Investing in the market portfolio: Your analysis suggest that the risk premium of the market is 6.2% and the standard deviation of stocks is 16.4%. You analyze the risk and return possibilities of a 1-year investment in the stock market and the risk-free asset.

a. Given the historical experience of stocks, what is the slope of the CML (the Sharpe ratio of stocks)?

b. The risk-free rate is 0.9%; this is the intercept of the CML. Using the slope from a., plot the CML in risk return space. What is the expected return of the risky portfolio P? (Hint: To find the expected return, add the current risk-free rate to the historical risk premium above; also note that the standard deviation is given.)

c. Your clients choose to invest 75% of a portfolio in the stock market and 25% in the risk-free asset. Given the risk return tradeoff of the CML, what is the expected return and standard deviation of their portfolio? Indicate the portfolio on the graph of the CML.

d. Now suppose that your clients would like to invest a proportion y of funds in the stock market so that the complete portfolio has a standard deviation of 12%. What is the proportion y and what is the expected return of the portfolio?

e. What is the optimal amount y that they should invest in the risky portfolio? (You are advising clients who have A=3.5.) What is the expected rate of return and standard deviation of the portfolio?