Remarks on the Diversify Page

Description: Some pairs of stocks have large positive correlations, that is, each one seems to go up and down at the same time as the other. Holding both stocks generates correlation risk that you can remove, and of course, one of these stocks is likely to be better than the other. If you want to reduce correlation risk in your portfolio of stocks, you could diversify your holdings. To diversify, you should avoid holding pairs of these positively correlated stocks. Instead, if you have an interest in some stock, you should look for other stocks that are negatively correlated with it. That is, any such other stock should go up if your stock of interest goes down, and the opposite. When you enter the ticker symbol of a stock of interest on the Diversify Page, you should see ticker symbols for stocks with the lowest and highest correlations expressed as percentages. You might note whether any of these extremely correlated stocks appear in your portfolio. If not, you might consider adding any of the ones with negative correlation. If you already hold some of both kinds, you might consider keeping the ones with negative correlations, and changing the ones with positive correlations or even changing the stock of interest itself. Reducing risk is never cost-free: you would then be holding stocks with lower average return, because gains in one may be partly cancelled by losses in another.

Discussion: There is at least one problem with this approach: during a market crash, almost all stocks go down at the same time, regardless of this attempt to diversify. There is no solution to this investment problem simply from choosing a mix of stocks in a portfolio. A crash also leads to a statistical result; many pairs of stocks then are likely to have positive correlations for a while. In a recent test, the average correlation of about 2800 stocks was close to 45%, rather than a more normal value closer to 0%. These correlations showed skew: most of the positive correlations reported on the right were much more extreme than the negative values toward the left. Conversely, relatively few pairs of stocks had negative correlations, so you saw the same ticker symbols among the negative correlations, over and over again. Some 2200 appearances of only 24 ticker symbols had these lowest correlations. This does not mean that these very negatively correlated stocks are now good purchases to go with almost any other stock you own, merely that before the crash, they might then have been a good investment!

Solution: One approach to the statistical part of the problem is to construct a weighted average market index. This index is composed of all the 2800 or so stocks being considered, after any price trend in each stock is removed. Next, each detrended stock is correlated with this average, and the proportional contribution from the index is removed from that stock, so the stock is no longer correlated with the index. Now whatever happened in common during the crash is mostly removed from the detrended stocks, and their uncommon correlations can be calculated as before. The method is illustrated in the Correlation Chart. The statistical result is almost perfectly symmetric, the average correlation is zero and the extremes of the correlations are about half as large as before. These adjusted correlations are milder because the individual stocks had correlated highly with this index, on average 67%, and this mutual positive correlation now is removed. The uncommon correlations reported in the Diversify Page more nearly represent day-to-day variations of individual stocks, rather than long-term trends or general market behavior. You might overlay the price charts of three stocks, the one with the reference ticker symbol that you typed in, and any two ticker symbols that were reported on the Diversify Page. Other than for trends, you may see the positively correlated stock and the reference move similarly, while the negatively correlated stock move oppositely to the other two. The more extreme the correlation coefficients, the more this should be true.

Warning: Once again, the past is not a very good guide to the future. As always, check other sources of information and check with a responsible and knowledgeable person before making an investment decision, rather than trusting these blind calculations as anything more than a hint.

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