Stocks A and B have the following probability distributions of expected future returns:
Probability | A | B | ||
0.1 | (7 | %) | (29 | %) |
0.1 | 6 | 0 | ||
0.5 | 16 | 22 | ||
0.2 | 24 | 30 | ||
0.1 | 31 | 42 |
%
%
Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.
Is it possible that most investors might regard Stock B as being less risky than Stock A?
-Select-IIIIIIIVVItem 4
Assume the risk-free rate is 4.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to four decimal places.
Stock A:
Stock B:
Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?
-Select-IIIIIIIVVItem 7
1.
=0.1*(-29%)+0.1*0%+0.5*22%+0.2*30%+0.1*42%
=18.3000%
2.
=sqrt(0.1*(-7%-15.80%)^2+0.1*(6%-15.80%)^2+0.5*(16%-15.80%)^2+0.2*(24%-15.80%)^2+0.1*(31%-15.80%)^2)
=9.9076%
3.
=18.64%/18.3000%
=1.018579235
4.
If Stock B is less highly correlated with the market than A, then
it might have a lower beta than Stock A, and hence be less risky in
a portfolio sense.
5.
=(15.80%-4.5%)/9.9076%
=1.140538576
6.
=(18.3000%-4.5%)/18.64%
=0.740343348
7.
In a stand-alone risk sense A is less risky than B. If Stock B is
less highly correlated with the market than A, then it might have a
lower beta than Stock A, and hence be less risky in a portfolio
sense.
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