Question

Consider the following scenario seen in class Expected Return 8% Standard Dev. Debt Fund 12% Equity Fund Risk-Free 13% 20% 5% Correlation 0.1 Risk Aversion (A) 2 Omega D 0 % MV Utility Omega E Standard Deviation Sharpe Ratio Expected Return 100% 13.00% 20.00% 0.400 9.00% 5% 95% 12.75% 19.07% 0.406 9.11% 10% 90% 12.50% 18.16% 0.413 9.20% 12.25% 17.27 % 15% 85% 0.420 9.27% 80% 16,41% 0.426 9.31% 20% 12.00% 25% 75% 11.75% 15.59% 0.433 9.32% 30% 70% 11.50% 14.80% 0.439 9.31% 35% 65% 11.25% 14.06% 0.445 9.27% 11.00% 0.449 40% 60% 13.36% 9.21% 45% 55% 10.75% 12.73% 0.452 9.13% 50% 50% 10.50% 12.17% 0.452 9.02% 55% 45% 10.25% 11.68% 0.449 8.89% 60% 40% 10.00% 11.29% 0.443 8.73% 65% 35% 9.75% 10.99% 10.80% 0.432 8.54% 30 % 70% 9.50% 0.417 8.33% 75% 25% 9.25% 10.72% 0.396 8.10% 80% 20% 9.00% 10.76% 0.372 7.84% 85% 15% 8.75% 0.344 7.56% 10.92% 90% 10% 8.50% 11.18% 0.313 7.25% 11.54% 95% 5% 8.25% 0.282 6.92% 100% 0% 8.00% 12.00% 0.250 6.56% Use this information to answer questions 3) and 4) 3) Which combination of the Debt Fund (D) and Equity Fund (E) (among the ones illustrated above) generates the minimum variance portfolio? Justify your answer Which combination of the Debt Fund (D) and Equity Fund (E (among the ones illustrated above) generates the most preferred portfolio? Justify your answer 4) Compute the exact composition of the tangency portfolio and its standard deviation

Answer 1

3)

(A) The minimum variance portfolio is the one where the overall standard deviation is the lowest Note variance = (standard deviation ^2 )

The portfolio with 75% Debt & 25% Equity = Standard Deviation of 10.72

(B) In general, the most preferred portfolio is the one with the maximum sharp ratio. This is becauseSharpe Ratio indicates the risk premium per unit standard deviation  Sharpe Ratio= Risk Premium/ Standard Deviation

Maximum Sharpe Ratio = Most Preferred Portfolio

Now we have two portfolios with a maximum Sharpe ratio of 4.52, hence we take the one with higher MV Utility which indicates the expected returns adjusted to variance (MV Utility = Expected Return (E.r) - Standard Deviation^2 X Constant

MV for the selected most preferred portfolio = 9.13%

The portfolio with 45% Debt & 55% Equity is the most preferred portfolio

4) Tangency Portfolio is the one with Maximum Sharpe Ratio or the most preferred portfolio

Exact Composition 45% Debt & 55% Equity and the 12.73 Standard Deviation