Asset r^{e 2}

Equities .12 .0400 .20

Debt .08 .0144 .12

T-bills r_f = .045

_E,D = .4

The weights of the risky assets in the optimal risky portfolio, P* are:

w_E* = .5225

w_D* = .4775

and the expected return/risk characteristics of the optimal risky portfolio:

r^e_P* = .1009

_P* = .1378

The weights of T-bills and the optimal risky portfolio in the optimal complete portfolio, C* for an investor with A=4 are:

y* = .7358

(1-y*) = .2642

and the expected return/risk characteristics of the optimal complete portfolio:

r^e_C* = .0861

_C* = .1014

a. Consider another investor who is more risk averse. This investors coefficient of risk aversion is A=7 and he has $2,000,000 to invest. How do the asset proportions in this investors optional risky portfolio differ from the investor with A=4? How does the complete portfolio allocation differ? How should the investor allocate his $2,000,000 (round to nearest $100)? What are the expected return/risk (standard deviation) characteristics of his optimal complete portfolio? Graph your results, showing the portfolio opportunity set, the capital allocation line and the indifference curve. Your friend, who has not taken Financial Economics but likes to give investment advice, believes that you are making a mistake in allocating the portfolio for the investor with A=7. He believes that T-bills should not be considered in the allocation decision and you should only allocate wealth between the two risky assets. If you follow your friends advice, you will choose the complete allocation from the portfolio opportunity set.

b. Solve for the formulas for the weight to equities and the weight to debt when you are only allocating between equities and debt (i.e., you need to maximize utility subject to being on the portfolio opportunity set).

c. What is the optimal allocation between equities and debt for an investor with A=7 when you are restricted to portfolio choices on the portfolio opportunity set? Demonstrate numerically and graphically that this is suboptimal to the unrestricted complete allocation of part a.

d. Another friend also believes that you are making a mistake in allocating the portfolio. She believes that the only risky asset that should be included in your risky portfolio is the risky asset with the highest Sharpe ratio. You follow her advice and optimally allocate wealth between T-bills and the risky asset with the highest Sharpe ratio (A=7). Demonstrate numerically and graphically that this is suboptimal to the complete allocation in part a.