Question

You invest $10000 in a risk asset with an expected rate of return of 0.124 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.04. If you have a risk-aversion parameter of 2.5, what is the expected return of your complete portfolio

Answer 1

Expected return is 11.06%.

Explanation:

Capital allocation between Optimal risky portfolio and risk free assets can be computed with following equation.

y = E(rp) - rf /A*θp^2

where,

E(rp) = Expected return of Portfolio

y = weight of risky portfolio

(1-y) = weight of risk free assets

rf = risk free rate

A = Coefficient of Risk Aversion

Фp= Standard deviation of risky portfolio

Putting the values,

y = {0.124-0.04}/{2.5*0.20^2}

by solving,

y = 0.84

Weight of risk free assets in complete portfolio = (1-y) = 1-0.84 = 0.16

Thus,

Expected return of complete portfolio:

E(r_c) = 0.124*0.84+0.04*0.16

E(r_c) = 11.06%