optimal portfolio

[ajsa]

Hi David,

I wonder if the optimal portfolio of portfolio management (the one with highest sharpe ratio) is the same optimal portfolio derived from risk management (the one equating the ratio of excess return over beta for each asset)? why?

Thanks,

 

[ajsa]

Hi David,

Could you pls take a look this when you have chance?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

It's a good connection, but i assume you mean Jorion's risk budgeting by maximizing the portfolio informatio ratio (IR) rather than the Treynor?
If so, although I do not *think* we can expect them to be the same
(i.e., imagine the capital market line that runs from Rf rate to tangent the portfolio curve, intersecting at highest Sharpe. If you shift up the Rf rate, the market portfolio [highest Sharpe] changes. For similar reason, I don't think we can expect them to be equal)

but I do think we might be able to view the IR optimization as a special case of mean variance (highest Sharpe) because:

IR = (portfolio return - benchmark return) / Std Dev (portfolio return - benchmark return)

and Sharpe is just a special case where the benchmark = riskfree rate, such that if and only if benchmark = RF:
IR = (portfolio return - riskfree) / Std Dev (portfolio return - riskfree) and
since RF is a constant, Std Dev (portfolio return - riskfree) = StdDev(portfolio return)
so IR = Sharpe iff benchmark = Rf rate

David