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1、第十章：风险与收益：市场历史的启示 因为公司的表现具有不可预见性。 投资者很容易看到最坏的投资结果，但是确很难预测到。 不是，股票具有更高的风险，一些投资者属于风险规避者，他们认为这点额 外的报酬率还不至于吸引他们付出更高风险的代价。 股票市场与赌博是不同的，它实际是个零和市场，所有人都可能赢。而且投 机者带给市场更高的流动性，有利于市场效率。 在80 年代初是最高的，因为伴随着高通胀和费雪效应。 有可能，当投资风险资产报酬非常低，而无风险资产报酬非常高，或者同时 出现这两种现象时就会发生这样的情况。 相同，假设两公司2 年前股票价格都为P0，则两年后G 公司股票价格为 1.1*0.9* P0
2、，而S 公司股票价格为0.9*1.1 P0，所以两个公司两年后的股价是一样 的。 8. 不相同，Lake Minerals 2 年后股票价格 = 100(1.10)(1.10) = $121.00 而 SmallTown Furniture 2 年后股票价格= 100(1.25)(.95) = $118.75 算数平均收益率仅仅是对所有收益率简单加总平均，它没有考虑到所有收益 率组合的效果，而几何平均收益率考虑到了收益率组合的效果，所以后者比较重 要。 不管是否考虑通货膨胀因素，其风险溢价没有变化，因为风险溢价是风险资 产收益率与无风险资产收益率的差额，若这两者都考虑到通货膨胀的因素，其差 额
3、仍然是相互抵消的。而在考虑税收后收益率就会降低，因为税后收益会降低。 11. R = ($104 92) + 1.45 / $92 = .1462 or 14.62% 12. Dividend yield = $1.45 / $92 = .0158 or 1.58% Capital gains yield = ($104 92) / $92 = .1304 or 13.04% 13. R = ($81 92) + 1.45 / $92= .1038 or 10.38% Dividend yield = $1.45 / $92 = .0158 or 1.58% Capital gains yie
4、ld = ($81 92) / $92 = .1196 or 11.96% 14.,1,15. a. To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (.34 +.16 + .19 .21 + .08)/5 = .1120 or 11.20% b. Using the equation to calculate variance, we find: Variance = 1/4(.34 .112)2 +
5、(.16 .112)2 + (.19 .112)2 + (.21 .112)2 + (.08 .112)2 = 0.041270 So, the standard deviation is: Standard deviation = (0.041270)1/2 = 0.2032 or 20.32% 16. a. To calculate the average real return, we can use the average return of the asset and the average inflation rate in the Fisher equation. Doing s
6、o, we find: (1 + R) = (1 + r)(1 + h)则r = (1.1120/1.042) 1=.0672 or 6.72% b. The average risk premium is simply the average return of the asset, minus the average real riskfree rate, so, the average risk premium for this asset would be: RP R f R= .1120 .0510= .0610 or 6.10% We can find the average re
7、al risk-free rate using the Fisher equation. The average real risk-free rate was:(1 + R) = (1 + r)(1 + h) r f = (1.051/1.042) 1= .0086 or 0.86% And to calculate the average real risk premium, we can subtract the average risk-free rate from the average real return. So, the average real risk premium w
8、as: rp r r f = 6.72% 0.86%= 5.85% Apply the five-year holding-period return formula to calculate the total return of the stock over the five-year period, we find: 5-year holding-period return = (1 + R1)(1 + R2)(1 +R3)(1 +R4)(1 +R5) 1 = (1 + .1843)(1 + .1682)(1 + .0683)(1 + .3219)(1 .1987) 1 = 0.5655
9、 or 56.55% To find the return on the zero coupon bond, we first need to find the price of the bond today. Since one year has elapsed, the bond now has 29 years to maturity, so the price today is: P1 = $1,000/1.0929 = $82.15 There are no intermediate cash flows on a zero coupon bond, so the return is
10、 the capital gains, or:R = ($82.15 77.81) / $77.81 = .0558 or 5.58% The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. This stock paid no dividend, so the return was: R = ($82.01 75.15) / $75.15 = .0913 or 9.13%,2,This is the return
11、for three months, so the APR is: APR = 4(9.13%) = 36.51% And the EAR is: EAR = (1 + .0913)4 1 = .4182 or 41.82% 21. To calculate the arithmetic and geometric average returns, we must first calculate the return for each year. The return for each year is: R1 = ($55.83 49.62 + 0.68) / $49.62 = .1389 or
12、 13.89% R2 = ($57.03 55.83 + 0.73) / $55.83 = .0346 or 3.46% R3 = ($50.25 57.03 + 0.84) / $57.03 = .1042 or 10.42% R4 = ($53.82 50.25 + 0.91)/ $50.25 = .0892 or 8.92% R5 = ($64.18 53.82 + 1.02) / $53.82 = .2114 or 21.14% The arithmetic average return was: RA = (0.1389 + 0.0346 0.1042 + 0.0892 + 0.21
13、14)/5 = 0.0740 or 7.40% And the geometric average return was: RG = (1 + .1389)(1 + .0346)(1 .1042)(1 + .0892)(1 + .2114)1/5 1 = 0.0685 or 6.85% To find the return on the coupon bond, we first need to find the price of the bond today. Since one year has elapsed, the bond now has six years to maturity
14、, so the price today is: P1 = $70(PVIFA8%,6) + $1,000/1.086 = $953.77 You received the coupon payments on the bond, so the nominal return was: R = ($953.77 943.82 + 70) / $943.82 = .0847 or 8.47% And using the Fisher equation to find the real return, we get: r = (1.0847 / 1.048) 1 = .0350 or 3.50% L
15、ooking at the long-term government bond return history in Table 10.2, we see that the mean return was 6.1 percent, with a standard deviation of 9.4 percent. In the normal probability distribution, approximately 2/3 of the observations are within one standard deviation of the mean. This means that 1/
16、3 of the observations are outside one standard deviation away from the mean. Or: Pr(R15.5) 1/3 But we are only interested in one tail here, that is, returns less than 3.3 percent, so: Pr(R 3.3) 1/6 You can use the z-statistic and the cumulative normal distribution table to find the answer as well. Doing so, we find: z = (3.3% 6.1)/9.4% = 1.00 Looking at the z-table, this gives a probability of 15.87%, or: Pr(R 3.3) .1587 or 15.87% The range of returns you would expect to see 95 percent
