For this project, you are going to evaluate the systematic risk of an investment portfolio. It can be an imaginary portfolio that you would like to put together to park your retirement savings, or your real 401(k) portfolio.

To simplify the project, we are not going to include bonds, ETFs, mutual funds, etc. Or in other words, we are going to investigate a portfolio composed of only stocks. For example, your ideal portfolio can comprise the following stocks: IBM (5%), APPL (5%), GOOG (10%), DIS (10%), C (5%), WMT (20%), ALM (5%), GM (10%), JNJ (10%), GE (5%), KFT (5%), MCD (10%). Note the weights in the parenthesis (percentage of total funding) have to add up to 100%. Your portfolio may include more stocks than this example because it normally takes more than 30 stocks (Statman, 1987) for a portfolio to be qualified as a well diversified portfolio. 

Beta measures the systematic risk (non-diversifiable risk) of a stock. Mysterious as it may sound, it can be easily found out by regressing the stock’s monthly excess return (return in excess of risk free rate) on market monthly excess return according to the following model:

                                                Equivalently                   Equivalently

                                    the dependent variable Y                        the independently variable X

 

where,

 is the return of stock i on month t;

 is the risk free return on month t, normally a 3-month treasury bill serves a good proxy;

 is the market return on month t, normally S&P 500 return serves a good proxy;

 is the beta for stock i;

 is the intercept for stock i;

 is the error term.

 

To find the beta for stock i, you need to obtain the data of  as dependent variable Y and  as the independent variable X. beta is simply the regression coefficient.

 

                                                Equivalently                   Equivalently

                                    the dependent variable Y                        the independently variable X

 

where,

 is the return of stock i on month t;

 is the risk free return on month t, normally a 3-month treasury bill serves a good proxy;

 is the market return on month t, normally S&P 500 return serves a good proxy;

 is the beta for stock i;

 is the intercept for stock i;

 is the error term.

To find the beta for stock i, you need to obtain the data of  as dependent variable Y and  as the independent variable X. beta is simply the regression coefficient.

After you find beta for each individual stock i, the portfolio beta is simply   where  is the weight of stock i in the portfolio.

Note you need to run regression analysis for each stock. If your portfolio contains 30 stocks, you will need to run 30 regressions and find 30 beta’s respectively. Comment on how you find beta is related to the stock’s industry (Finance? Manufacturing? Retail? Utility?) or relate to the company’s size (market capitalization). For example, it is generally accepted that utility stocks have low beta’s while technology stocks have high beta’s.

In your report, I am looking for:

1. What stocks are in your portfolio? What is the weight (percentage of total investment) for each stock?

2. What is the historical period you choose to access the data? (Example: Jan 1981- Dec 2000)

3. Report beta for each stock.

4. Report beta for the portfolio.

5. Any observations on beta’s are encouraged.

 

Reference:

Statman, M. (1987), “How Many Stocks Make a Diversified Portfolio?”, Journal of Finance and Quantitative Analysis, pp 353-363.