Assume that the risk-free rate is 5% and that the market risk premium is 5%. Wha
ID: 2625433 • Letter: A
Question
Assume that the risk-free rate is 5% and that the market risk premium is 5%.
What is the required rate of return on a stock with a beta of 0.8? Round your answer to two decimal places.
%
What is the required rate of return on a stock with a beta of 1.1? Round your answer to two decimal places.
%
What is the required return on the market? Round your answer to two decimal places.
%
2. A stock's return has the following distribution:
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return if This
Demand Occurs (%)
Weak
0.1
-50%
Below average
0.2
-6
Average
0.4
9
Above average
0.2
30
Strong
0.1
75
1.0
Calculate the stock's expected return. Round your answer to two decimal places.
%
Calculate the standard deviation. Round your answer to two decimal places.
%
3. The market and Stock J have the following probability distributions:
Probability rM rJ
0.3 14% 21%
0.4 8 7
0.3 17 11
Calculate the expected rate of return for the market. Round your answer to two decimal places.
%
Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
%
Calculate the standard deviation for the market. Round your answer to two decimal places.
%
4. Suppose rRF = 6%, rM = 8%, and rA = 13%.
Calculate Stock A's beta. Round your answer to two decimal places.
---------
If Stock A's beta were 1.0, then what would be A's new required rate of return? Round your answer to two decimal places.
%
5. Suppose you manage a $4.975 million fund that consists of four stocks with the following investments:
Stock
Investment
Beta
A
$500,000
1.50
B
425,000
-0.50
C
1,100,000
1.25
D
2,950,000
0.75
If the market's required rate of return is 8% and the risk-free rate is 3%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.
%
6. Stock R has a beta of 2.4, Stock S has a beta of 0.45, the expected rate of return on an average stock is 10%, and the risk-free rate is 7%. By how much does the required return on the riskier stock exceed the required return on the riskier stock exceed that on the less risky stock? Round your answer to two decimal places.
%
Calculate the standard deviation for Stock J. Round your answer to two decimal places.
%
Demand for the
Company's Products
Probability of This
Demand Occurring
Rate of Return if This
Demand Occurs (%)
Weak
0.1
-50%
Below average
0.2
-6
Average
0.4
9
Above average
0.2
30
Strong
0.1
75
1.0
Explanation / Answer
1. Assume that the risk-free rate is 5% and that the market risk premium is 5%.
What is the required rate of return on a stock with a beta of 0.8? Round your answer to two decimal places.
the required rate of return on a stock = 5%+ 0.8*5%= 9.00%
What is the required rate of return on a stock with a beta of 1.1? Round your answer to two decimal places.
the required rate of return on a stock = 5%+ 1.1*5%= 10.50%
What is the required return on the market? Round your answer to two decimal places.
the required return on the market = 5%+5%= 10.00%
2. A stock's return has the following distribution:
Calculate the stock's expected return. Round your answer to two decimal places.
stock's expected return= 0.1*(-50%) + 0.2*(-6%) + 0.4*9% + 0.2*30%+ 0.1*75%= 10.90%
Calculate the standard deviation. Round your answer to two decimal places.
standard deviation = sqrt(0.1*(-50%-10.90%)^2 + 0.2*(-6%-10.90%)^2 + 0.4*(9%-10.90%)^2 + 0.2*(30%-10.90%)^2+ 0.1*(75%-10.90%)^2)= 30.22%
3. The market and Stock J have the following probability distributions:
Probability rM rJ
0.3 14% 21%
0.4 8 7
0.3 17 11
Calculate the expected rate of return for the market. Round your answer to two decimal places.
the expected rate of return for the market= 0.3*14% + 0.4*8% + 0.3*17%= 12.50%
Calculate the expected rate of return for Stock J. Round your answer to two decimal places.
the expected rate of return for Stock J = 0.3*21% + 0.4*7% + 0.3*11%= 12.40%
Calculate the standard deviation for the market. Round your answer to two decimal places.
standard deviation for the market = sqrt(0.3*(14%-12.50%)^2 + 0.4*(8%-12.50%)^2 + 0.3*(17%-12.50%)^2)= 3.85%
4. Suppose rRF = 6%, rM = 8%, and rA = 13%.
Calculate Stock A's beta. Round your answer to two decimal places.
Stock A's beta = (13%-6%)/(8%-6%)= 3.50
If Stock A's beta were 1.0, then what would be A's new required rate of return? Round your answer to two decimal places.
A's new required rate of return = 6%+ 1*(8%-6%) = 8.00%
5. If the market's required rate of return is 8% and the risk-free rate is 3%, what is the fund's required rate of return? Do not round intermediate calculations. Round your answer to two decimal places.
fund's beta = (500000*1.5 + 425000*(-0.5) + 1100000*1.25 + 2950000*0.75)/( 500000 + 425000+ 1100000+ 2950000)=0.83
fund's required rate of return = 3%+0.83*(8%-3%)= 7.15%
6. Stock R has a beta of 2.4, Stock S has a beta of 0.45, the expected rate of return on an average stock is 10%, and the risk-free rate is 7%. By how much does the required return on the riskier stock exceed the required return on the riskier stock exceed that on the less risky stock? Round your answer to two decimal places.
required return of R = 7%+2.4*(10%-7%)= 14.20%
required return of S = 7%+0.45*(10%-7%)= 8.35%
Difference = 14.20%-8.35%=5.85%
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