Question

An investor with risk aversion A=2 is allocating $100,000 between T-bills with a return of 0.01, and a risky portfolio with E(r) = 0.05 and σ = 0.15. The risky portfolio is comprised of 60% stocks and 40% bonds; the investor cannot change the stock/bond mix within the risky portfolio. How much money should be invested in stocks?

Select one:

a. $88,889

b. $53,333

c. $15,000

d. $60,000

e. $30,000

Answer 1

Given that,

Risk free rate Rf = 0.01

risk aversion of investor A = 2

risky portfolio has following features,

E(r) = 0.05

σ = 0.15

The risky portfolio is comprised of 60% stocks and 40% bonds

in an optimal complete portfolio, weight of risky portfolio y is

y = (E(r) - Rf)/A*σ^2 = (0.05-0.01)/(2*0.15^2) = 0.8889

So, weight o risky portfolio is 0.8889 or 88.89%

So, weight of stock = 60% of 88.89% = 53.33%

So, investment in stock = 53.333% of 100000 = $53333

Option b is correct.