The Correlation Problem

What are the odds of flipping a fair coin and getting tails four times in a row? There are 16 possible outcomes for four coin flips:

H H H H   H H H T   H H T T   H T T T
T T T T   T T T H   T T H H   T H H H
T H T H   H T H T   T H H T   H T T H
T H T T   T T H T   H T H H   H H T H

The odds of flipping four tails in a row are 1 out of 16, a 6.25% (or .5^4) probability. Unlikely, but not that unlikely. In a hundred coin flips, the odds say that you’ll probably see it happen six times.

Now let’s say that you have an investment approach that you feel confident will produce winning transactions 50% of the time and the wins will be 3x the size of the losses. Potentially, a good edge for delivering long term growth. Further, let’s say that you are the cautious type and would like to plan your position sizes to be able to survive a real outlier – make it ten consecutive losses. With a 50% win rate, what is the probability of incurring 10 losses in a row?

On the surface, the answer is pretty basic. With 50% odds, it’s the same as calculating coin flips – the answer is .5^10 which is a 1/1024 chance or 0.09% probability. Very unlikely. If you flipped a coin (made a transaction) once/month, you could go hundreds of years without seeing 10 tails (losses) in a row. Unfortunately, coin flipping statistics don’t have much to do with investing statistics.

The outcome of each coin flip is independent of the one that preceded it. There is no influence on the coin from one flip to the next. Investments, on the other hand, almost always have some type of correlation to each other. As we saw most recently in the fall of 2008, even asset classes that are normally non-correlated, like stocks & commodities, can very quickly become highly correlated. When investors become risk averse they don’t differentiate between risky asset classes and we shouldn’t expect them to. Losing money in stocks is no better or worse than losing money in real estate or silver or junk bonds. A flight to safety means just that – a flight away from risk in any form.

If we want to plan our position sizes to withstand an extended streak or widespread occurrence of losses, limiting heat (intended risk) by position is crucial, but not as important as limiting the total heat of the entire portfolio. An investor that trusts diversification to save him from disaster is playing with fire. Just ask a Greek or Italian investor how well that diversified stock/government bond/real estate portfolio is working out…