Студопедия
Случайная страница | ТОМ-1 | ТОМ-2 | ТОМ-3
АвтомобилиАстрономияБиологияГеографияДом и садДругие языкиДругоеИнформатика
ИсторияКультураЛитератураЛогикаМатематикаМедицинаМеталлургияМеханика
ОбразованиеОхрана трудаПедагогикаПолитикаПравоПсихологияРелигияРиторика
СоциологияСпортСтроительствоТехнологияТуризмФизикаФилософияФинансы
ХимияЧерчениеЭкологияЭкономикаЭлектроника

Solution to Integrative problem. 1. Holding-period returns for market, Reynolds Computer, and Andrews

Читайте также:
  1. Andy Rooney is a television commentator who usually talks about the pleasures and problems of everyday life. Here he tells us about a teacher that he liked very much.
  2. Ar/39Ar isotopic age of Svyatoy Nos Peninsula (Transbaikalia) granulites and problem of its geodynamic interpretation
  3. Britons attitude to the problem of migration
  4. C. Is radical feminism to blame for any social problems (e.g. increasing
  5. Categorical Gene Models and the Problem of Small Effect Size
  6. Compare the problems in the U.S.A. and the U.K.
  7. CONFERENCE ON POLLUTION PROBLEMS

 

1. Holding-period returns for Market, Reynolds Computer, and Andrews

Market Reynolds Computer Andrews

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

  May 1090.82       20.60       24.00    
  June 1133.84 3.94% 0.0007   23.20 12.62% 0.0067   26.72 11.33% 0.0065
  July 1120.67 -1.16% 0.0006   27.15 17.03% 0.0158   20.94 -21.63% 0.0619
  Aug 957.28 -14.58% 0.0251   25.00 -7.92% 0.0153   15.78 -24.64% 0.0778
  Sept 1017.01 6.24% 0.0025   32.88 31.52% 0.0733   18.09 14.64% 0.0130
  Oct 1098.67 8.03% 0.0046   32.75 -0.40% 0.0023   21.69 19.90% 0.0277
  Nov 1163.63 5.91% 0.0022   30.41 -7.15% 0.0134   23.06 6.32% 0.0009
  Dec 1229.23 5.64% 0.0019   36.59 20.32% 0.0252   28.06 21.68% 0.0340
  Jan 1279.64 4.10% 0.0008   50.00 36.65% 0.1037   26.03 -7.23% 0.0110
  Feb 1238.33 -3.23% 0.0020   40.06 -19.88% 0.0592   26.44 1.58% 0.0003
  Mar 1286.37 3.88% 0.0007   40.88 2.05% 0.0006   28.06 6.13% 0.0008
  Apr 1335.18 3.79% 0.0006   41.19 0.76% 0.0014   36.94 31.65% 0.0806
  May 1301.84 -2.50% 0.0014   34.44 -16.39% 0.0434   36.88 -0.16% 0.0012
  June 1372.71 5.44% 0.0018   37.00 7.43% 0.0009   37.56 1.84% 0.0002
  July 1328.72 -3.20% 0.0020   40.88 10.49% 0.0037   23.25 -38.10% 0.1710
  Aug 1320.41 -0.63% 0.0004   48.81 19.40% 0.0224   22.88 -1.59% 0.0023
  Sept 1282.71 -2.86% 0.0017   41.81 -14.34% 0.0353   24.78 8.30% 0.0026
  Oct 1362.93 6.25% 0.0025   40.13 -4.02% 0.0072   27.19 9.73% 0.0042
  Nov 1388.91 1.91% 0.0000   43.00 7.15% 0.0007   26.56 -2.32% 0.0031
  Dec 1469.25 5.78% 0.0021   51.00 18.60% 0.0201   24.25 -8.70% 0.0143
  Jan 1394.46 -5.09% 0.0040   38.44 -24.63% 0.0845   32.00 31.96% 0.0824
  Febr 1366.42 -2.01% 0.0011   40.81 6.17% 0.0003   35.13 9.78% 0.0043
  Mar 1498.58 9.67% 0.0071   53.94 32.17% 0.0769   44.81 27.55% 0.0591
  Apr 1452.43 -3.08% 0.0019   50.13 -7.06% 0.0132   30.23 -32.54% 0.1281
  May 1420.60 -2.19% 0.0012   43.13 -13.96% 0.0339   34.00 12.47% 0.0085
  Sum   30.07% .0689     106.62%       77.95% .7958
                           

 

2. Average

Monthly

Return 1.25% 4.44% 3.25%

 

Standard

Deviation 5.47% 16.93% 18.60%

 


3.


