Question

1. 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.

2. 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

1. Volatility increases the risk of the portfolio. Risk is the movement of prices away from the mean. If the movement from mean price of the shares is too much, that means the shares can move upwards or downwards steeply. As there is more volatility, there is more movement, hence there is more risk. Hence Andrew has made a sound statement

2. Here the recommendation is to diversify the portfolio such that the overall risk reduces giving the same or more than the present return.It is recommended to invest 1.5 m in Equity and 3.5m in bond.

Present Return is 7%

Expected Return on new portfolio= (1.5*7% + 3.5* 16%)/ 5 = 0.67/ 5 = 13.30%

Expected Risk of the portfolio can be found using Standard Deviation

i.e SD of portfolio = Square Root of (Weight A^2 * SD a ^2 + Weight b^2 * SD b ^2 + 2 * Wt A * Wt b * SD a * SD b * Correration)

= Square Root of (0.3^2 * 0.35^2 + 0.7^2 * 0.18^2 + 2 * 0.30 * 0.70 * 0.35 * 0.18 * 0.1)

= Square Root ( 0.011025+ 0.015876+ 0.0026)

= 0.1718

= 17.18%

Hence we observe that total return has increased from 7% to 13.30% and risk has fallen to 17.18% from 18%.