Question
Consider the following information.
State of the economy | Returns asset: A B C D E
Excellent | 12% 8% ‐4% 20% 4%
Normal | 10% 7% 5% 14% 4%
Recession | 2% 6% 9% 0% 4%
It is equally likely that economy will be in an excellent state or in a recession. However, it is three times more likely that the economy will be in a normal state than that it will be in the excellent state.
a) Jim has saved up $2000 which he would like to invest in a portfolio of the five assets. He invests $1000 in the risk free asset, and $250 in each of the four risky assets. Calculate the Sharpe ratio of his total portfolio.
b) Alternatively, Jim borrows $1000 at the risk free rate and invests that plus his total savings in an equally weighted portfolio of assets A, B, C and D. What ishis Sharpe rationow?
c) Suppose there is another asset F, which has a perfect negative correlation with asset Aand a standard deviation of 15%. Suppose Jim invests his savings of $2000 in a portfolioof asset A and F. How many dollars should he invest in asset F such that his portfolio isrisk free?
