Stock-Price Beta Estimation for Google, Inc. Statisticians use the Greek letter beta to signify the slope coefficient in a linear relation. Financial economists use this same Greek letter to signify stock-price risk because betas are the slope coefficients in a simple linear relation that links the return on an individual stock to the return on the overall market in the capital asset pricing model (CAPM). In the CAPM, the security characteristic line shows the simple linear relation between the return on individual securities and the overall market at every point in time:

Rit= i + i RMt + i ,

where Rit is the rate of return on an individual security i during period t, the intercept term is described by the Greek letter (alpha), the slope coefficient is the Greek letter (beta) and signifies systematic risk (as before), and the random disturbance or error term is depicted by the Greek letter (epsilon). At any point in time, the random disturbance term has an expected value of zero, and the expected return on an individual stock is determined by and .

At any point in time, the random disturbance term has an expected value of zero, and the expected return on an individual stock is determined by and . The slope coefficient shows the anticipated effect on an individual securitys rate of return following a 1 percent change in the market index. If = 1.5, then a 1 percent rise in the market would lead to a 1.5 percent hike in the stock price, a 2 percent boost in the market would lead to a 3 percent jump in the stock price, and so on. If = 0, then the rate of return on an individual stock is totally unrelated to the overall market. The intercept term shows the anticipated rate of return when either = 0 or RM = 0. When > 0, investors enjoy positive abnormal returns. When < 0, investors suffer negative abnormal returns. Investors would celebrate a mutual fund manager whose portfolio consistently generated positive abnormal returns ( > 0). They would fire portfolio managers that consistently suffered negative abnormal returns ( < 0). In a perfectly efficient capital market, the CAPM asserts that investor rates of return would be solely determined by systematic risk and both alpha and epsilon would equal zero, = = 0. As shown in Figure 16.8, managers and investors can estimate beta for individual stocks by using a simple ordinary least-squares regression model. In this simple regression model, the dependent Y-variable is the rate of return on an individual stock, and the independent X-variable is the rate of return on an appropriate market index. Within this context, changes in the stock market rate of return are said to cause changes in the rate of return on an individual stock. In this example, beta is estimated for Google, Inc., (ticker symbol: GOOG), the Mountain View, California provider of free Internet search and targeted advertising services. The price data used to estimate beta for GOOG were downloaded from the Internet at the Yahoo! Finance Web site (http://finance.yahoo.com). Weekly returns for GOOG and for the Nasdaq stock market were analyzed over the 52-week trading period ending on May 29, 2007, as shown in Table 16.6. 518 Chapter 16 In this case, as predicted by the CAPM, = 0.0026 (t = 0.70). For a typical week when the Nasdaq market return was zero (essentially flat) during this initial 52-week trading period, the return for GOOG common stockholders was 0.26 percent. Because < 1, GOOG was less volatile than the Nasdaq market during this period. During a week when the Nasdaq market rose by 1 percent, GOOG rose by 0.9588 percent; during a week when the Nasdaq market fell by 1 percent, GOOG fell by 0. 9588 percent. The slope coefficient = 0.9588 is statistically significant (t = 5.32). This means that returns on GOOG stock had a statistically significant relationship to returns for the Nasdaq market during this period. In the case of GOOG, the usefulness of beta as risk measures is undermined by the fact that the simple linear model used to estimate stock-price beta fails to include other important systematic influences on stock market volatility. In the case of GOOG, for example, R2 information shown in Figure 16.8 indicates that only 36.1 percent of the total variation in GOOG returns can be explained by variation in the Nasdaq market. This means that 63.9 percent of the variation in weekly returns for GOOG stock is unexplained by such a simple regression model.

A. Describe some of the attributes of an ideal risk indicator for stock market investors.

B. On the Internet, go to Yahoo! Finance (or msnMoney) and download weekly price information over the past year (52 observations) for GOOG and the Nasdaq market. Then, enter this information in a spreadsheet like Table 16.6 and use these data to estimate GOOG=s beta. Describe any similarities or dissimilarities between your estimation results and the results depicted in Figure 16.8.

C. Estimates of stock-price beta are known to vary according to the time frame analyzed; length of the daily, weekly, monthly, or annual return period; choice of market index; bull or bear market environment; and other nonmarket risk factors. Explain how such influence can undermine the usefulness of beta as a risk indicator. Suggest practical solutions.