Can Two Wrongs Make a Right?

By Joe Ferreira

This is the 3rd part of a series. If you have not read the others: “Diversification or Di-WORSE-ification" and “Ancient Greek Investment Advice”, I recommend you do so before starting this one.

Chances are you’ve heard the phrase “Two wrongs don’t make a right”. Generally, this is very wise advice. But is it possible sometimes, just sometimes, a little bad could do some good?

As you probably assumed, this post won’t be a philosophical discussion about ethics or Sicilian vigilante justice. So let’s jump to the chase. What does this have to do with investing? The answer is a relatively unknown paradox called Shannon’s Demon.

First, let’s set the stage. You own a portfolio with two investments (not very diversified!). What happens if over time both investments lose money? Your immediate impulse is probably to say the portfolio would also lose money. Normally, you would be right. But is that always the case?

In reality, that portfolio could still produce a positive return despite both underlying investments losing money. How is that possible? The two key elements are correlation and rebalancing.

We covered rebalancing conceptually last time. We touched on correlation briefly in the first part of this series, but we will expand upon it now. 

Correlation is how closely the performance of one asset is tied to another. If two assets are perfectly positively correlated, they would perform exactly the same.  If one is up 5%, the other would be up 5%. Correlation can work the other way as well. If two investments are perfectly negatively correlated, they would be a mirror of each other. If one is down 5%, the other would be up 5%.

A diversified portfolio contains investments that do not have perfect positive correlation. Although ideally you want everything you own to always go up in value, we know investing isn’t that simple. All investors must deal with volatility (asset values going up and down). But volatility can be used for good if you have the discipline to rebalance in the face of it.

Now for Shannon’s Demon. The graph below shows the performance of two negatively correlated stocks and a portfolio split evenly with 50% in each stock. The portfolio rebalances (i.e. sells some of one and buys some of the other) the stocks back to 50% at the end of each time interval.

As you can see, both stocks lost money over the full period. In this example, if you had just bought and held both stocks, you would have lost about 33% of your money. However, if you had rebalanced after each time interval, your portfolio would have been up 15% - quite the difference!

Like all great magic tricks, there is no sorcery at work. In this case, pure math can defy logic and come up with a pretty interesting result. So the next time someone tells you “Two wrongs don’t make a right”, ask them if they’ve ever heard of Shannon’s Demon.