 

4 Reynolds’s returns have a great amount of volatility with some correlation to the market returns.

The same can be said of Andrews. The returns show a great amount of volatility that followed the market returns only part of the time.

 

5. Monthly returns of a portfolio of equal amounts of Reynolds and Andrews.

Monthly

Returns

  June 11.98%
  July -2.32%
  August -16.27%
  September 23.08%
  October 9.74%
  November -0.41%
  December 21.02%
  January 14.70%
  February -9.16%
  March 4.09%
  April 16.20%
  May -8.28%
  June 4.65%
  July -13.81%
  August 8.90%
  September -3.00%
  October 2.84%
  November 2.43%
  December 4.95%
  January 3.66%
  February 7.97%
  March 29.87%
  April -19.80%
  May -0.75%
     
  Average return 3.84%
  Standard deviation 12.29%

 



6.

 

 

We see in this new graph where both stocks are included as a single portfolio that the relationship of the stocks with the market approximates an average of the relationships taken alone. Note the reduction in volatility that occurs when risk is diversified even between just two stocks.


7. Monthly holding-period returns for long-term government bonds

(ki- )2

  June 5.70% 0.48% 0.000000%
  July 5.68% 0.47% 0.000001%
  August 5.54% 0.46% 0.000004%
  September 5.20% 0.43% 0.000023%
  October 5.01% 0.42% 0.000041%
  November 5.25% 0.44% 0.000020%
  December 5.06% 0.42% 0.000036%
  January 5.16% 0.43% 0.000027%
  February 5.37% 0.45% 0.000012%
  March 5.58% 0.47% 0.000003%
  April 5.55% 0.46% 0.000004%
  May 5.81% 0.48% 0.000000%
  June 6.04% 0.50% 0.000005%
  July 5.98% 0.50% 0.000003%
  August 6.07% 0.51% 0.000006%
  September 6.07% 0.51% 0.000006%
  October 6.26% 0.52% 0.000016%
  November 6.15% 0.51% 0.000009%
  December 6.35% 0.53% 0.000022%
  January 6.63% 0.55% 0.000050%
  February 6.23% 0.52% 0.000014%
  March 6.05% 0.50% 0.000005%
  April 5.85% 0.49% 0.000000%
  May 6.15% 0.51% 0.000009%

 

Average

Monthly

Return 0.48%

 

Standard

Deviation 0.04%

 


8. Monthly portfolio returns when portfolio consists of equal amounts invested in Reynolds, Andrews, and long-term government bonds.

 

(ki- )2

  June 8.14% 0.0029
  July -1.39% 0.0017
  August -10.69% 0.0180
  September 15.53% 0.0164
  October 6.63% 0.0015
  November -0.13% 0.0008
  December 14.15% 0.0131
  January 9.94% 0.0052
  February -5.95% 0.0075
  March 2.88% 0.0000
  April 10.95% 0.0068
  May -5.36% 0.0065
  June 3.27% 0.0000
  July -9.04% 0.0138
  August 6.10% 0.0011
  September -1.83% 0.0021
  October 2.07% 0.0000
  November 1.79% 0.0001
  December 3.48% 0.0001
  January 2.63% 0.0000
  February 5.49% 0.0008
  March 20.08% 0.0301
  April -13.04% 0.0248
  May -0.33% 0.0009
  Sum 65.36% 0.1542

 

2.72%

Std. Dev.. 8.19%

 


9. Comparison of average returns and standard deviations

Average Standard

Returns Deviations

Reynolds 4.44% 16.93%

Andrews 3.25% 18.60%

Government security 0.48% 0.04%

Reynolds & Andrews 3.84% 12.29%

Reynolds, Andrews, 2.72% 8.19%

& government security

Market 1.25% 5.47%

From the findings above, we see that higher average returns are associated with higher risk (standard deviations), and that by diversification we can reduce risk, possibly without reducing the average return.

10. Based on the standard deviations, Andrews has more risk than Reynolds, 18.60 percent standard deviation versus 16.93 percent standard deviation. However, when we only consider systematic risk, Andrews is slightly less risky--Reynolds's beta is 1.96 compared to Andrews’ beta of 1.49. (The betas given here for Reynolds and Andrews come from financial services who calculate firms' betas. These are not consistent with the graphs above where we see Andrews' returns as being more responsive to the general market. We are seeing the problem of using only 24 months of returns as we have done.)

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

Market Return = 1.25 % Average Monthly Return X 12 Months = 15%.

