Question

An investor is faced with two risky asset portfolios (each of which is highly diversified within its asset class) an equity fund and a bond fund. The investor is aware that asset returns are not always normally distributed, but is nonetheless prepared to use the normal distribution as a tool for the estimation of approximate portfolio risks and expected returns. The equity fund has a forecast expected return of +11 % pa over the time horizon of 12 months, and the investor is more than 99.7% sure that the range of outcomes will lie between a worst case scenario of about-34%pa and a best case scenario of approximately+56%pa. The bond fund has a forecast expected return over the time horizon of +4% pa, and an interval between worst and best case scenarios of -8%pa to +16%pa. The covariance between the equity fund and the bond fund is believed to be approximately +6. There is a perfectly competitive banking system, where interest rate margins for customers such as this investor have been driven down to zero. The current interest rate on 12 month deposits is 1%pa. 1. Calculate the risk and expected return of portfolios with (i) weights of 25% for the equity fund and 75% for the bond fund and (ii) 75% for the equity fund and 25% for the bond fund. (10%). 2. Graph a minimum variance frontier, based on your answers to parts 1, 4 and 5 above. Provide a clear and concise explanation of what the frontier shows. (10%) 3. Add an approximate capital allocation line (CAL) to your diagram. Provide a clear and concise explanation of what the CAL shows. (10%)

Answer 1

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