Using the Fisher equation, the real return was:(1 + R) = (1 + r)(1 + h)r = (1.0412 / 1.03) – 1 = .0109 or 1.09%5.The nominal return is the stated return, which is 12.30 percent. Using the Fisher equation, the real returnwas:(1 + R) = (1 + r)(1 + h)r = (1.121)/(1.03) – 1 = .0883 or 8.83%6.Using the Fisher equation, the real returns for long-term government and corporate bonds were:(1 + R) = (1 + r)(1 + h)rG= 1.059/1.03 – 1 = .0282 or 2.82%rC= 1.063/1.03 – 1 = .0320 or 3.20%7.The average return is the sum of the returns, divided by the number of returns. The average return for eachstock was:[]%7.80or.0780509.16.17.21.08.1=+-++===NxXNiiDownloaded by Kin Ho ([email protected])lOMoARcPSD|4966429

[]%60.14or.1460526.21.14.38.16.1=+-++===NyYNiiRemembering back to “sadistics,” we calculate the variance of each stock as:()()()()()()(){}()()()()(){}048680.146.26.146.21.146.14.146.38.146.16.151020670.078.09.078.16.078.17.078.21.078.08.1511222222222222122=-+--+-+-+--==-+--+-+-+--=--==YXNiiXNxxσσσThe standard deviation is the square root of the variance, so the standard deviation of each stock is:σX= (.020670)1/2= .1438 or 14.38%σY= (.048680)1/2= .2206 or 22.06%8.We will calculate the sum of the returns for each asset and the observed risk premium first. Doing so,we get:YearLarge co. stock returnT-bill returnRisk premium19703.94%6.50%-2.56%197114.304.369.94197218.994.2314.761973–14.697.29–21.981974–26.477.99–34.46197537.235.8731.3633.3036.24–2.94a.The average return for large company stocks over this period was:Large company stocks average return = 33.30% / 6 = 5.55%And the average return for T-bills over this period was:T-bills average return = 36.24% / 6 = 6.04%Downloaded by Kin Ho ([email protected])lOMoARcPSD|4966429

b.Using the equation for variance, we find the variance for large company stocks over this periodwas:Variance = 1/5[(.0394 – .0555)2+ (.1430 – .0555)2+ (.1899 – .0555)2+ (–.1469 – .0555)2+(–.2647 – .0555)2+ (.3723 – .0555)2]Variance = 0.053967And the standard deviation for large company stocks over this period was:Standard deviation = (0.053967)1/2= 0.2323 or 23.23%Using the equation for variance, we find the variance for T-bills over this period was:Variance = 1/5[(.0650 – .0604)2+ (.0436 – .0604)2+ (.0423 – .0604)2+ (.0729 – .0604)2+(.0799 – .0604)2+ (.0587 – .0604)2]Variance = 0.000234And the standard deviation for T-bills over this period was:Standard deviation = (0.000234)1/2= 0.0153 or 1.53%c.The average observed risk premium over this period was:Average observed risk premium = –2.94% / 6 = –0.49%The variance of the observed risk premium was:Variance = 1/5[(–.0256 – (–.0049))2+ (.0994 – (–.0049))2+ (.1476 – (–.0049)))2+(–.2198 – (–.0049))2+ (–.3446 – (–.0049))2+ (.3136 – (–.0049))2]Variance = 0.059517And the standard deviation of the observed risk premium was:Standard deviation = (0.059517)1/2= 0.2440 or 24.40%d.Before the fact, for most assets the risk premium will be positive; investors demand compensationover and above the risk-free return to invest their money in the risky asset. After the fact, theobserved risk premium can be negative if the asset’s nominal return is unexpectedly low, the risk-free return is unexpectedly high, or if some combination of these two events occurs.9.a.To find the average return, we sum all the returns and divide by the number of returns, so:Average return = (.07 –.13 +.21 +.34 +.15) / 5Average return = .1280, or 12.80%Downloaded by Kin Ho ([email protected])lOMoARcPSD|4966429

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