(The average returns for the market over a two-year period may be high or low relative to the longer-term past, and as a result should not be considered as “typical” investor expectations. For instance, if we used information from Ibbotson & Sinquefield for the years 1926-2002, the market risk premium—market return less risk-free rate—was 8.4 percent, and not the 19 percent that we use below. The point: Do not think two years fairly captures what we can expect in the future?)

Reynolds:

23.64% = 6% + (15% - 6%) X 1.96

Andrews:

19.41% = 6% + (15% - 6%) X 1.49

And if we used the market premium of 8.4 percent:

Reynolds:

22.46% = 6% + 8.4% X 1.96

Andrews:

18.52% = 6% + 8.4% X 1.49


Solutions to Problem Set B

 

6-1B.

krf =.05 +.07 + (.05 x.07)

krf =.1235

or

12.35% = nominal rate of interest

 

6-2B.

krf =.03 +.05 + (.03 x.05)

krf =.0815

or

8.15% = nominal rate of interest

 

6-3B.

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

Probability Return Expected Return Deviation

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

.15 -3% -0.45% 4.788

.30 2 0.60 0.127

.40 4 1.60 0.729

.15 6 0.901.683

= 2.65% s2 = 7.327%

s = 2.707%

 

No, Gautney should not invest in the security. The security’s expected rate of return is less than the rate offered on treasury bills.

 

6-4B.

Security A:

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

Probability Return Expected Return Deviation

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

0.2 - 2% -0.4% 69.19%

0.5 19 9.5 2.88

0.3 25 7.521.17

= 16.6% s2 = 93.24%

s = 9.66%


Security B:

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

Probability Return Expected Return Deviation

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

0.1 5% 0.5% 2.704%

0.3 7 2.1 3.072

0.4 12 4.8 1.296

0.2 14 2.82.888

= 10.2% s2 = 9.96%

s = 3.16%

 

Security ASecurity B

= 16.6% = 10.2%

s = 9.66% s = 3.16%

 

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

 

6-5B.

 

Common Stock A:

 

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

Probability Return Expected Return Deviation

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

0.2 10% 2.0% 2.89%

0.6 13 7.8 0.38

0.2 20 4.07.69

= 13.8% s2 = 10.96%

s = 3.31%

Common Stock B

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

Probability Return Expected Return Deviation

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

0.15 6% 0.9% 5.67%

0.30 8 2.4 5.17

0.40 15 6.0 3.25

0.15 19 2.857.04

= 12.15% s2 = 21.13%

s = 4.60%

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

6-6B.

(a) = + Beta

= 8 % + 1.5 (16% - 8%)

= 20%

 

(b) The 20 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.

 

6-7B. Eye balling the characteristic line for the problem, the rise relative to the run is about 1.75. That is, when the S & P 500 return is four percent Bram's expected return would be about seven percent. Thus, the beta is also approximately 1.75 (7 ÷ 4).

 

6-8B.

+ x Beta =

A 6.75% + (12% - 6.75%) x 1.40 = 14.10%

B 6.75% + (12% - 6.75%) x 0.75 = 10.69%

C 6.75% + (12% - 6.75%) x 0.80 = 10.95%

D 6.75% + (12% - 6.75%) x 1.20 = 13.05%

 

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

= 7.5% + (10.5% - 7.5%) x 0.85

= 10.05%

6-10B. 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;

Dupree = 8.5% + (12.8% - 8.5%) x 0.82 = 12.03%

Yofota = 8.5% + (12.8% - 8.5%) x 0.57 = 10.95%

MacGrill = 8.5% + (12.8% - 8.5%) x 0.68 = 11.42%

 

6-11B.

O'Toole Baltimore

Time Price Return Price Return

1 $22 $45

2 24 9.09% 50 11.11%

3 20 -16.67% 48 -4.00%

4 25 25.00% 52 8.33%

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,


6-12B.

(a) Sugita Market

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

1 1.80% 0.01% 1.50% 0.06%

2 -0.50 5.68 1.00 0.06

3 2.00 0.01 0.00 1.56

4 -2.00 15.08 -2.00 10.56

5 5.00 9.71 4.00 7.56

6 5.00 9.71 3.00 3.06

Sum 11.30 40.20 7.50 22.86

 

1.88% 1.25%

(Sum ÷ 6)

22.60% 15.00%

Variance 8.04% 4.58%

(Sum ÷ 5)

2.84% 2.14%

 

b.

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

= 8% + [(15% - 8%) X 1.18] = 16.26%

c. Sugita's historical return of 22.6 percent exceeds what we would consider a fair return of 16.26 percent, given the stock's systematic risk.

