Question

Consider the following probability distributions for stocks A and B:

State	Probability	Return on A	Return on B
1	.3	7%	-9%
2	.5	11%	14%
3	.2	-16%	26%

A. What is the correlation between stocks A and B? Please give your answer in decimal form rounded to the third decimal place.

B. What is the standard deviation of returns for stock A? Please give your answer in percent rounded to the nearest basis point.

C. What is the standard deviation of stock B? Please give your answer in percent rounded to the nearest basis point.

Answer 1

a) Using correl function in excel for the 2 data sets (return on A, return on B) gives us correlation of -0.667

b) Expected return of A = (30% * 7%) + (50% * 11%) + (20% * -16%) = 4%

Standard deviation of investment = Square root of investment variance

where investment variance = Sum of (Probability of scenario x Square of (Expected return in scenario - Expected return of investment A)) = (30% * Square of (7% - 4%)) + (50% * Square of (11% - 4%)) + (20% * Square of (-16% - 4%))

Hence, standard deviation of stock A = 10.35%

c) Expected return of B = (30% * -9%) + (50% * 14%) + (20% * 26%) = 10%

Standard deviation of investment = Square root of investment variance

where investment variance = Sum of (Probability of scenario x Square of (Expected return in scenario - Expected return of investment B)) = (30% * Square of (-9% - 10%)) + (50% * Square of (14% - 10%)) + (20% * Square of (26% - 10%))

Hence, standard deviation of stock B = 12.93%