Question

You are considering investing in one of Fidelity's mutual funds. Based on the information provided in the prospectus, you believe the expected return of this Fidelity fund is 0.12 and its expected standard deviation is 0.32. Assume Treasury bill (risk-free security) currently returns 0.03 per year and you have estimated that your risk aversion coefficient, A, is 4.

What is the optimal weight, y*, of this Fidelity mutual fund (risky portfolio) in your final complete portfolio?

(The optimal weight refers to the weight of risky portfolio in the final complete portfolio that will make your utility for the complete portfolio to be highest.)

Please round your answer to the fourth decimal. For example, 0.1234.

Answer 1

We use an excel solver to solve the problem

Utility function is given by = E(p)-0.5*A*(s(p))^2

s(p) is the standard deviation of the portfolio

E(p) is the expected return on the portfolio

We need to maximize the Utility function

The portfolio expected return is the weighted average of the individual expected returns.

Since, the standard deviation of a risk-free asset is 0, the portfolio standard deviation equals the weight times the standard deviation of the risky-portfolio

E(p) = w(f)*r(f) + w(r)*r(r)

w(f) and w(r) are the weight of the risk-free portfolio and risky portfolio in the final complete portfolio

r(f) and r(r) are the returns of the risk-free portfolio and risky portfolio in the final complete portfolio

Using an excel solver with the following constraints,

Solving, we get

	Weights	E[r]	Std. dev
Risky portfolio	0.2197	0.12	0.32
Risk-free	0.7803	0.03	0
Portfolio	1	4.98%	7.03%
Utility function	3.989%
A	4.0

Hence, the optimal weight ie. the weight of risky portfolio in the final complete portfolio = 0.2197