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Question 5 : Your client has $10,000,000 of cash available for investment. The expected return on your equity market fund is 25% per year with a standard deviation of 50%, that on your risky long-term corporate bond fund is 15% per year with a standard deviation of 20%, and you estimate the unconditional correlation between the annual returns of these two risky funds at 0.30. The annual rate of return on risk-free government bills 10%. 1: Determine the expected return and standard deviation of the portfolio with (a) the minimum possible variance and (b) the best risk-return trade-off that can be formed out of the two risky funds and compare the reward-to-risk (or Sharpe) ratios of these portfolios to those of its constituents, i.e., equity and bond funds. 2: Determine your clients optimal capital allocation between the risk-free government bills and the optimal risky portfolio constructed above if her utility function is quadratic with a risk aversion coefficient of A = 5 and compute the expected return and standard deviation of the resulting optimal complete portfolio. 3: Suppose your client desires to keep the standard deviation of her complete portfolio at a maximum level of 20%. Determine the portfolio with the maximum rate of return that would be able to satisfy this constraint. 4: Determine the range of risk aversion coefficients between which an investor would optimally invest all wealth in the optimal risky portfolio and nothing in risk-free government bills if the annualized rate of return on risk-free government bills is 9% in case the client is lending and 12% in case the client is borrowing. 5: Suppose you convince your client to include a commodity fund among her set of feasible investments. The commodity fund your company runs has an expected return of 9% per year, an annual standard deviation of 16%, and a return correlation of -0.30 with the equity fund and -0.10 with the bond fund. Compute the optimal weights assigned to each fund and determine the risk and return parameters of the resulting portfolio