We are trying to get a sense of how an investor you are advising is trading off risk and return. After several long discussions you come to the conclusion that his level of risk aversion is somewhere between A=3 or 4. A) Draw the indifference curve in risk-return space corresponding to a utility level of 0.05 for an investor with a risk aversion coefficient A=3. Choose standard deviations ranging from 0 to 0.3 in 0.05 steps B) Now draw the indifference curve corresponding to a utility level of 0.05 for an investor with risk aversion coefficient A=4. C) Comparing your answers to part a and b. what do you conclude about the two indifference curves? Particularly, comment on the slope and how this reflects the differences in risk aversion.
You convince your client to think more about how to mix different assets. You first focus on splitting the investment between a broad based index of the US stock market (M) and T-bills. Your analysis tells you that E(rm)=9%, σm=18% . T-bills offer a 2% risk-free rate of return. A) You first take a close look at the investment choices. What is the Sharpe ratio of the market? B)If your investor wanted to achieve an expected return of 8% by mixing by T-bills and the market portfolio M, what fraction y of funds would she invest in the risky asset? C) If your client has risk aversion A=3, what is her optimal investment weight y in the risky asset? What does your client have to do in order to achieve this optional mix of the two assets? D) Due to recent market turmoil following the failure of the US bailout, you update your estimate of future volatility over the next year to σm=24%. What is the new optimal investment weight y?