Question

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

Probability	A		B
0.1	(5	%)	(37	%)
0.1	3		0
0.6	14		21
0.1	20		29
0.1	31		45

1. Calculate the expected rate of return, , for Stock B ( = 13.30%.) 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 = 20.55%.) 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.

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:

Answer 1

a & b]	STOCK A:
	Probability [p]	Rate of return [%]   [r]	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	0.10	-5	-0.50	-18.30	334.89	33.49
	0.10	3	0.30	-10.30	106.09	10.61
	0.60	14	8.40	0.70	0.49	0.29
	0.10	20	2.00	6.70	44.89	4.49
	0.10	31	3.10	17.70	313.29	31.33
			13.30			80.21
	Expected return			13.30
	Variance			80.21
	SD = 80.21^0.5 =			8.96
	Coefficient of variation = 8.96/13.3 =		0.67
	STOCK B:
	Probability [p]	Rate of return [%]   [r]	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	0.10	-37	-3.70	-53.30	2840.89	284.09
	0.10	0	0.00	-16.30	265.69	26.57
	0.60	21	12.60	4.70	22.09	13.25
	0.10	29	2.90	12.70	161.29	16.13
	0.10	45	4.50	28.70	823.69	82.37
			16.30			422.41
	Expected return			16.30
	Variance			422.41
	SD = 422.41^0.5 =			20.55
	Coefficient of variation = 20.55/16.3 =		1.26
c]	Sharpe ratio = [Expected return-Risk free rate]/Standard deviation
	Stock A = (13.3-3.5)/8.96 =		1.09
	Stock B = (16.3-3.5)/20.55 =		0.62