# Mean-Variance question

I was wondering whether the optimal portfolio has the highest Sharpe ratio in ALL cases. Is is possible (and when) to have an optimal portfolio without having highest Sharpe ?

Construct the CML tangent to the min-variance frontier and you’ll find the point with highest Sharpe ratio. See also http://en.wikipedia.org/wiki/Modern_portfolio_theory Now of course “optimal” is in the eye of the beholder. Above we assume that the investor’s sole objective function is Sharpe ratio. If the investor is more risk averse, then she may find a different portfolio to be “optimal”. See e.g. http://en.wikipedia.org/wiki/Post_modern_portfolio_theory

Okay. So it is the highest Sharpe. But I also got another question. If you have a MV frontier of two assets (say A & B), is the optimal portfolio’s sharpe ratio higher than the sharpe of A & B ? Cuz if you have a straight line MVF (corr. coefficient = 1) then it seem like one of your assets will most likely be the optimal portfolio. So its sharpe would equal A or B’s sharpe ratios. What do you think ?

2x2equals4 Wrote: ------------------------------------------------------- > If you have a MV frontier of two assets (say A & > B), is the optimal portfolio’s sharpe ratio higher > than the sharpe of A & B ? If it’s not, there’s no point to diversifying. > Cuz if you have a straight line MVF (corr. > coefficient = 1) then it seem like one of your > assets will most likely be the optimal portfolio. > So its sharpe would equal A or B’s sharpe ratios. > > What do you think ? Yes, I think in that case your portfolio would be 100% of the asset with the better Sharpe ratio.