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ANSWERS TO END-OF-CHAPTER QUESTIONS 6-1. Historical returns are realized returns, such as those reported by Ibbotson Associates. Expected returns are returns expected to occur in the future. They are the most likely returns for the future, although they may not actually be realized because of risk. 6-2. A Total Return can be calculated for any asset for any holding period. Both monthly and annual TRs are often calculated, but any desired period of time can be used. 6-3. Total return for any security consists of an income (yield) component and a capital gain (or loss) component . The yield component relates dividend or interest payments to the price of the security. The capital gain (loss) component measures the gain or loss in price since the security was purchased. While either component can be zero for a given security over a specified time period, only the capital change component can be negative. 6-4. TR , another name for holding period return , is a decimal or percentage return, such as +.10 or -15%. The term “holding period return” is sometimes used instead of TR. Return relative adds 1.0 to the TR in order that all returns can be stated on the basis of 1.0 (which represents no gain or loss), thereby avoiding negative numbers so that the geometric mean can be calculated. 6-5. The geometric mean is a better measure of the change in wealth over more than a single period. Over multiple periods the geometric mean indicates the compound rate of return , or the rate at which an invested dollar grows, and takes into account the variability in the returns. The geometric mean is always less than the arithmetic mean because it allows for the compounding effect--the earning of interest on interest. 6-6. The arithmetic mean should be used when describing the average rate of return without considering compounding. It is the best estimate of the rate of return for a single period. Thus, in estimating the rate of return for common stocks for next year, we use the arithmetic mean and not the geometric mean. The reason is that because of variability in the returns, we will have to earn, on average, the arithmetic rate in order to achieve a compound rate of growth which is given by the smaller geometric mean. 6-7. See Equation 6-11. Knowing the arithmetic mean and the standard deviation for a series, the geometric mean can be approximated. 6-8. An equity risk premium is the difference between stocks and a risk-free rate (proxied by

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the return on Treasury bills). It represents the additional compensation, on average, for taking the risk of equities rather than buying Treasury bills. 6-9. As Table 6-6 shows, the risk (standard deviation) of large common stocks was about two and one-half times that of government and corporate bonds. Therefore, common stocks are clearly more risky than bonds, as they should be since larger returns would be expected to be accompanied by larger risks over long periods of time.
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