Question

In a universe with four risky assets the market portfolio is comprised of an equally weighted combination of those assets. This market portfolio has an expected return of 8% and a variance of 12%. Assume, that in addition a risk-free asset with return of 1% exists. What percentage of each risky asset will an investor with Utility function U(r) = E(r) – 0.4 var(r) hold in his portfolio?

1. 18%
2. 20%
3. 27%
4. 30%

Answer 1

Given that,

A market portfolio is consist of 4 equally weighted risky assets.

For market portfolio,

Expected return Rm = 8%

Variance Vm = 12%

Risk free rate Rf = 1%

Utility function for investor is U(r) = E(r) - 0.4Var(r)

Utility function is denote as: U = E(r) − 0.5A*Var(r)

So, Here 0.5A = 0.4

=> A = 0.8

So for an investor with A = 0.8, weight of market portfolio is

weight of market portfolio y = E(Rm - Rf)/(A*Vm) = (0.08 - 0.01)/(0.8*0.12) = 0.7292

So, weight of market portfolio is 72.92%

Since market portfolio is made of 4 equally weighted risky asset, weight of each asset = weight of market portfolio/4

=> Weight of each risky asset = 0.7292/4 = 0.1823 of approx 18%

Option a is correct.