Question

Q1) There is a 23.70% probability of a below average economy and a 76.30% probability of an average economy. If there is a below average economy stocks A and B will have returns of -8.00% and 4.90%, respectively. If there is an average economy stocks A and B will have returns of 13.60% and -4.10%, respectively. Compute the standard deviation for stock a and b.

Answer 1

Expected return = sum of probability * return

standard deviation = [ sum of probability * ( return - expected return )^2 ] ^0.5

Calculation of mean & variance for A
Economy	Return (x)	Probability (P)	Px	x - mean	(x - mean)^2	P(x - mean)^2
Below Average	-8	0.237	-1.896	-16.4808	272	64.37
Average	13.6	0.763	10.377	5.1192	26	20.00
		Mean	8.481		Variance	84.36851136

Standard deviation = 84.37^0.5 = 9.19%

Calculation of mean & variance for B
Economy	Return (x)	Probability (P)	Px	x - mean	(x - mean)^2	P(x - mean)^2
Below Average	4.9	0.237	1.161	6.867	47	11.18
Average	-4.1	0.763	-3.128	-2.133	5	3.47
		Mean	-1.97		Variance	14.647311

Standard deviation = 14.65^0.5 = 3.83%