Stocks A and B have the following probability distributions of expected future returns:
Probability | A | B | ||
0.1 | (10 | %) | (35 | %) |
0.1 | 3 | 0 | ||
0.5 | 12 | 23 | ||
0.2 | 20 | 25 | ||
0.1 | 30 | 36 |
%
%
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?
Expected returns=Sum(probability*returns)
Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))
Coefficient of variation=Standard deviation/Expected returns
Sharpe Ratio=(Expected returns-risk free rate)/Standard deviation
1.
=0.1*(-35%)+0.1*0%+0.5*23%+0.2*25%+0.1*36%
=16.60%
2.
=sqrt(0.1*(-10%-12.30%)^2+0.1*(3%-12.30%)^2+0.5*(12%-12.30%)^2+0.2*(20%-12.30%)^2+0.1*(30%-12.30%)^2)
=10.08%
3.
=19.13%/16.60%
=1.15241
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.
=(12.30%-4.5%)/10.08%
=0.77381
6.
=(16.60%-4.5%)/19.13%
=0.63251
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.
Stocks A and B have the following probability distributions of expected future returns: Probability A B...
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