End-of-chapter problems. Solutions to problems Set a

Solutions to Problems Set A

6-1A.

k_rf =.045 +.073 + (.045 x.073)

k_rf =.1213

or

12.13% = nominal rate of interest

6-2A.

k_rf =.064 +.038 + (.064 x.038)

k_rf =.1044

or

10.44% = nominal rate of interest

6-3A.

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

.15 -1% -.15% 2.223%

.30 2 0.60% 0.217%

.40 3 1.20% 0.009%

.15 8 1.20%3.978%

= 2.85% s² = 6.427%

s = 2.535%

No, Pritchard should not invest in the security. The level of risk is excessive for a return which is less than the rate offered on treasury bills.

6-4A.

Common Stock A:

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

0.3 11% 3.3% 4.8%

0.4 15 6.0 0.0

0.3 19 5.74.8

= 15.0% s2 = 9.6%

s = 3.10%

Common Stock B

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

0.2 -5% -1.0% 41.472%

0.3 6 1.8 3.468

0.3 14 4.2 6.348

0.2 22 4.431.752

= 9.4% s² = 83.04%

s = 9.11%

Common Stock A is better. It has a higher expected return with less risk.

6-5A.

Common Stock A:

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

0.2 - 2% -0.4% 69.9%

0.5 18 9.0 0.8

0.3 27 8.131.8

= 16.7% s² = 102.5%

s = 10.12%

Common Stock B:

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

0.1 4% 0.4% 2.704%

0.3 6 1.8 3.072

0.4 10 4.0 0.256

0.2 15 3.06.728

= 9.2% s² = 12.76%

s = 3.57%

Common Stock ACommon Stock B

= 16.7% = 9.2%

s = 10.12% s = 3.57%

We cannot say which investment is "better." It would depend on the investor's attitude toward the risk-return tradeoff.

6-6A.

(a) = + Beta

= 6 % + 1.2 (16% - 6%)

= 18%

(b) The 18 percent "fair rate" compensates the investor for the time value of money and for assuming risk. However, only nondiversifiable risk is being considered, which is appropriate.

6-7A. Eye balling the characteristic line for the problem, the rise relative to the run is about 0.5. That is, when the S & P 500 return is eight percent Aram's expected return would be about four percent. Thus, the beta is also approximately 0.5 (4 ÷ 8).

6-8A.

+ x Beta =

A 6.75% + (12% - 6.75%) x 1.50 = 14.63%

B 6.75% + (12% - 6.75%) x 0.82 = 11.06%

C 6.75% + (12% - 6.75%) x 0.60 = 9.90%

D 6.75% + (12% - 6.75%) x 1.15 = 12.79%

6-9A.` = + (Market Return - Risk-Free Rate) X Beta

= 7.5% + (11.5% - 7.5%) x 0.765

= 10.56%

6-10A. If the expected market return is 12.8 percent and the risk premium is 4.3 percent, the riskless rate of return is 8.5 percent (12.8% - 4.3%). Therefore;

Tasaco = 8.5% + (12.8% - 8.5%) x 0.864 = 12.22%

LBM = 8.5% + (12.8% - 8.5%) x 0.693 = 11.48%

Exxos = 8.5% + (12.8% - 8.5%) x 0.575 = 10.97%

6-11A.

Asman Salinas

Time Price Return Price Return

1 $10 $30

2 12 20.00% 28 -6.67%

3 11 -8.33 32 14.29

4 13 18.18 35 9.38

A holding-period return indicates the rate of return you would earn if you bought a security at the beginning of a time period and sold it at the end of the period, such as the end of the month or year.

6-12A.a. Zemin Market

Month k_b (k_b - )² k_b (k_b - )²

1 6.00% 16.00% 4.00% 8.03%

2 3.00 1.00 2.00 0.69

3 1.00 1.00 -1.00 4.69

4 -3.00 25.00 -2.00 10.03

5 5.00 9.00 2.00 0.69

6 0.00 4.00 2.00 0.69

Sum 12.00 56.00 7.00 24.82

2.00% 1.17%

(Sum ÷ 6)

24.00% 14.04%

Variance 11.20% 4.97%

(Sum ¸ 5)

3.35% 2.23%

b. = + (Market Return - Risk-Free Rate) X Beta

= 8% + [(14% - 8%) X 1.54] = 17.24%

c. Zemin's historical return of 24 percent exceeds what we would consider a fair return of 17.24 percent, given the stock's systematic risk.

