Question

An investor is indifferent between investing 30% and 120% in a risky portfolio with E(r)=12% and standard deviation of 25% and a risk free T-bill yielding 3%. What is the investors risk aversion?

Answer 1

let y1 = 30% = 0.30

y2 = 120% = 1.20

E(r) = e =12% = 0.12

standard deviation = s = 25% = 0,25

risk free rate , r = 3% = 0.03

let the investor risk aversion = A

[y1*(e-r)] - [(1/2)*A*y1*y1*s*s] = [y2*(e-r)] - [(1/2)*A*y2*y2*s*s]

[0.30*(0.12-0.03)] - [(1/2)*A*0.3*0.3*0.25*0.25] = [1.20*(0.12-0.03)] - [(1/2)*A*1.2*1.2*0.25*0.25]

0.027 - 0.0028125 A = 0.108 - 0.045A

0.045A - 0.0028125 A = 0.108 - 0.027

0.0421875A = 0.081

A = 0.081/0.0421875 = 1.92

investor risk aversion , A = 1.92