Question

1. You place $75,000 in Stock A and $25,000 in Stock B and hold the portfolio for one year. Stock A's return is 12% and Stock B's return is 8%. What is the expected return on your portfolio?

2. Consider the following information about three stocks (A, B, and C): all have the same return variance; correlation (A,B) = .65; correlation (A,C) = -.10; correlation (B,C) = 0. Which of the following portfolios will have the lowest return variance:
   1. half in A and half in B
   2. half in A and half in C
   3. half in B and half in C?

3. Stock A has expected return of .11 and return variance of .02. Stock B has expected return of .10 and return variance of .03. The return correlation between Stock A and B is .15.
   1. Find the expected return of a portfolio consisting of $20,000 in Stock A and $60,000 in Stock B.
4. 2. Find the return standard deviation for the portfolio described in part a.

Answer 1

1) Weight of Stock A = $75000 / ($75,000 + $25,000) = 0.75, Weight of Stock B = 0.25

Expected return = return of Stock A x Weight of stock A + return of Stock B x weight of stock B = 12% x 0.75 + 8% x 0.25 = 11%

If the individual stock return variances are the same, then that combination will have the lowest portfolio variance which has the lowest correlation, i.e., A and C (-.10). So, half in stock A and stock B.

2) a) Weight of Stock A = $20,000 / ($20,000 + $60,000) = 0.25, Weight of Stock B = 0.75

Expected return of portfolio = 0.25 x 0.11 + 0.75 x 0.10 = 0.1025 or 10.25%

b) Portfolio variance = (Variance of Stock A x Weight of stock A)2 + (Variance of Stock B x Weight of stock B)2 + 2 x Variance of Stock A x Weight of stock A x Variance of Stock A x Weight of stock A x r = (0.02 x 0.25)2 + (0.03 x 0.75)2 + 2 x 0.02 x 0.25 x 0.03 x 0.75 x .15 = 0.000565 or 5.65%2

Portfolio standard deviation = (variance)2 = (0.000565)2 = 0.02377 or 2.38%