Question

a. Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has just advised her not to invest in stocks of oil refining industry because their prices tend to have much higher volatility relative to other stocks. Is Andrew’s advice sound? Explain.

b. Karen currently has $5 million invested in a long-term bond fund which has an expected return of 7% and a standard deviation of 18%. Her son, Michael, recommends her to consider changing to invest 30% of the $5 million in an equity fund and the remainder in the bond fund. The equity fund has an expected return of 16% and a standard deviation of 35%. The correlation between the fund returns is 0.1. Should Karen follow Michael’s recommendation? Explain with calculations.

Answer 1

a. Andrew's advice is not sound because even though volatility of oil refining industry is high , the correlation of stock might be negative with respect to portfolio of stocks . Hence overall standard deviation of portfolio might decrease. If correlation is higher then this advice would be sound. Without knowing the correlation it is difficult to predict whether stocks in refining industry should be added or not.
b. The expected return of Portfolio =Weight of Equity*Return of Equity+Weight of Debt*Return of Debt
=30%*16%+70%*7% =9.7%
Standard Deviation of Portfolio =((Weight of Equity*Standard Deviation of Equity)^2+(Weight of Debt*Standard Deviation of Debt)^2+2*Weight of Equity*Standard Deviation of Equity*Weight of Debt*Standard Deviation of Debt*Correlation)^0.5
=((30%*35%)^2+(70%*18%)^2+2*30%*70%*35%*18%*0.1)^0.5=17.19%
The Coefficient of Variation of Bond =Standard Deviation/Expected Return =18%/7% =2.57
The Coefficient of Variation of Equity =Standard Deviation/Expected Return =35%/16% =2.19
The Coefficient of Variation of Portfolio=Standard Deviation/Expected Return =17.19%/9.7% =1.77
Since the Coefficient of Variation of Portfolio is lowest Portfolio should be accepted.