Your client's current portfolio is fully invested in a country index fund C which has an expected return of r_C=8% and a volatility of _C=15%. The (global) market portfolio has an expected return of 12% and a variance of 0.04. The covariance of the country index fund C and the (global) market portfolio is _Cm=0.02. The risk-free rate is 4%.

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

(3 points) What is the Sharpe ratio of your client's current portfolio (i.e., country index fund C)?

(7 points) You advise your client to invest in an efficient portfolio instead. 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?

(2 points) Compute the beta of the country index fund C.

You discover that country index fund C has an expected return r_C=10%, not 8% as stated above, but that its volatility and covariance with the market are unchanged. (Note that this would mean that the country index fund C has a positive alpha of _C=2%.) Use this information to answer parts (d) and (e).

(5 points) Consider a portfolio P consisting of a weight of 60% on the (global) market portfolio and a weight of 40% on the country index fund C. What is the expected return, volatility, and Sharpe ratio of portfolio P?

(3 points) Suppose the client invests in a new 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%?