Question

a) Manuel is a rational investor whose risk preferences follow the utility function U=E[r]-0.5×Aσ^2 . He has decided to allocate his wealth of $100,000 between a portfolio of risky assets and the risk-free asset. The standard deviation of the portfolio of risky assets is 40% and its expected return is 25%. The risk-free rate is 7%. The expected return on Manuel’s complete portfolio is 20.5%. What is Manuel’s coefficient of risk aversion?

The expected return on the optimal complete portfolio is:

E(r_C) = y* E(r_P) + (1- y*) r_f

Hence:

0.205 = y* 0.25 + (1- y*) 0.07

Which solves to give y* = 0.75

We then have:

y* = (E(r_P)-r_f)/(A σ^2_P) = (0.25-0.07)/(A(0.4)^2)

which solves to give A=1.5

How to get this formula  y* = (E(r_P)-r_f)/(A σ^2_P) = (0.25-0.07)/(A(0.4)^2) ?

Answer 1

SEE THE IMAGE. ANY DOUBTS, FEEL FREE TO ASK. THUMBS UP PLEASE

AS YOU HAVE ALREADY SOLVED FOR "y*"

I HAVE SOLVED THE SEOND PART OF FINDING "A"