small P R O JECT

1

Project Description and Guideline

FIN 350

Summer Session III, 2021

Instructor: Dr. Y. Ma

Portfolio Risk Diversification Analysis and CAPM

PURPOSE

• To study the portfolio diversification effect and the roles of stock correlation coefficient and weight on the portfolio return and risk.

• To estimate the stock’s beta and alpha values using the security characteristic line (SCL) and to compute the abnormal returns on a stock using the CAPM approach.

DATA COLLECTION

• Obtain the Daily Stock Price and Index Information

Collect the daily stock price for two companies and one stock market index (e.g., the

S&P 500 Index) over the past four months. You can download the daily price and index

data from Yahoo Finance website or other sources.

Steps (Using Yahoo)

− Go to the yahoo site: https://finance.yahoo.com

− Type the stock symbol in the Search area

− Click the Historical Data tab and select daily prices

− Download the stock price over the last four months

− The index symbols are: ^DJI (Dow Jones Industrial Average) ^GSPC (S&P 500)

^IXIC (NASDAQ)

The adjusted close price from the Yahoo historical prices is already adjusted for stock

dividend and stock split. As such, you may compute the daily return for both the stock

and index as follows:

• Stock Daily Return

𝑟𝑡 = (𝑃𝑡 − 𝑃𝑡−1)

𝑃𝑡−1 ⁄

Where rt = the stock return on day t

Pt = the stock adjusted close price on day t

Pt-1= the stock adjusted close price on day t-1

• Index Daily Return

1

)1( ,

− −−=

tIndex tIndextIndex

tmr

2

Where rm, t = the market return on day t

Index t = the index adjusted close price on day t

Index t-1= the stock adjusted close price on day t-1

• Stock Return and Standard Deviation Estimation

− Compute stock and index returns from the price and index values.

− Compute the daily average return as a measure of expected return.

− Compute the standard deviation of stock daily returns.

− Use the daily returns to estimate the correlation coefficient between the two stocks.

Use r1 and r2, σ1 and σ2 to denote the average daily return and the standard deviation. For

best results, you would like to select two stocks of which the higher return stock also has

a standard deviation.

PORTFOLIO RISK AND RETURN ANALYSIS

• A Two-Stock Portfolio Risk & Return Measures

122121 2 2

2 2

2 1

2 1 2  wwwwp ++=

r P = w1 r1 + w2 r2

Where σ p and r P are portfolio risk and return

w1 and w2 are the weights of the two stocks in the portfolio

12 is the correlation coefficient between the two stocks

• Risk Diversification Analysis

(1) The effect of stock weight (Frontier Portfolio)

Use 10 different weight combinations for the two stocks and compute the portfolio's

expected rate of return and standard deviation. Then, use these data to draw your

frontier portfolio and interpret the results.

In Excel, select Insert, click Charts tab, and then choose Scatter. Remember the

horizontal (X) axis is the standard deviation and the vertical (Y) axis is the expected

return. If you put p values first and then rp values in the next (right) column, then

Excel will automatically take p as the horizontal axis and rp as the vertical axis.

(2) The least risk portfolio

Use the true correlation coefficient to find out what combination of weights will

generate the least risky portfolio, that is, with the least standard deviation.

In Excel, under Data, you may find Solver tab. Solver is an add-in function. If you

don’t see it, you just need to add it. In Solver window, put the cell of p in “Set

Objective” cell, and choose Min in “To” cell, and select the cell of w1 in “By

Changing Variable Cells”.

3

The easiest way to do this part is to copy a line from the earlier steps in computing

portfolio risk and return. Then, apply the solver tool.

(3) The effect of stock correlation coefficient

Use the weights you obtained in the previous step of finding the least risky portfolio

and 10 different values of correlation coefficients (You may want to evenly spread

out the 10 correlations between –1 and +1, just for demonstration purpose).

APPLICATION OF CAPM

• Estimating Beta () and Alpha ()

Use the security characteristic line (SCL) method (the regression below) to estimate

the  and  values for each stock and interpret the results.

Regression Equation: rt= +  rM, t + e t

• Use CAPM to Estimate Abnormal Returns

CAPM Model: rt = rRF+i (rM,t - rRF)

Where rRF is the risk-free rate (the 10-year T-bond yield).

The daily abnormal return is defined as the difference between actual return and

required return estimated by the CAPM model, ARt=rt – [rRF+i (rM,t - rRF). Compute

the daily abnormal returns for the most recent 10 days and the average abnormal

returns over this period for each of the two stocks.

REPORT FORMAT AND REQUIREMENTS

• The final report needs to be typed and single-spaced.

• A cover page is required with the following information:

− The names of the stocks and index used

− Students’ names

• For each step in the project, provide a brief and clear explanation and/or interpretation.

• For regression analysis, attach the Excel results in table format at the end.

• Students can complete the project individually or as a group of no more than 3 students.