My returns are meant to be uncorrelated with the market. Are they?
Today I will analyze the correlation of contemporaneous returns on my portfolio with those of S&P 500 index. Just as I would have hoped, the correlation between returns of the stock-and-option portfolio and those of the index has been close to zero since when I started using my current set of models.
The input data are prepared as follows.
A series of dates is considered. This series covers all business days since late 2003 and until now. Prior to this, these were some missing data. The returns for the whole portfolio, the portfolio excluding the impact of trades in futures, and the S&P 500 index are computed for consecutive pairs of dates. I then compute rolling correlations. For a given date, I take a window of the series of returns that includes the preceding 6 months, take the series of index returns and returns for either the full portfolio, or the portfolio ex-futures, and compute the sample correlation.
The result is an estimate of correlation between daily returns, on the same day, of the index and of my portfolio (or the portfolio ex-futures). The estimates are available from early 2004 (the dates of the first 6 months are lost because to estimate the correlation for a given date, I need to have data for all of the preceding 6 months) until present. The results are shown in the following chart.
Reviewing the above chart, I cannot explain the strongly negative correlations seen at the end of 2004 and the start of 2005. To understand this, I would need to review the positions at that time - for example, whether they were balanced between puts and calls or whether one option kind was traded in preference to the other. I think this negative correlation was due to an outright short position (not short volatility - this would not be unusual at all, but actually short one or more stocks). This position or rather, some trading that preceded me taking this position, were in violation of the rules that I impose on the type of positions that I allow myself to take.
Since then, I have been much more diligent in avoiding directional positions in stocks. As the chart shows, the correlation (for the stock-and-option portfolio) was quite small since the middle of 2005. It has been positive, which is not very good. However, this reflects the basic fact that a portfolio short in volatility tends to decline in value, as the volatility rises when the market experiences a decline. This positive correlation is hard to avoid.
To explain the positive and not-so-small (around 20% during the recent months) correlation between the returns of the whole portfolio and the index, I would need to research the correlation between the major foreign currencies and S&P 500. This is not a very interesting subject in the context of my typical positions. For example, if the Euro happened to be somewhat correlated with S&P 500, this would not mean much as I do not trade any pure correlation products. If I were aggressive in utilizing margin or the Value-at-Risk allotment for the entire portfolio, then the co-dependency between futures and stocks would be of importance. However, the risks being taken are quite moderate (I wish there were more good trade ideas!) In the long run this correlation simply does not matter.
Summary
I have observed that the correlation between my trading in stocks and options has been small and positive over the latest year. Its small magnitude is reasonable, as most of the time the positions are delta-neutral. The small positive value might be due to mis-hedging - meaning that I need to hold small short-the-stocks positions in addition to whatever hedges my models tell me to hold. Alternatively, it might be the evidence of me not buying insurance against a sudden drop in the market. Time will tell.