Case

Chapter 17

C.

The minimax decision strategy is to choose the decision alternative that will minimize the maximum opportunity loss or regret. In this problem, the maximum possible regret is associated with the upgrade decision. This maximum possible regret can be avoided by choosing the no upgrade decision, the minimax strategy.

CASE STUDY FOR CHAPTER 17 Stock-Price Beta Estimation for the Royal Dutch Petroleum Company Statisticians use the Greek letter beta to signify the slope coefficient in a linear relation. Financial economists use this same Greek letter β 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 : R it = α i + β i R Mt + ε 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 α (alpha), the slope coefficient is the Greek letter β (beta) and signifies systematic risk (as before), and the random disturbance or error term is depicted by the Greek letter ε (epsilon). At any point in time, the random disturbance term ε has an expected value of zero. This means that the expected return on an individual stock is determined by α and β. The slope coefficient β shows the anticipated effect on an individual security=s rate of return following a 1% change in the market index. If β = 1.5, then a 1% rise in the market would lead to a 1.5% hike in the stock price, a 2% boost in the market would lead to a 3% jump in the stock price, and so on. If β = 0, then the rate of return on an individual stock is totally unrelated to the overall market. The intercept term α shows the anticipated rate of return when either β = 0 or RM = 0. When α > 0, investors enjoy positive abnormal returns. When α < 0, investors suffer negative abnormal returns. Investors would celebrate a mutual fund manager whose portfolio consistently generated positive abnormal returns (α > 0). They would fire portfolio managers that consistently suffered negative abnormal returns (α < 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, α = ε = 0. Figure 17.8 here As shown in Figure 17.8, 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 Presented by Suong Jian & Liu Yan, MGMT Panel , Guangdong University of Finance. - 532 -

Risk Analysis this example, beta is estimated for the Royal Dutch Petroleum Company (ticker symbol: RD), the holding company for the Royal Dutch/Shell Group of Companies. Present in more than 145 countries and territories worldwide, the Royal Dutch/Shell Group of Companies are engaged in the business of exploration and production of natural gas, electric power, oil products, chemicals and related products. The price data used to estimate beta for RD were downloaded for free from the Internet at the Yahoo! Finance Web site (http://finance.yahoo.com/q/hp?s=RD). Monthly returns for RD and for the Standard & Poor=s 500 were analyzed over a five-year period (60 observations), as shown in Table 17.7. In this case, as predicted by the CAPM, α = 0.0021 .0. During a typical month when the overall market return is zero (essentially flat), the return for RD common stockholders is expected to be zero as well. The slope coefficient β = 0.6892 is statistically significant (t = 5.47). There is a meaningful empirical relationship between movement in the overall market and RD stock, at least on a statistical basis. Because β < 1, RD is less volatile than the overall market. During a month when the overall market rises by 1%, RD can be expected to rise by 0.69%; during a month when the market falls by 1%, RD can be expected to fall by 0.69%. Table 17.7 here The usefulness of betas as risk measures can be 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 RD, for example, R2 information shown in Figure 17.8 indicates that only 34.03% of the total variation in RD returns can be explained by variation in the overall market. This means that 65.97% of the variation in weekly returns for RD stock is unexplained by such a simple regression model. Although the amount of explained variation is statistically significant, it may not be economically meaningful in the sense of providing investors with consistently useful risk information.

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 RD and the S&P 500. Then, enter this information in a spreadsheet like Table 17.7 and use these data to estimate RD=s beta. Describe any similarities or dissimilarities between your estimation results and the results depicted in Figure 17.8. Estimates of stock-price beta are known to vary according to the time frame analyzed; C. 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.

CASE STUDY SOLUTION

Presented by Suong Jian & Liu Yan, MGMT Panel , Guangdong University of Finance. - 533 -

Chapter 17

A. An ideal measure of stock market risk would be simple to derive, accurate and consistent from one year to another. With an ideal risk measure, investors are able to control the risk exposure faced during volatile markets with well-targeted and well-timed investment buy/sell decisions. For example, suppose an elderly investor wants to maintain an exposure to the equity markets during retirement, but wants to limit risk to regulate the possibility of devastating losses. With an ideal risk measure, retired investors could precisely tilt portfolio allocation toward securities with low risk characteristics. Alternatively, if an investor anticipated a surge in stock prices following a decline in interest rates, precise risk measures could help such an investor tilt an investment portfolio toward more volatile stocks. The usefulness of stock market risk indicators diminishes to the extent that they fail to provide accurate and consistent measures of risk exposure from one year to another. In fact, an important limitation of risk estimators derived from the CAPM is that they vary from one period to another in ways that prove highly unpredictable. When betas vary from one year to another in ways that are essentially random and unpredictable, betas fail to provide investors with a risk assessment tool that can be used to effectively manage portfolio risk. B. It will be a real eye-opener to students when they estimate stock-price beta for RD over a more recent time period using weekly returns and compare those results with the beta estimate derived from the monthly returns reported in Table 17.7 for the June, 1999 to June, 2004 time period, as shown in Figure 17.8. Stock-price beta estimates often vary markedly depending upon the time frame analyzed, and according to the daily, weekly, monthly, or annual return interval examined. Such differences, if severe, can undermine the credibility of stockprice betas as useful risk indicators. C. Empirical 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. For example, estimates of beta tend to be imperfect risk measures because return volatility for the overall market is very difficult to measure. On the nightly news, when commentators talk about the market being up or down, they often refer to moves in the DJIA. Whereas the DJIA offers good insight concerning changes in the prices of large blue chip companies, it offers little insight concerning volatility in the returns earned by investors in smaller high-tech stocks. From the perspective of many individual and institutional investors, the S&P 500 Index gives superior insight concerning moves in the overall market, but like the DJIA, the S&P 500 is dominated by large blue chip companies. Although the Nasdaq and Russell 2000 indexes are popular measures of high-tech and smaller stocks, they are much less informative about changes in the overall market. While there is a high degree of correlation in rates of return earned on the DJIA, S&P 500, Nasdaq, and Russell 2000 indexes, slight differences can have big effects on beta estimates. Presented by Suong Jian & Liu Yan, MGMT Panel , Guangdong University of Finance. - 534 -

Risk Analysis

From a theoretical perspective, the most appropriate benchmark would be a market index that included all capital assets, including stocks, bonds, real estate, collectibles, and so on. Unfortunately, no such market index is available. To greater or lesser degree, this affects the accuracy of all beta estimates and undermines confidence in beta as an accurate measure of security risk. Another important problem faced in obtaining consistent and reliable beta estimates is the fact that beta estimates are sensitive to the length of time over which stock return data are measured. When beta estimates differ according to daily, weekly, monthly or annual returns, the usefulness of stock-price beta as a consistent measure of risk is greatly diminished. The presence of market index bias and return interval bias, among other problems, makes it imperative that beta comparisons among individual companies reflect identical estimation periods, return intervals, and appropriate market benchmarks.

Presented by Suong Jian & Liu Yan, MGMT Panel , Guangdong University of Finance. - 535 -