Question

2. You have decided to dissect you grandparent's investment "portfolio” to determine their expected return on the portfolio and the risk associated with their investments. You were under the impression that your grandparents had a wide array of securities that they were investing in, however, you find that they have invested all of their retirement money into two securities. The first security (45 percent of the portfolio) has an expected return of 17.1 percent with a retu standard deviation of 41.2 percent. The other security (55 percent of the portfolio) has an expected return of 15.3 percent with a return standard deviation of 31.5 percent. You have looked at the correlation of returns between the two securities and have found that the correlation coefficient is 0.63. What is the expected return of the portfolio and the risk associated with the investment?

Answer 1

Expected Return of the Portfolio is the weighted average return of individual stocks

Expected Return = W1 X R1 + W2 x R2

Expected Return = .45 X 17.10+ .55 x 15.30

Expected Return = 16.11%

Where,

W1= Weight in Security 1 i.e. 45%

W2= Weight in Security 2 i.e. 55%

R1= Return of Security 1 i.e. 17.10%

R2= Return of Security 2 i.e. 15.30%

Risk associated with the investment is measured by the standard Deviation

StandardDeviation=

(W1 x 01)2 + (W2 x 02)2 + 2 x W1 XW2 X01 X 02 x corr (1,2)

V.45 X 41.20 )2 + (.55 X 31.50)2 + 2 X 45 X.55 X 41.20 x 31.50 X 0.63

Standard Deviation of the Portfolio =32.38%

Where,

W1= Weight in Security 1 i.e. 45%

W2= Weight in Security 2 i.e. 55%

σ1 = Standard Deviation of Security 1 i.e. 41.20%

σ2 = Standard Deviation of Security 2 i.e. 31.50%

Corr(1,2) = Correlation Coefficient between Security 1 and Security 2 i.e. 0.63