Question

A stock's returns have the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring	Rate of Return If This Demand Occurs
Weak	0.1	(32%)
Below average	0.3	(14)
Average	0.4	11
Above average	0.1	36
Strong	0.1	55
	1.0

Assume the risk-free rate is 2%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.

Stock's expected return:   %

Standard deviation:   %

Coefficient of variation:  

Sharpe ratio:  

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

Probability	A	B
0.3	(12%)	(23%)
0.1	5	0
0.2	11	24
0.2	20	26
0.2	38	41

1. Calculate the expected rate of return, , for Stock B ( = 10.70%.) 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 = 24.85%.) Do not round intermediate calculations. Round your answer to two decimal places.
     %

   Now calculate the coefficient of variation for Stock B. 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-IIIIIIIVVItem 4

3. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two 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-IIIIIIIVVItem 7

Answer 1

1. Stock's Expected Return =0.1*-32%+0.3*-14%+0.4*11%+0.1*36%+0.1*55% =6.1%
Standard Deviation =(0.1*(-32%-6.1%)^2+0.3*(-14%-6.1%)^2+0.4*(11%-6.1%)^2+0.1*(36%-6.1%)^2+0.1*(55%-6.1%)^2)^0.5
=24.5864% or 24.59%
Coefficient of Variation =Standard Deviation/Expected return =24.5864%/6.1% =4.031 or 4.03
Sharpe Ratio =(Expected Return -Risk Free Rate)/Standard Deviation=(6.1%-2%)/24.5864% =0.167 or 0.17


2.

a. Expected Return of Stock B =0.3*-23%+0.1*0%+0.2*24%+0.2*26%+0.2*41% =11.30%

b. Standard Deviation of Stock A =(0.3*(-12%-10.70%)^2+0.1*(5%-10.70%)^2+0.2*(11%-10.70%)^2+0.2*(20%-10.70%)+0.2*(38%-10.70%)^2)^0.5 =22.20%

Coefficient of Variation of B =Standard Deviation/Expected return =24.85%/11.30% =2.20

Option III is correct option. 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.

d. Sharpe Ratio of A =(Expected Return of A-Risk Free Rate)/Standard Deviation =(11.30%-2.5%)/22.20% =0.40
Sharpe Ratio of B =(Expected Return of A-Risk Free Rate)/Standard Deviation =(10.70%-2.5%)/24.85% =0.33

e. Option II is correct option 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.