suppose a risk-averse investor can choose a portfolio from among N assets with returns that are independent of one another, all of which however have identical expected returns [E(Ri) = E(Rj)] and identical variances [sigma sq i = sigma sq j].
what will be the composition of his optimal portfolio?
Oct 22nd 2009, 08:32 AM
under only these assumptions it should be equally weighted portfolio from N assets.
Oct 22nd 2009, 08:38 AM
kk that's what i thought too! (Rofl)
is it because all the assets have the same return and risk, and by having an equally weighted portfolio would yield the highest return and diversified the non market risk?
Oct 22nd 2009, 08:49 AM
return of portfolio will be the same for any combination of N, but under the assumption of zero correlation it is best diversified portfolio. Also because of these assumptions it is very unreal and strictly speaking return and variance of portfolio will not change for any combination of N
Oct 22nd 2009, 08:57 AM
Ohh.. so for any combination of his portfolio, he will still get the same return and variance?
and since it's zero correlation, that's why an equally weighted portfolio would be the optimal to diverse the risk
am i right to say that? (Rofl)
thanks for helping!
Oct 22nd 2009, 09:35 AM
yes, if you have same return and same variance across all assets, it will be the same. But if you take return as mean and risk as std. deviation, when you try to compute correlation, you will find that it will not be 0 at all so you can't have such assets under these assumptions. But strictly under yours, best is equally diversified portfolio because for risk averse investor, more diversified is better than less. But if you throw away that, it's similar for all combinations, because you still get something*1 (all weights have to sum to 1, you don't state otherwise).
So for answer, depends how exactly is question stated. If it is some kind of test question, I would answer it does not matter. It's commonly used that risk-averse means minimize the risk=std. dev. If it is some from real life consulting question I would answer equally diversified.