6-13B

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

p = (0.10)(12%) + (0.25)(11%) + (0.15)(15%) + (0.30)(9%) + (0.20)(14%)

= 11.7%


 

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

ßp = (0.10)(1.00) + (0.25)(0.75) + (0.15)(1.30) + (0.30)(0.60) + (0.20)(1.20)

= 0.90

 

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, 2, 3, and 5. "Losers" would be those stocks falling below the security market line, that being stock 4.

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.


6-14B

a) Market Hilary’s

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

Jul-02 1328.72     21.00    
Aug-02 1320.41 -0.63% 0.0002 19.50 -7.14% 0.0211
Sep-02 1282.71 -2.86% 0.0013 17.19 -11.85% 0.0369
Oct-02 1362.93 6.25% 0.0031 16.88 -1.80% 0.0084
Nov-02 1388.91 1.91% 0.0001 18.06 6.99% 0.0000
Dec-02 1469.25 5.78% 0.0026 24.88 37.76% 0.0924
Jan-03 1394.46 -5.09% 0.0034 22.75 -8.56% 0.0254
Feb-03 1366.42 -2.01% 0.0007 26.25 15.38% 0.0064
Mar-03 1498.58 9.67% 0.0080 33.56 27.85% 0.0419
Apr-03 1452.43 -3.08% 0.0014 43.31 29.05% 0.0470
May-03 1420.60 -2.19% 0.0008 43.50 0.44% 0.0048
Jun-03 1454.60 2.39% 0.0003 43.50 0.00% 0.0054
Jul-03 1430.83 -1.63% 0.0005 43.63 0.30% 0.0050

 

Sum 8.52% 0.0225 88.42% 0.2948

 

b) 0.71% 7.37%

Standard deviation 4.52% 16.37%


 
 

c)

 

d. The Hilary’s returns for the last six months of 2002 and the first six months of 2003 were partially correlated, but with a lot of the variance in the stock’s returns, clearly not explained by the market—as would be expected.


6-15B

Stock A

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

Probability Return Expected Return Deviation

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

0.10 -4% -0.40% 16.384%

0.30 2 0.60 13.872

0.40 13 5.20 7.056

0.20 17 3.40 13.448

= 8.80% s2 = 50.76%

s = 7.125%

Stock B

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

Probability Return Expected Return Deviation

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

0.13 4% 0.52% 13.658%

0.40 10 4.00 7.225

0.27 19 5.13 6.092

0.20 23 4.60 15.31

= 14.25% s2 = 42.285%

s = 6.503%

Stock C

 

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

Probability Return Expected Return Deviation

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

0.20 -2% -0.40% 27.145%

0.25 5 1.25 5.406

0.45 14 6.30 8.515

0.10 25 2.50 23.562

= 9.65% s2 = 64.628%

s = 8.039%

 

Stock B has a higher expected rate of return with less risk than Stocks A and C.


 

6-16B

 

+ x Beta =

K 5.5% + (11% - 5.5%) x 1.12 = 11.66%

G 5.5% + (11% - 5.5%) x 1.30 = 12.65%

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

U 5.5% + (11% - 5.5%) x 1.02 = 11.11%

6-17B

Watkins Fisher

Time Price Return Price Return

1 $40 $27

2 45 12.50% 31 14.81%

3 43 -4.44 35 12.90

4 49 13.95 36 2.86

 

6-18B

(a) = + Beta

 

= 4% + 0.95 (7% - 4%)

= 6.85%

 

(b) = + Beta

 

= 4 % + 1.25 (7% - 4%)

= 7.75%

(c) If beta is 0.95:

 

Required rate = 4 % + 0.95 (10% - 4%)

of return

= 9.7%

If beta is 1.25:

 

Required rate = 4 % + 1.25 (10% - 4%)

of return

= 11.5%


Дата добавления: 2015-10-30; просмотров: 122 | Нарушение авторских прав


Читайте в этой же книге: Джеральдина Чаплин: истории из кино и жизни написаны на её лице. | CHAPTER OUTLINE | END-OF-CHAPTER QUESTIONS | END-OF-CHAPTER QUESTIONS | END-OF-CHAPTER PROBLEMS | SOLUTION TO INTEGRATIVE PROBLEM | Bond A B C D E | CHAPTER OUTLINE | END-OF-CHAPTER QUESTIONS | Solutions to Problem Set A |
<== предыдущая страница | следующая страница ==>
END-OF-CHAPTER PROBLEMS| CHAPTER OUTLINE

mybiblioteka.su - 2015-2024 год. (0.06 сек.)