2. Problem /44 points, question parts (a.), b.), etc.) have equal weights /

Mr. Jerome K. Muffins (30 years old, stable employment) plans his investment for retirement. Having observed the rapid growth of Montreal's real estate market, he would like to invest some of his savings into a real estate fund. He is considering investing the rest of his savings into either a corporate bonds fund or an equity fund (due to his personal preferences he prefers to hold no more than two different risky assets in his portfolio). Key properties of the three funds in question, measured over the past 10-year window, are summarized in the two tables below. Risk-free interest rate is 1.5%.

Fund characteristics

Equity Bonds Real Estate

Correlation matrix

Stocks Equity 1

Bonds 0.6 Real Estate 0.3

Expected return 13%

7% 6%

Standard Deviation 18%

9% 7%

Real estate

1

Bonds

1 0.4

a.) Please, advise Mr. Muffins which of the two other funds (Equity vs. Bonds) to choose, and which should be the proportions of the real estate and another fund in his portfolio. What would be the expected return, the standard deviation and the Sharpe ratio of such a portfolio? Please, provide all necessary calculations.

b.) Assume Mr. Muffins has also an opportunity to invest into risk-free T-bills with an expected return of 1.5% besides two risky funds, so that his portfolio can contain T-Bills and two funds (Real estate & Equity or Real estate & Bonds). He estimates his risk aversion coefficient at A=11. How would that new information alter your advice regarding his optimal portfolio? If you would suggest a different portfolio from a.), please report its expected return, standard deviation and Sharpe ratio. Please, provide all necessary calculations.

c.) If Mr. Muffins would like to know whether the optimal portfolio established in a.) outperforms the stock market, what could you tell him, given that: Equity fund market beta is 0.9, Bonds fund market beta is 0.3, Real estate fund market beta is 0.12, and expected stock market return is 11.4%? Please, provide all necessary calculations.

d.) Which considerations are simplified out or left out from the discussion in the problem and parts a.), b.) and c.)?