest level of risk…

Risk & Return

𝜇

𝜎

They called it, the Minimum Variance Portfolio

Efficient Frontier Output