Problem 5-5 Suppose your expectations regarding the stock market are as follows:

ID: 2710372 • Letter: P

Question

Problem 5-5

Suppose your expectations regarding the stock market are as follows:

State of the Economy

Probability

HPR

Boom

0.4

35%

Normal growth

0.5

Recession

0.1

–13

Answer

Mean= .0208

Standard Deviation: 14.42%

Problem 5-6

The stock of Business Adventures sells for $35 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows:

Dividend

Stock price

Boom

$1.20

$45

Normal economy

1.20

Recession

.60

Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected Return = 35%

Standard deviation =45.42%

Problem 6-6

Consider the following table:

Stock Fund

Bond Fund

Scenario

Probability

Rate of Return

Severe recession

0.05

43%

12%

Mild recession

0.25

17%

12%

Normal growth

0.40

14%

Boom

0.30

31%

Mean return %

Variance

c. Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 4 decimal places.)

Covariance

rev: 03_07_2013_QC_27638

Mean Return 10%

Variance .2216

Covariance = -.0174

Problem 6-7

Consider the following table:

Stock Fund

Bond Fund

Scenario

Probability

Rate of Return

Severe recession

0.15

34%

10%

Mild recession

0.20

18%

Normal growth

0.35

14%

Boom

0.30

24%

Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 4 decimal places.)

Covariance

rev: 10_11_2013_QC_37085

Mean Return =.03

Variance =.05313

b)Covariance .0013

Problem 7-4

Here are data on two companies. The T-bill rate is 4.6% and the market risk premium is 5.6%.

Company

$1 Discount Store

Everything $5

Forecast return

12%

11%

Standard deviation of returns

11%

13%

Beta

1.5

What would be the fair return for each company, according to the capital asset pricing model (CAPM)?(Round your answers to 2 decimal places.)

Discount store= 3.1%

Everything = 3.6%

Problem 7-9

What must be the beta of a portfolio with E(rP) = 31.00%, if rf = 4% and E(rM) = 19%? (Round your answer to 2 decimal places.)

Beta of portfolio

1.8

Problem 7-15

Consider the following information:

Portfolio

Expected Return

Standard Deviation

Risk-free

5.0%

Market

13.0

11.0

Calculate the sharpe ratios for the market portfolio and portfolio A. (Round your answers to 2 decimal places.)

Sharpe Ratio

Market portfolio

.23

Portfolio A

.25

If the simple CAPM is valid, state whether the above situation is possible?

Yes

rev: 03_20_2013_QC_28295

Problem 7-17

Consider the following information:

Portfolio

Expected Return

Beta

Risk-

free

7 %

Market

11.0

1.0

10.0

1.8

Calculate the expected return of portfolio A with a beta of 1.8. (Round your answer to 2 decimal places.)

Expected return

12.4%

What is the alpha of portfolio A. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Alpha

.0561

If the simple CAPM is valid, state whether the above situation is possible?

Problem 7-21

A share of stock is now selling for $85. It will pay a dividend of $7 per share at the end of the year. Its beta is 1. What do investors expect the stock to sell for at the end of the year? Assume the risk-free rate is 7% and the expected rate of return on the market is 17%. (Round your answer to 2 decimal places.)

Expected selling price

87.35

Problem 7-28

Assume both portfolios A and B are well diversified, that E(rA) = 12.4% and E(rB) = 13.2%. If the economy has only one factor, and A = 1 while B = 1.1,What must be the risk-free rate? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Risk-free rate

4.4

State of the Economy

Probability

HPR

Boom

0.4

35%

Normal growth

0.5

Recession

0.1

–13

Explanation / Answer

Since, there are multiple questions having multiple parts, the first 2 have been answered.

___________

Problem 5-5

The mean can be calculated with the use of following formula:

Mean = Probability of Boom*HPR under Boom + Probability of Normal*HPR under Normal + Probability of Recession*HPR under Recession

______

Using the values provided in the question, we get,

Mean = .4*35% + .5*18% + .10*-13% = .217

______

To calculate standard deviation, we first need to calculate the variance. The formulas for calculating variance and standard deviation are given below:

Variance = Probability of Boom*(HPR under Boom - Mean Return)^2 + Probability of Normal*(HPR under Normal - Mean Return)^2 + Probability of Recession*(HPR under Recession - Mean Return)^2

Standard Deviation = (Variance)^(1/2)

______

Variance = .4*(.35 - .217)^2 + .5*(.18 - .217)^2 + .10*(-.13 - .217)^2 = .019801

Standard Deviation = (.019801)^(1/2) = 14.07%

_____________

Problem 5-6

The holding period return can be calculated with the use of following formula:

HPR = (Ending Stock Price + Dividend - Stock Sale Price)/Stock Sale Price*100

______

HPR (Boom) = (45 + 1.20 - 35)/35*100 = 32%

HPR (Normal) = (38 + 1.20 - 35)/35*100 = 12%

HPR (Recession) = (26 + .60 - 35)/35*100 = -24%

______

To calculate standard deviation, we need to calculate the mean of holding period returns. Here, the probability of each state of economy is equal (1/3).

The mean can be calculated with the use of following formula:

Mean = Probability of Boom*HPR under Boom + Probability of Normal*HPR under Normal + Probability of Recession*HPR under Recession

______

Using the values provided in the question, we get,

Mean = 1/3*32% + 1/3*12% + 1/3*-24% = .067

______

To calculate standard deviation, we first need to calculate the variance. The formulas for calculating variance and standard deviation are given below:

Variance = Probability of Boom*(HPR under Boom - Mean Return)^2 + Probability of Normal*(HPR under Normal - Mean Return)^2 + Probability of Recession*(HPR under Recession - Mean Return)^2

Standard Deviation = (Variance)^(1/2)

______

Variance = 1/3*(.32 - .067)^2 + 1/3*(.12 - .067)^2 + 1/3*(-.24 - .067)^2 = .053689

Standard Deviation = (.053689)^(1/2) = 23.17%

______

When investment is made 50% in Business Adventures and Treasury Bills.

Expected Return = Investment in Business Adventures*Expected HPR + Investment in Treasury Bills*Expected Return on Treasury Bills = 50%*.067 + 50%*.04 = 5.33%

______

Standard Deviation = .50*Standard Deviation for Business Adventures = .50*23.17% = 11.59%

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