Question

You have been given the price at t -0 (Po) and probability distribution for the price at t-1 (Pi) for three stocks Pi Boom (30%) 70 50 Normal (50%) 60 35 50 Recession (20% 50 20 40 Po Stock A Stock B Stock C 30 45 a. What is the expected holding-period return for each stock? b. What is the expected standard deviation for each stock? C. Suppose the risk-free rate of return is 2%. What is the Sharpe ratio for each stock? d. Which stock will vou choose to hold?

Please show all work and equations as needed.

Answer 1

prob	return	prob*return	p*(x - mean)^2
0.3	27.2727%	0.081818182	0.003812231
0.5	9.0909%	0.045454545	0.002386777
0.2	-9.0909%	-0.018181818	0.012591074

Expected return of A = 10.91%

standard dev = 13.7077%

For B:

prob	return	prob*return	p*(x - mean)^2
0.3	66.6667%	0.2	0.093267218
0.5	16.6667%	0.083333333	0.001657484
0.2	-33.3333%	-0.066666667	0.039147842

Expected return = 21.67%

Standard dev = 36.6159%

For c:

prob	return	prob*return	p*(x - mean)^2
0.3	22.2222%	0.066666667	9.25926E-06
0.5	11.1111%	0.055555556	0.005570988
0.2	-11.1111%	-0.022222222	0.021487654

expected return = 10.00%

SD = 16.4523%

Sharpe ratio = (expected return - risk free rate)/SD

choose the one with highest Sharpe ratio