Question

1. The market and Stock A have the following probability distributions: Return on Return on Probability market Stock A 0.2 18% 16% 0.3 12% 14% 1 0 .5 10% 11% a. Calculate the expected rates of return for the market and Stock A. b. Calculate the coefficient of variation for the market and Stock A (Standard deviation for market is 3.0265% and standard deviation for Stock A is 2.0224%).

Answer 1

Probability	Return on market	Return on A
0.2	18%	16%
0.3	12%	14%
0.5	10%	11%

Part a

Expected return is calculated using the formula:

E[R] = p₁*R₁ + p₂*R₂ + p₃*R₃

Expected return of market = E[R_M] = 0.2*18% + 0.3*12% + 0.5*10% = 12.2%

Expected return on stock A = E[R_A] = 0.2*16% + 0.3*14% + 0.5*11% = 12.9%

Part b

Coefficient of variation = CV = Standard deviation/Expected return

CV for market

Standard deviation of market = σ_M = 3.0265%, Expected rteun of market = E[R_M] = 12.2%

Coefficient of variation for market = CV_M = σ_M/E[R_M] = 3.0265%/12.2% = 0.248073770491803

CV for stock A

Standard deviation of Stock A = σ_A = 2.0224%, Expected rteun of stock A = E[R_A] = 12.9%

Coefficient of variation for stock A = CV_A = σ_A/E[R_A] = 2.0224%/12.9% = 0.15677519379845