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...

  • $\begingroup$ What is your back-testing period? And am I correct assuming that you're mostly focusing on stocks? $\endgroup$
    – ikh
    Mar 14 '13 at 0:18
  • $\begingroup$ I run the optimizer each week to dervice holdings or the week ahead, going back 12yrs..it is not a single period anomaly. holding down the correlations generates substantial outperformance through the entire sample period. I am running the analysis on currencies. thanks for your interest... $\endgroup$
    – Richard
    Mar 14 '13 at 2:13
  • $\begingroup$ Are your backtested performance results Sharpe ratios or returns? The tangency portfolio in a no-covariance scenario could have higher returns (but lower Sharpe) than where you have positive and possibly negative covariances. $\endgroup$
    – Joshua
    Mar 18 '13 at 3:57

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

  • $\begingroup$ Thanks RICH! re the data - we look only at the major developed currencies vs the USD (ie G10 currencies). the forecast model generates fresh expected returns every week ahead period. For the covariance matrix we draw on the 52weeks preceeding the week ahead period in question, using this period to measure historical volatility in each currency and the correlations. The frustration is that the results ex-correlation are too good to ignore - we have gone back 12 years in backtesting so it doesnt sound like a one time anomaly. this may be a classic case of facts clashing with theory... $\endgroup$
    – Richard
    Mar 14 '13 at 22:30
  • $\begingroup$ @Richard I have found a link to forex. They calculate various correlations between currencies. I don't know all details of their calculations but it seems that the correlations are highly unstable. This would mean that projecting them to the future causes a bias. Could this be true? Can you tell us something (graph, numbers) about the correlations of USD/EUR and USD/JPY e.g. are these numbers very instable? Are the volatilies more stable? $\endgroup$
    – Ric
    Mar 15 '13 at 12:43

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