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
18
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
38
Recession
.60
26
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
Rate of Return
Severe recession
0.05
43%
12%
Mild recession
0.25
17%
12%
Normal growth
0.40
14%
9%
Boom
0.30
31%
4%
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
Rate of Return
Severe recession
0.15
34%
10%
Mild recession
0.20
18%
6%
Normal growth
0.35
14%
7%
Boom
0.30
24%
3%
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
1
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%
0%
Market
13.0
35
A
11.0
24
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 %
0
Market
11.0
1.0
A
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?
No
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
18
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%