Question

26-) Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%,respectively. The beta of A is .8 while that of B is 1.5. The T-Bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%.
a-) If you currently hold a market -index portfolio, would you choose to add either of these portfolios to your holdings? Explain.
b-) If instead you could invest only in bills and one of these portfolios, which would you choose?

Answer 1

a) For a diversified portfolio, relevant risk is beta.

Treynor Ratio = (Rp - Rf) / beta

For A, Treynor = (11% - 6%) / 0.8 = 6.25% and for B, Treynor = (14% - 6%) / 1.5 = 5.33%

Treynor highlights the excess return per unit of market risk. As Portfolio A has higher Treynor ratio, it offers higher risk-reward option for a diversified portfolio.

b) For a single position, Standard Deviation is more important risk measure.

Sharpe Ratio = (Rp - Rf) / SDp

For A, Sharpe Ratio = (11% - 6%) / 10% = 0.5, For B, Sharpe Ratio = (14% - 6%) / 31% = 0.26

Sharpe Ratio highlights the excess returns per unit of total risk. Portfolio A has higher Sharpe Ratio and hence, you should choose that over B.