Financial Mathematics Text

Monday, June 9, 2014

Gold, Hedges and Correlations

Today I'm going to touch on a sort of theme I have here and that's regarding on how to assess correlated data. How much can we actually read into it? How do we determine that there's a fundamental relationship that, not only holds well in the past but will continue to do so in the future?

To do that I'll be taking a quick look at gold and why I consider the "inflation hedge myth". In short, gold is not an inflation hedge. At least not on any reasonable time scale.

What is a hedge?

I'll go ahead and quote wikipedia on this one:
A hedge is an investment position intended to offset potential losses/gains that may be incurred by a companion investment. In simple language, a hedge is used to reduce any substantial losses/gains suffered by an individual or an organization.
What one wants in a hedge is that it increases (or decreases) in value when another asset increases (or decreases) in value. This means the assets have to be correlated. Which direction the correlation is doesn't matter so much as one potentially has the option to other go "long" or "short" the hedge and thereby gain whichever exposure one is lacking.

Is gold an inflation hedge?

One condition that needs to be satisfied here is that gold ought to be correlated with some measure of inflation. I've used CPI from FRED (yes the one that includes food and energy... people make a huge deal out of that but this one and "core" CPI don't look much different if you look at rolling averages.)

As it turns out, from 1995-2000, gold was a great inflation hedge. If you wanted to hedge your exposure to inflation, all you had to do was short gold.

Of course that's just an anomaly. What's the general trend? Here's 5Y trailing rolling correlation between gold and CPI.

So there's actually a good correlation through much of the history. But some of that is negative correlation while other parts have positive correlation. Apparently, if you wanted an inflation hedge during some five year periods, you should have shorted gold, not owned it.

But perhaps 5 years is too short of a time span. Gold goes up with prices over the long haul, right?

I guess it depends upon how long. For example, from peak to trough (Jan. 1980 to Apr. 2001) the real price of gold went from $2043 to $349, a real loss of 83% for a period of over 21 years. So how long is long enough? Perhaps the correlations are good on, say, the 100 year level. But who has 100 years to wait it out?

Correlation Caution

So back to the theme. While I don't think gold is a good inflation hedge, that's not what's important here. What's important is that one can take a long string of data and find interesting relationships. That doesn't mean those relationships have any deeper meaning. 

I discussed some of the ways we can "test" whether or not a relationship holds good over time here and here. In particular, out of sample testing is required along with some theoretical grounds on why this particular relationship (and not one of the infinitely many others) will continue to hold in the future.

I've also noted how it's quite common, apparently, in the financial world to come up with really pretty charts of two correlated variables and ascribe deeper meaning to it when, perhaps, there shouldn't be any (see here.) But to show you how bad it can get, I give you this site . . .

Spurious Correlations

So there's an entire website devoted to finding correlations between two (often) entirely unrelated variables: Spurious Correlations.

For example, I can only conclude that Nicolas Cage needs to star in less films (source):

Although apparently it's inversely correlated with helicopter accident deaths. So perhaps we should proceed with caution whether or not we need to advise Mr. Cage to perform in more or less films.

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