Question

7.6

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

Probability	A		B
0.1	(11	%)	(27	%)
0.2	2		0
0.4	13		18
0.2	23		30
0.1	32		36

1. Calculate the expected rate of return, , for Stock B ( = 12.30%.) 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 = 17.70%.) 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 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

   -Select-IIIIIIIVVItem 4

3. Assume the risk-free rate is 3.5%. 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 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

   -Select-IIIIIIIVVItem 7

Answer 1

a) Expected Rate of Return for Stock A= Ri * Pi

= 0.1*(-11%)+ 0.2*2% + 0.4*13% + 0.2*23% + 0.1*32% = 0.123 or 12.3 %

Expected Rate of Return for Stock B= Ri * Pi

= 0.1*(-27%)+ 0.2*0% + 0.4*18% + 0.2*30% + 0.1*36% = 0.141 or 14.1 %

b)

Pi	R %	( R - E[R] )	[ (R - E[R] ) 2 ] * pi
0.1	- 11	( -11 -12.3 ) = - 23.3	54.289
0.2	2	(2 - 12.3) = - 10.3	21.218
0.4	13	(13 - 12.3) = 0.7	0.196
0.2	23	(23 - 12.3) = 10.7	22.89
0.1	32	(32 - 12.3 ) = 19.7	38.80

Total (R - E[R] ) ^{2 =} 1152.05

Standard Deviation=

= 11.72 %

the coefficient of variation for Stock B= Standard Deviation/Expected return = ( 17.70 /14.1 ) * 100

= 1.25

option III

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.

c)   Sharpe ratio Formula =

Sharpe Ratio for Stock A =

= 0.75

Sharpe Ratio for Stock B =

= 0.59

option II

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.