Question

You have estimated how Stock A’s return will vary.

Economy                      Probability                         Return

Below average                0.3                                     -6%

Average                           0.4                                      12%

Above average               0.3                                      26%

What is the standard deviation of Stock A?

Stock B has an expected return of 15%, and a standard deviation of 20%. The returns of the two stocks are not perfectly correlated; the correlation coefficient is 0.7. You have put together a portfolio that consists of 50% Stock A and 50% Stock B. What is the expected return of your portfolio and what is the standard deviation of your portfolio?

Answer 1

Computation of Stock A's expected return and standard deviation

Stock A's expected return = Probability rate of return

= [0.3 (-6%)] + [0.4 12%] + [0.3 26%] =  10.8%

Stock A's standard deviation = Probability (Rate of return - exected return)2

= {[-6%-10.8]2(0.3) + [12%-10.8%]2(0.4) +[26% - 10.8%]2(0.3)}

= 12.43

As per information given in question, stock B's expected return is 15% and standard deviation is 20%

correlation coefficient is 0.7

weight of stock A in portfolio is 50% and weight of stock B in portfolio is 50%.

Computation of expected return and standard deviation of portfolio

Expected return of portfolio = [weight of stock A expected return of stock A] + [weight of stock B expected return of stock B]

=[0.5 10.8%] + [0.5 15%] = 12.9%

Standard deviation of portfolio = [(weight of stock A)2(standard deviation of stock A)2]+[(weight of stock B)2(standard deviation of stock B)2] + [2 weight of stock A standard deviation of stock A weight of stock B standard deviation of stoc B correlation coefficient]

={[0.5 12.43]2 + [0.5 20]2 + [2 0.50.512.43200.7]}

=15.02%

Therefore expected return of portfolio is 12.9% and standard deviation is 15.02%