The required return on a common stock can be computed using the Capital Asset Pricing Model (CAPM). This model was developed in the 1960’s and was largely credited to William Sharpe, who won a Nobel Prize for his contribution in 1990. (Sullivan, 2006) The CAPM uses statistical analysis to relate the risk of an individual stock to its expected return. The premise is that investors must be compensated for the time value of money and the risk of undertaking the investment.

The formula for the CAPM is expressed as:

RSTOCK = RRF + β( RM “– RRF)

Where:

RSTOCK = the Return of the individual security

RRF = the Risk-free rate of return (usually the going rate on short-term Treasury Bills)

β = the beta coefficient, a measure of riskiness of the stock relative to the riskiness of the market. A beta of 1 means that the stock has the same level of risk as the overall market. A beta of less than 1 means less risk than the overall market, and more than 1 means it is more risky.

RM = the Return of the market

For example, using this model we can compute the required return for IBM stock if we know a few things. We must know:

1.The going rate on Short-term Treasury Bills. This approximates the Risk-free rate.

2.The rate of return for the S&P 500. This is traditionally used to approximate the Return of the market.

3.The beta coefficient of the stock. This can be computed using the historical rates of return for the individual stock and the historical rates of return for the market using a regression analysis. Or, you can look it up on YahooFinance.com!

Let’s assume that the Risk-free rate is 3%, the Return of the S&P is 10%, and the Beta for IBM is 0.9. Here’s our calculation:

RIBM = 3% + 0.9(10% “–3%) = 9%

This means that IBM must have a 9% return in order to compensate investors for putting their money in IBM stock instead of elsewhere.

Directions:

1.Select a publicly traded company. (You may use the same company you researched for the Discussion Board in Units 1 and 2. Remember a company may only be used once! So, be sure to check the board and make sure that another student has not already selected this company.)

2.Go to www.finance.yahoo.com (Links to an external site.) Enter the company’s stock symbol in the “Get Quotes” box. If you do not know the stock symbol, you can enter the company’s name in the search tool.

3.Search for the company’s Beta coefficient on the Summary page. It should be on the far right under Key Statistics. Make a note of this number.

4.Next go to the Trading Information area of the page. Just scroll down to find it. Here you will find the 52-week change for the stock and for the S&P 500. Write these numbers down.

5.Next, scroll back up and search across the top area of the stock chart and summary info for the Market Data. Click the drop down menu and select US Treasury Bond rates. There should be 3-month, 6-month, 2-year, etc. Select the 6-month rate, and make a note of this number.

6.Using the information above (the stock’s Beta, the rate on the 6-month Treasury and the average 52-week return for the S&P 500) compute the required rate of return for your stock. In other words, plug these numbers into the CAPM model.

7.Compare the required rate of return that you just computed with the 52-week change for the security. What do you notice? How does the required rate of return compare with the actual 52-week return? In your opinion, is this stock a good investment? Please explain your answer.