Question

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

Probability	A		B
0.1	(7	%)	(28	%)
0.2	5		0
0.4	15		18
0.2	22		28
0.1	29		46

1. Calculate the expected rate of return, , for Stock B ( = 13.60%.) 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 = 19.06%.) Do not round intermediate calculations. Round your answer to two decimal places.
3. Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.
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.

Answer 1

Answer:

a. the expected rate of return

Probability	A ( % Return )	Expected Return of Stock A	B ( % Return )	Expected Return of Stock B
0.1	(7)	= 0.1 X (7%) = (0.7 %)	(28)	= 0.1 X (28%) = (2.8%)
0.2	5	= 0.2 X 5% = 1%	0	= 0.2 X 0 = 0%
0.4	15	= 0.4 X 15% = 6%	18	= 0.4 X 18% = 7.2%
0.2	22	= 0.2 X 22% = 4.4%	28	= 0.2 X 28% = 5.6%
0.1	29	= 0.1 X 29% = 2.9%	46	= 0.1 X 46% = 4.6%
		13.60%		14.60 %

b. the standard deviation of expected returns :

Probability	A( % ) Return	Variance A - $\bar{A}$	( A - $\bar{A}$ )2	P X ( A - $\bar{A}$ )2	B ( % ) Return	Variance B - $\bar{B}$	( B - $\bar{B}$ )2	P X ( B - $\bar{B}$ )2
0.1	(7)	= (7) - 13.6= - 20.6	424.36	42.44	(28)	=(28 ) -14.6= -42.60	1814.76	181.48
0.2	5	= 5 -13.6 = 8.6	73.96	14.79	0	=0-14.6= -14.6	213.16	42.63
0.4	15	=15-13.6= 1.4	1.96	0.78	18	= 18-14.6= 3.4	11.56	4.624
0.2	22	=22-13.6= 8.4	70.56	14.11	28	= 28-14.6 = 13.4	179.56	35.91
0.1	29	=29-13.6= 15.4	237.16	23.72	46	= 46-14.6 = 31.4	985.96	98.60
	$\sum$		808					363.24

$\sigma A$ = $\sqrt{808}$ = 28.43

$\sigma B$ = = 19.06

V363.24

C. the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.

Coefficient of Variation of Stock B = Standard Deviation of B / Mean of B = 19.06 / 13.60 = 1.40

Here we taken mean value as expected return

d. 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.

Sharpe Ratio = ( Return of Stock - Risk Free Return ) /

o stock

Sharpe Ratio A = ( 13.60 - 4.5 ) % / 28.43 = 0.32

Sharpe Ratio B = ( 14.60 - 4.5 ) % / 19.06 = 0.53