## 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:

R_{small} = [(6.85-9.30)+22.87+10.18-21.56+44.63)] / (6*100) = 8.95%

The average return on T-Bills is:

R_{T-Bills} = (6.16+5.47+6.35+8.37+7.81+5.60)/6 = /(6*100) = 6.63%

STD Calculation for Small Stock Returns
R_{small,t} | R_{small,t}-R_{small} | [R_{small,t} - R_{small}]^{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
R_{small,t} | R_{small,t}-R_{small} | [R_{small,t} - R_{small}]^{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.

R_{p} = .03(.10)+.7(.20) = .17 = 17%

variance_{p} = .3^{2}(.05)^{2} + .07^{2}(.15)^{2} = .01125

sigma _{p} = (.01125)^{1/2} = .10607 = 10.61%

b.

R_{p} = .09(.10)+.1(.20) = .11 = 11%

variance_{p} = .9^{2}(.05)^{2} + .01^{2}(.15)^{2} = .00225

sigma _{p} = (.00225)^{1/2} = .04743 = 4.74%

10.20

The slope of the capital market line is:

(R _{m} - R_{f})/sigma _{m} = (12-5)/1= = .7

a. R_{P} = 5 + .7*7 = 9.9%

b. sigma _{p} = (R _{p} - R _{f})/.07 = (20-5)/.7 = 21.4%