Question

Assume perfect capital markets. The table below gives the probability distributions of a share of the Omega corporation and the broad stock market.

State	S1	S2	S3
Probability	25%	50%	25%
Omega	-4%	1%	10%
Market	-3%	2%	5%

1. What is the expected return on the Omega share and on the Broad stock Market?
2. What is the risk (standard deviation) of the Omega share and the risk (standard deviation) of the Market?
3. What is the market beta of the Omega share?

Answer 1

Expected return on Omega Share is 0.25(-4%)+0.5(1%)+0.25(10%) = 2%

Expected return on broad stock market is 0.25(-3%)+0.5(2%)+0.25(5%) = 1.5%

Risk of Omega share is the square root of summation of {(x-mean)^2*p(x)}. So, it gives sqrt{(-4%-2%)^2*0.25+(1%-2%)^2*0.5+(10%-2%)^2*0.25} = sqrt(0.00255) = 5.05%

Risk of broad stock market is the square root of summation of {(x-mean)^2*p(x)}. So, it gives {(-3%-1.5%)^2*0.25+(2%-1.5%)^2*0.5+(5%-1.5%)^2*0.25} = sqrt(0.000825) = 2.87%

To calculate market beta, we can use the formula, Beta=Covariance/Variance of the market. Calculating Covariance, summation of (Return1-average return1)*(Return2-average return2)/n-1. which gives 0.000519. So, Beta=0.000519/2.87%^2 which is 0.6287.