The Sharpe Ratio of the market portfolio is . . The standard deviation of the market portfolio return is %. The risk-free rate is = %. Suppose there is a stock S with standard deviation = % and zero correlation with the market portfolio. Consider a portfolio with weight invested in the market portfolio and weight in the stock.

a) What is the of portfolio when = %?

b) What is the expected return of market portfolio, the stock and the portfolio when = %?

c) What is the standard deviation of the return of portfolio when = %?

d) It is March 2020, and the stock market just dropped by 30%. A friend of yours call you in distress saying he just lost 60% of his investment in that stock market crash. You know his portfolio was a mix of the market portfolio and the risk-free asset. What can you infer about the size of your friends investment in the stock market (i.e., the weight he put on the market portfolio)? Assume the risk-free rate remains % at the time of the stock market crash.