Question

Stocks A and B have the following probability distributions of expected future returns:

Probability	A		B
0.1	(13	%)	(21	%)
0.2	6		0
0.5	16		20
0.1	20		29
0.1	40		45

1. Calculate the expected rate of return, , for Stock B ( = 13.90%.) Do not round intermediate calculations. Round your answer to two decimal places.

     %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 17.22%.) Do not round intermediate calculations. Round your answer to two decimal places.

     %

   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?

   1. If Stock B is more 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.
   2. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. 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.
   4. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   5. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.

   -Select which one is correct.

3. Assume the risk-free rate is 1.5%. 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?

   1. In a stand-alone risk sense A is less risky than B. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. 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.
   3. 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 higher beta than Stock A, and hence be more risky in a portfolio sense.
   4. In a stand-alone risk sense A is more 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.
   5. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.

   -Select which one is correct.

Answer 1

Answer:

Part a. and Part b.
Probability	A	B	PirAi	PirBi	Std.DivA	Std.Div.B
0.1	-13%	-21%	-1.30%	-2.10%	0.72%	1.32%
0.2	6%	0	1.20%	0.00%	0.12%	0.47%
0.5	16%	20%	8.00%	10.00%	0.02%	0.11%
0.1	20%	29%	2.00%	2.90%	0.04%	0.19%
0.1	40%	45%	4.00%	4.50%	0.68%	0.88%
			13.90%	15.30%	12.61%	17.22%
Coefficient of variation for stock B =		1.13
				0.91
In multiple choice questions, the correct answer is IV
If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
Part c.
Sharpe Ratio = (Expected return - Risk free rate) / Standard deviation
Stock A	0.9837
Stock B	0.8013
In multiple choice questions, the correct answer is III
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 higher beta than Stock A, and hence be more risky in a portfolio sense.

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