Finding your 401(k) beta For this project, you are going to evaluate the systema

Question

Finding your 401(k) beta

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%u2019s monthly excess return (return in excess of risk free rate) on market monthly excess return according to the following model:

R_it-R_ft=%u03B1_i+%u03B2_i (R_mt-R_ft )+e_it

Equivalently Equivalently

the dependent variable Y the independently variable X

where,

R_it is the return of stock i on month t;

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

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

%u03B2_i is the beta for stock i;

%u03B1_i is the intercept for stock i;

e_it is the error term.

To find the beta for stock i, you need to obtain the data of R_it-R_ft as dependent variable Y and R_mt-R_ft 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 %u03B2_p=%u2211_(i=1)^n%u2592w_i %u03B2_i where w_i 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%u2019s respectively. Comment on how you find beta is related to the stock%u2019s industry (Finance? Manufacturing? Retail? Utility?) or relate to the company%u2019s size (market capitalization). For example, it is generally accepted that utility stocks have low beta%u2019s while technology stocks have high beta%u2019s.

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%u2019s are encouraged.

Reference:

Statman, M. (1987), %u201CHow Many Stocks Make a Diversified Portfolio?%u201D, Journal of Finance and Quantitative

Explanation / Answer

Your investment portfolios overall return depends on the performance of each individual investment in the portfolio. A stock that makes up a greater percentage of your portfolio influences your overall returns more than a stock that makes up a lower percentage. These percentages are also known as a stocks portfolio weight. The total weight of all investments in a portfolio equals 100 percent. As stock prices change, each stocks portfolio weight also fluctuates. Calculate these weights periodically to make sure your portfolio stays in line with your investment strategy. Step 1 Determine the number of shares you own of each stock in your portfolio. For example, assume you own 1,000 shares of Stock A, 5,000 shares of Stock B and 3,000 shares of Stock C. Step 2 Look up each stocks current market price on any financial website that provides stock quotes, or get the prices from your broker. In this example, assume the prices of Stocks A, B and C are $30, $20 and $25, respectively. Step 3 Multiply the number of shares of each stock by its price to determine the market value of your investment in each stock. In this example, multiply 1,000 by $30 to get a $30,000 investment in Stock A. Your other investment values would be $100,000 for Stock B and $75,000 for Stock C. Step 4 Add together your investment in each stock. Add the value of the other investments in the portfolio, if any, to your result to determine your portfolios total value. Continuing the example, assume Stocks A, B and C are the only investments in your portfolio. Add $30,000, $100,000 and $75,000 to get a total portfolio value of $205,000. Step 5 Divide the value of your investment in each stock by your portfolios total value. Multiply each result by 100 to calculate the percentage portfolio weight of each stock. Concluding the example, divide Stock As value of $30,000 by $205,000 to get 0.146. Multiply 0.146 by 100 to get 14.6 percent. Stock B would make up 48.8 percent of your portfolio. Stock C would make up 36.6 percent. Because Stock B has the highest weight of 48.8 percent, its performance impacts the portfolios overall returns more than Stock C and significantly more than Stock A.

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