How Correlation Affects Portfolio Optimization and Backtests
Summary
The document asks whether a Sharpe-ratio portfolio optimizer should ignore correlations after a backtest appears stronger with a diagonal covariance matrix. Setting off-diagonal covariances to zero can remove offsetting holdings, leaving positions more directly aligned with expected returns while individual asset volatilities still influence their size. The response cautions that correlation can matter substantially, especially in minimum-variance portfolios, where a higher-volatility asset may be included because it diversifies the rest of the portfolio.
The discussion raises estimation quality and stability as possible reasons full-covariance optimization may not improve results: historical correlations can vary enough that they offer little guidance for a coming week. The post does not provide a controlled comparison, data details, or evidence that suppressing correlation is generally valid. Its practical lesson is to treat apparent backtest improvement cautiously and examine the assets, observation frequency, and estimation window before drawing conclusions. The answer is based largely on the respondent’s experience with equity and long/short portfolios, while the question concerns currencies.
Key ideas
- Zeroing off-diagonal covariance terms removes correlation-based hedges from the optimized portfolio.
- Diversification can make a higher-volatility asset valuable in a minimum-variance portfolio.
- Unstable historical correlations may be poor estimates of relationships over a shorter forecast horizon.
- A better backtest after suppressing correlations alone does not establish that the method is sound.
- Interpretation depends on the assets, return frequency, and history used to estimate covariance.
Tags
Full text
# Is Optimization ignoring correlation valid? # Is Optimization ignoring correlation valid? 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... ## Answer by Richi Wa (score 2) https://quant.stackexchange.com/a/7530 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
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