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 Class | Nominal | Real | Approx. |
Common Stocks | 12.2% | 8.7% | 9.2% |
L/T Corp. Bonds | 5.7% | 2.4% | 2.5% |
L/T Govt. Bonds | 5.2% | 1.9% | 2.0% |
U. S. T-Bills | 3.7% | .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,t | Rsmall,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,t | Rsmall,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%