Correlation

Correlation ought to be a straightforward topic. It simply describes how closely two prices move in tandem. This is important in the investment world as we need to know whether the assets in all our portfolios tend to go up and down at the same time or not.

By including assets that do not move in lock-step with each other we can aim to reduce the overall volatility of the portfolio; losses in one part of the portfolio will be offset by gains in another part. This is one of the pillars of portfolio diversification. For example, investment textbooks teach us that equity and bond prices typically move in opposite directions and a portfolio with an allocation to both asset classes will typically experience a smoother ride than a purely equity equivalent.

This basic concept became extrapolated in the post-crisis world into the ‘risk on, risk off’ trade. Investors betting on prices rising were said to be ‘risk on’; those taking the contrary position, or ‘risk off’, were merely aiming to avoid losses. In fact an old-fashioned balanced portfolio would typically have given the best of both worlds without the need for all this meaningless short-term re-assessment.

We can take this further. If you were to believe that the price of gold were about to rise, one potential tactic would be to buy gold mining shares. Historic data, and logic, suggest that if the gold price goes up, so do the companies that get it out of the ground. You would not however usually buy coffee, the consumption of which has nothing to do with gold. The concept of correlation is intricately linked to that of causation, yet causation should be – quite literally – sat on caution: umbrella sales have a tendency to rise during particularly wet winters, though this certainly does not mean that if we all bought fewer umbrellas we would enjoy more clement weather.

Statisticians express correlation as a number between –1 and +1. That number tells us two things: the direction of movement (if they move together or in opposite directions), and the strength of that relationship. A reading of zero tells us the two are unequivocally unrelated: their movements relative to each other are random. At +1 we reach “perfect correlation”: without fail the two prices will move in parallel. At the other end of the scale, a negative number indicates two prices that move in opposite directions.

Unfortunately there is huge caveat to the use of correlation in portfolio construction. Statistical analysis only tells what has happened in the past, not what the chances are that this will continue into the future. Previously uncorrelated assets have a horrible tendency to become suddenly highly correlated at the very worst of times: during a crisis. In the 2008/09 Great Financial Crisis, the dash for cash was such that that investors sold anything that they could. Thus all the fancy mathematical models that had predicted portfolios with beautifully uncorrelated assets would be “low risk” turned out to be bunkum. Correlations and risks are not constant through time, and neither, therefore, should portfolios.

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