Question

You manage a risk portfolio with an expected rate of return of 17% and a stdev of 27%. The T-Bill rate is 7%.

q) Suppose your clients degree of risk aversion is A=4, what proportion, y, of the total investment should be invested in your fund? What is the expected return and stdev of this new portfolio? The utility function is U=log[E[R]-1/2A σ2]

Answer 1

Given that,

Expected return on risky portfolio Rr = 17%

Standard deviation sdr = 27%

Risk free rate Rf = 7%

degree of risk aversion A = 4

So, weight of risky asset y in complete portfolio is calculated using formul

y = (Rr - Rf)/(A*sdr^2) = (0.17 - 0.07)/(4*0.27^2) = 0.3429 or 34.29%

So, expected return on this portfolio is weighted average return on its assets =

E(p) = y*Rr + (1-y)*Rf = 0.3429*17 + (1 - 0.3429)*7 = 10.43%

Standard deviation of portfolio is

SD(p) = y*sdr = 0.3429*27 = 9.26%