Question

Consider the following information:

            State    Probability      A           B       

             Boom 0.6                    20%     -5%        

            Bust     0.4                    -10% 10%

1. What are the expected return and standard deviation of stock A and stock B?

2. If you invest 50% of your money in stock A and 50% of your money in stock B, what are the expected return and standard deviation for the portfolio as a whole (considering both states of the economy)?

3. Use the results of a-c to explain the benefit of diversification.

Answer 1

a)

Expected return =

P = probability

R = rate of return

Standard deviation =

X = return with respect probability

X' = expected return

So,

Expected return of A = 8%

B = 1%

Standard deviation of A = 14.70%

Standard deviation of B = 7.35%

b)

here first we have to calculate correlation between both stocks

correlation = covariance (A,B) / (Standard deviation A *Standard deviation B)

Covariance = P*(A-A')*(B-B')

when correlation = -1

Expected return of portfolio =

W = weights of each stock

R = expected return

Expected return of portfolio = (0.5*8%) + (0.5 * 1%) = 4.5%

when correlation = -1

Standard deviation of portfolio = Wa * Standard deviation of A - Wb * Standard deviation of B

= (0.5*14.70%) - (0.5*7.35%)

= 3.67%

c)

If we observe that return of A is higher than Return of B at the same time risk (Standard deviation) of Stock A also higher than risk of Stock B.by diversifying we get a average return for a reduced risk.i.e., standard deviation of combining both stocks is less than standard deviation of both individual stocks resulting in reducing the risk.

Formulas will be as follows: