You convince your client to think more about how to mix different assets. You fi
ID: 2778496 • Letter: Y
Question
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%, m=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 m=24%. What is the new optimal investment weight y?
Explanation / Answer
A) Sharp Ratio = (Mean portfolio return - Risk free rate) / Standard deviation of portfolio return
= (9% - 2%) / 18%
= (0.09 - 0.02) / 0.18
= 0.39
B) Mean return on portfolio = Rf + (Rp - Rf)y
9% = 2% + (8% - 2%)y
6% y = 9% - 2%
6% y = 7%
y = 0.07 / 0.06 = 1.17
C) y* = (Rp - Rf) / 0.01A2
= (9% - 2%) / (0.01 * 3 * 18%2)
= 0.07 / 0.000972
= 72.02
Therefore, If client has risk aversion A=3, optimal investment weight y in the risky asset will be 72.02% and in the T-bill will be (100% - 72.02% = 27.98%).
D) Portfolio standard deviation = y * 18%. If you update your estimate of future volatility over the next year to m = 24%, then
y = 24% / 18% = 133% is the new optimal investment weight y.
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