Your client's current portfolio is fully invested in a country index fund C with an expected return of rc=5% and a volatility of σc=15%. The (global) market portfolio has an expected return of 8% and a variance of 0.04. The beta of the country index fund C is βc=0.5. The risk-free rate is 2%.


In parts (a) and (b) below, assume that the CAPM holds and that the (global) market portfolio is the tangent portfolio.

a.   What is the Sharpe ratio of your client's current portfolio?

b.  You advise your client to instead invest in an efficient portfolio. If your client keeps the volatility of the portfolio the same as in the current portfolio (i.e., country index fund C), what should the portfolio weights in the efficient portfolio be, and what are the expected return and Sharpe ratio of this efficient portfolio?

c.   You discover that the country index fund C has a positive alpha of αc=1% and so its expected return is rc=6%, not 5% as stated above. Its volatility and beta are unchanged. You recommend that your client invest in a portfolio P consisting of a weight of 60% on the market portfolio and a weight of 40% on country index fund C.

 What is the expected return, volatility, and Sharpe ratio of portfolio P?

 Hint: To compute the volatility, you need to determine the covariance between the country index fund C and the market from the information above.

Suppose the client invests in portfolio N, which combines portfolio P and the risk-free asset. What expected return can the client achieve if they choose the weights so that portfolio N has a volatility of 15%?

Answer rating: 100% (QA)

a The Sharpe ratio of the clients current portfolio can be calculated as the excess return of the portfolio over the riskfree rate 5 2 3 divided by th... View the full answer