The "Beta" of a Stock contrast, a stock with a B > 1 is riskier than the mar- Ainvestor needs a financial incentive to take a ket portfolio and thus commands a higher expected fundamental idea of modern finance is that an risk. Said differently, the expected return' on a risky excess return. investment, R, must exceed the return on a safe, or The "beta" of a stock has become a workhorse risk-free, investment, R7. Thus the expected excess of the investment industry, and you can obtain esti- return, R - R, on a risky investment, like owning mated betas for hundreds of stocks on investment stock in a company, should be positive. firm websites. Those betas typically are estimated At first it might seem like the risk of a stock by OLS regression of the actual excess return on should be measured by its variance. Much of that the stock against the actual excess return on a broad ,however, can be reduced by holding other market stocks in a “portfolio"–in other words, by diversify- risk, index. The table below gives estimated betas for seven ing your financial holdings. This means that the right U.S. stocks. Low-risk producers of consumer sta- way to measure the risk of a stock is not by its vari- ples like Kellogg have stocks with low betas; riskier ance but rather by its covariance with the market. stocks have high betas. The capital asset pricing model (CAPM) formal- izes this idea. According to the CAPM, the expected Company Estimated excess return on an asset is proportional to Verizon (telecommunications) 0.0 expected excess return on a portfolio of all available assets (the "market portfolio"). That is, the CAPM Wal-Mart (discount retailer) 0.3 Kellogg (breakfast cereal) Waste Management (waste disposal) 0.5 says that 0.6 R - R = B(Rm - R), Google (information technology) Ford Motor Company (auto producer) 1.0 (4.12) 1.3 where R, is the expected return on the market Bank of America (bank) 2.2 portfolio and 8 is the coefficient in the population Source finance.yahon.com regression of R - R; on Rm - Rf. In practice, the risk-free return is often taken to be the rate of inter- 'The return on an investment is the change in its price plus est on short-term U.S. government debt. Accord- any payout (dividend) from the investment as a percentage ing to the CAPM, a stock with a B<1 has less risk than the market portfolio and therefore has a lower and sold on December 31 for $105, would have a return of expected excess return than the market portfolio. In R- [($105 – $100) + $2.50]/$100 – 7.5%. of its initial price. For example, a stock bought on January 1 for $100, which then paid a $2.50 dividend during the year

Read the box “The ‘Beta’ of a Stock” in the attachment.a. Suppose that the value of β is greater than 1 for a particular stock.Show that the variance of (R - Rf) for this stock is greater than thevariance of (Rm - Rt).b. Suppose that the value of β is less than 1 for a particular stock. Is itpossible that variance of (R - Rf) for this stock is greater than thevariance of (Rm - Rt)? (Hint: Don’t forget the regression error.) c. In a given year, the rate of return on 3-month Treasury bills is 2.0%and the rate of return on a large diversified portfolio of stocks (theS&P 500) is 5.3%. For each company listed in the table in the box,use the estimated value of β to estimate the stock’s expected rate ofreturn.