Assume that you have two stocks, Stock X and Stock Y. Additionally, there are 3

Question

Assume that you have two stocks, Stock X and Stock Y. Additionally, there are 3 possible states of the world:

-Boom

-Normal Growth

-Recession

Here are the probabilities of each state and the stocks’ returns in each state:

Calculate the following:

1. The expected return for Stock X and Stock Y.

2. The variance of Stock X and Stock Y.

3. The standard deviation of Stock X and Stock Y.

Lastly, state which stock exhibits less risk and why.

Boom (Probability = 0.2) Normal Growth (Probability = 0.55) Recession (Probability = 0.25) Stock X 0.5 0.15 -0.22 Stock Y -0.05 0.11 0.2

Explanation / Answer

Stock X is riskier as it has higher standard deviation

Stock X Scenario Probability Return =rate of return * probability Actual return -expected return(A) (A)^2* probability Recession 0.25 -0.22 -0.055 -0.3475 0.030189063 Normal 0.55 0.15 0.0825 0.0225 0.000278438 Boom 0.2 0.5 0.1 0.3725 0.02775125 Expected return = sum of weighted return = 12.75% Sum(Variance)= 0.05821875 Standard deviation= Standard deviation of stock X =(sum)^(1/2) 24.13% Stock Y Scenario Probability Return =rate of return * probability Actual return -expected return(B) (B)^2* probability Recession 0.25 0.2 0.05 0.0995 0.002475063 Normal 0.55 0.11 0.0605 0.0095 4.96375E-05 Boom 0.2 -0.05 -0.01 -0.1505 0.00453005 Expected return = sum of weighted return = 10.05% Sum(Variance)= 0.00705475 Standard deviation= Standard deviation of stock Y =(sum)^(1/2) 8.40%

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