6-13A.

a. The portfolio expected return, p, equals a weighted average of the individual stock's expected returns.

p = (0.20)(16%) + (0.30)(14%) + (0.15)(20%) + (0.25)(12%) + (0.10)(24%)

= 15.8%

b. The portfolio beta, ßp, equals a weighted average of the individual stock betas

ßp = (0.20)(1.00) + (0.30)(0.85) + (0.15)(1.20) + (0.25)(0.60) + (0.10)(1.60)

= 0.95

c. Plot the security market line and the individual stocks

d. A "winner" may be defined as a stock that falls above the security market line, which means these stocks are expected to earn a return exceeding what should be expected given their beta or systematic risk. In the above graph, these stocks include 1, 3, and 5. "Losers" would be those stocks falling below the security market line, which are represented by stocks 2 and 4 ever so slightly.

e. Our results are less than certain because we have problems estimating the security market line with certainty. For instance, we have difficulty in specifying the market portfolio.

6-14A a.

Market Mathews

Month Price kt (kt- )² Price kt (kt- )²

Jul-02	1328.72			34.50
Aug-02	1320.41	-0.63%	0.0002	41.09	19.10%	0.0170
Sep-02	1282.71	-2.86%	0.0013	37.16	-9.56%	0.0244
Oct-02	1362.93	6.25%	0.0031	38.72	4.20%	0.0003
Nov-02	1388.91	1.91%	0.0001	38.34	-0.98%	0.0050
Dec-02	1469.25	5.78%	0.0026	41.16	7.36%	0.0002
Jan-03	1394.46	-5.09%	0.0034	49.47	20.19%	0.0199
Feb-03	1366.42	-2.01%	0.0007	56.50	14.21%	0.0066
Mar-03	1498.58	9.67%	0.0080	65.97	16.76%	0.0114
Apr-03	1452.43	-3.08%	0.0014	63.41	-3.88%	0.0099
May-03	1420.60	-2.19%	0.0008	62.34	-1.69%	0.0060
Jun-03	1454.60	2.39%	0.0003	66.84	7.22%	0.0001
Jul-03	1430.83	-1.63%	0.0005	66.75	-0.13%	0.0038

Sum 8.52% 0.0225 72.79% 0.1048

b)

Average monthly return 0.71% 6.07%

Standard deviation 4.52% 9.76%

c)

d. Mathews returns seem to correlate to the market returns during the majority of the year, but show great volatility.

6-15A

Stock 1

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

0.15 2% 0.30% 6.048%

0.40 7 2.80 0.729

0.30 10 3.00 0.817

0.15 15 2.25 6.633

= 8.35% s² = 14.227%

s = 3.77%

Stock 2

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )²P(ki)

0.25 -3% -0.75% 85.56%

0.50 20 10.00 10.13

0.25 25 6.25 22.56

= 15.50% s² = 118.25%

s = 10.87%

Stock 3

(A) (B) (A) x (B) Weighted

Probability Return Expected Return Deviation

P(ki) (ki) (ki- )2P(ki)

0.10 -5% -0.50% 36.1%

0.40 10 4.00 6.4

0.30 15 4.50 0.3

0.20 30 6.00 51.2

= 14.00% s² = 94.0%

s = 9.7%

We cannot say which investment is "better." It would depend on the investor's attitude toward the risk-return tradeoff.

6-16A

+ x Beta =

H 5.5% + (11% - 5.5%) x 0.75 = 9.63%

T 5.5% + (11% - 5.5%) x 1.40 = 13.20%

P 5.5% + (11% - 5.5%) x 0.95 = 10.73%

W 5.5% + (11% - 5.5%) x 1.25 = 12.38%

6-17A

Williams Davis

Time Price Return Price Return

1 $33 $19

2 27 -18.18% 15 -21.05%

3 35 29.63 14 -6.67

4 39 11.43 23 64.29

6-18A

(a) = + Beta

= 5 % + 1.2 (9% - 5%)

= 9.8%

(b) = + Beta

= 5 % + 0.85 (9% - 5%)

= 8.4%

(c) If beta is 1.2:

Required rate = 5 % + 1.2 (12% - 5%)

of return

= 13.4%

If beta is 0.85:

Required rate = 5 % + 0.85 (12% - 5%)

of return

= 10.95%

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