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Unformatted text preview: 64 standard deviations above the mean. This corresponds to a probability of (much) less than 0.5%. The actual answer is ≈ .000001321%, or about once every 1 million years. 26. It is impossible to lose more than 100 percent of your investment. Therefore, return distributions are truncated on the lower tail at –100 percent. Challenge 27. Using the z-statistic, we find: z = (X – µ)/σ z = (0% – 11.7%)/20.6% = –0.568 Pr(R=0) ≈ 28.50% 28. For each of the questions asked here, we need to use the z-statistic, which is: z = (X – µ)/σ a. z1 = (10% – 6.2%)/8.4% = 0.4523 This z-statistic gives us the probability that the return is less than 10 percent, but we are looking for the probability the return is greater than 10 percent. Given that the total probability is 100 percent (or 1), the probability of a return greater than 10 percent is 1 minus the probability of a return less than 10 percent. Using the cumulative normal distribution table, we get: Pr(R=10%) = 1 – Pr(R=10%) = 32.55% 267 For a return less than 0 percent: z2 = (0% – 6.2%)/8.4 = –0.7381 Pr(R<10%) = 1 – Pr(R>0%) = 23.02% b. The probability that T-bill returns will be greater than 10 percent is: z3 = (10% – 3.8%)/3.1% = 2 Pr(R=10%) = 1 – Pr(R=10%) = 1 – .9772 ≈ 2.28% And the probability that T-bill returns will be less than 0 percent is: z4 = (0% – 3.8%)/3.1% = –1.2258 Pr(R=0) ≈ 11.01% c. The probability that the return on long-term corporate bonds will be less than –4.18 percent is: z5 = (–4.18% – 6.2%)/8.4% = –1.2357 Pr(R=–4.18%) ≈ 10.83% And the probability that T-bill returns will be greater than 10.56 percent is: z6 = (10.56% – 3.8%)/3.1% = 2.181 Pr(R=10.56%) = 1 – Pr(R=10.56%) = 1 – .9854 ≈ 1.46% 268 CHAPTER 11 RETURN AND RISK: THE CAPITAL ASSET PRICING MODEL
Answers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique portion of the total risk can be eliminated at little cost. On the other hand, there are some risks that affect all investments. This portion of the total risk of an asset cannot be costlessly eliminated. In other words, systematic risk can be controlled, but only by a costly reduction in expected returns. a. b. c. d. e. f. systematic unsystematic both; probably mostly systematic unsystematic unsystematic systematic 2. 3. 4. 5. 6. No to both questions. The portfolio expected return is a weighted average of the asset’s returns, so it must be less than the largest asset return and greater than the smallest asset return. False. The variance of the individual assets is a measure of the total risk. The variance on a welldiversified portfolio is a function of systematic risk only. Yes, the standard deviation can be less than that of every asset in the portfolio. However, β p cannot be less than the smallest beta because β p is a weighted average of the individual asset betas. Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would be equal to the risk-free rate. It is also possible to have a negative beta; the return would be less than the risk-free rate. A negative beta asset would carry a negative risk premium because of its value as a diversification instrument. The covariance is a more appropriate measure of a security’s risk in a well-diversified portfolio because the covariance reflects the effect of the security on the variance of the portfolio. Investors are concerned with the variance of their portfolios and not the variance of the individual securities. Since covariance measures the impact of an individual security on the variance of the portfolio, covariance is the appropriate measure of risk. 7. 8. If we assume that the market has not stayed constant during the past three years, then the lack in movement of Southern Co.’s stock price only indicates that the stock either has a standard deviation or a beta that is very near to zero. The large amount of movement in Texas Instrument’ stock price does not imply that the firm’s beta is high. Total volatility (the price fluctuation) is a function of both systematic and unsystematic risk. The beta only reflects the systematic risk. Observing the standard deviation of price movements does not indicate whether the price changes were due to systematic factors or firm specific factors. Thus, if you observe large stock price movements like that of TI, you cannot claim that the beta of the stock is high. All you know is that the total risk of TI is high. The wide fluctuations in the price of oil stocks do not indicate that these stocks are a poor investment. If an oil stock is purchased as part of a well-diversified portfolio, only its contribution to the risk of the entire portfolio matters. This contribution is measured by systematic risk or beta. Since price fluctuations in oil stocks reflect diversifiable plus non-diversifiable risk, observing the st...
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