## Problem Set I: Suggested Answers

9.2
Purchase Price=\$10,400/200 = \$52.00
a. Total dollar return = \$600 + 200(\$54.25-\$52)= \$1,050
b. Capital gain = 200(\$54.25-52)=\$450
c. Percentage Return = \$1,050/\$10,400 = 10.10%
d. Dividend Yield = \$600/(200*52) = 5.77%

9.5
You can find the nominal returns, I, on each of the securities in the text. The inflation rate, pi, for the period is also in thetext. It is 3.2%. The real return, r, is (1+I)/(1+pi) -1. An approximation to the real rate is r= i - pi. Notice that the approximation is good when the nominal interest rate is close to the inflation rate.
Asset ClassNominal Real Approx.
Common Stocks12.2%8.7%9.2%
L/T Corp. Bonds5.7%2.4%2.5%
L/T Govt. Bonds5.2%1.9%2.0%
U. S. T-Bills3.7%.05%.05%

9.8
Five Year Holding Period Return
= (1-.0491)(1+.2141)(1+.2551)(1+.0627)(1+.3216)-1
= 98.64%

9.18
The average return on small company stocks is:
Rsmall = [(6.85-9.30)+22.87+10.18-21.56+44.63)] / (6*100) = 8.95%
The average return on T-Bills is:
RT-Bills = (6.16+5.47+6.35+8.37+7.81+5.60)/6 = /(6*100) = 6.63%

STD Calculation for Small Stock Returns
Rsmall,tRsmall,t-Rsmall[Rsmall,t - Rsmall]2
.0685-.020950.000439
-.0930-.182450.033288
.2287.139250.019391
.1018.012350.000153
-.2156-.305050.093056
.4463.356850.127342
Total = .273667
Variance = 5.47%
Standard Deviation = 23.40%

STD Calculation for T-Bill Returns
Rsmall,tRsmall,t-Rsmall[Rsmall,t - Rsmall]2
.0616-.004667.000022
.0547-.011567.000134
.0635-.002767.000008
.0837.017433.000304
.0781.011833.000140
.0560-.010267.000105
Total = .000713
Variance = .01%
Standard Deviation = 1.19%

9.19
The range with 95% probability is: [mean - 2*std, Mean +2*std]
range = [17.5 - 2*8.5,17.5 + 2*8.5]
range = [.5%, 34.5%]

10.9
a.
Rp = .03(.10)+.7(.20) = .17 = 17%
variancep = .32(.05)2 + .072(.15)2 = .01125
sigma p = (.01125)1/2 = .10607 = 10.61%
b.
Rp = .09(.10)+.1(.20) = .11 = 11%
variancep = .92(.05)2 + .012(.15)2 = .00225
sigma p = (.00225)1/2 = .04743 = 4.74%

10.20
The slope of the capital market line is:
(R m - Rf)/sigma m = (12-5)/1= = .7
a. RP = 5 + .7*7 = 9.9%
b. sigma p = (R p - R f)/.07 = (20-5)/.7 = 21.4%