I have a fairly pedestrian optimization problem: Max sharpe, subject to a x% vol target. I have a set of expected returns, asset vols and a correlation matrix. I am finding that when i set the off-diagonals of my covariance matrix to 0 (ie assume zero corelation, independant views on assets) my backtested performance results are substantially better than optimization including the full covariance matrix. Its clear what is going on here - this approach removes hedge positions (ie: negative holdings in assets with a small positive expected return (and vice versa) that are highly correlated with other assets.) As a result my holdings are always aligned with my expected returns, but the individual asset volatilities still scale the holding. The conlcusion from these results is that one should max exposure to my expected returns and I should "suppress" the correlation matrix. My question is: is this valid? Would anyone really use this approach...thanks in advance for any thoughts...
I had to answer because of your name, and becaue I deal with portfolio optimization often.
In my world of equities correlation does matter a lot. If one follows the thoughts e.g. here then it matters most. I deal with minimum-variance construction (no expected return, of course some constraints on the weights) and there I often see positions that come into the min.var portfolio despite relatively high volatility due to low correlation to the rest of the portfolio. So in my mind: correlation does matter. I have more experience with long only portfolios but I have seen similar in long/short settings.
So you deal with currencies. If your optimization works with vola and expected returns then your expectations must work really good! One reason why taking correlations into account does nt improve the result even further could be because they vary too much in the long history that you use. Therefore they do not tell you enough for the coming week.
Tell us some more about the data: how many currencies? Weekly returns? Which observation period for the covariance matrix?
Edit: I found a funny maybe useful app by FOREX on currency correlations. They seem to change a lot: http://www.forexticket.co.uk/en/tools/01-01-correlation