Minyan Mailbag: Can Correlations Describe Markets?
Linear statistics, like correlation, or volatility for that matter, are actually meaningless when trying to describe the real world.
Do you know (offhand) the correlation (coefficient) among the dollar, gold, rates, and money supply? Obviously, supply and demand measures ultimately determine the investment choices and time preferences.
It would seem that the ongoing push on the money supply should produce inflation (and inflation attracts dollar investment), but at the same time monetary expansion shouldn't allow dollar strength indefinitely. If we had free access to the money supply would we find it has less effect on rates, the dollar, or is the question just so nonlinear as to be absurd?
I hope the question is not too obtuse.
The correlation between these is basically zero. The reason may surprise you; it is because linear statistics, like correlation, or volatility for that matter, are actually meaningless when trying to describe the real world.
There are two aspects to this. First, in the real world, the relationships between variables used for models attempting to describe market behavior (like the Fed's asset pricing model) actually change over time and in price. This cannot be the case if statistical models are to be predictive. Depending on other variables like commodity prices, a drop in interest rates may affect stocks differently. Linear models cannot account for this.
Secondly, these models can only describe relationships statistically in normal times two ways. First, when volatility (the measure of volatility is flawed, but not the concept) is low. Secondly, when flows in and out of various assets are dominated more by the level of risk taking than anything else. What really matters is how assets behave under stress, the small percentage of times that relationships vastly (and quickly) change. These changes are called "tail" events.
I think that your "feeling" that correlations between money supply, the dollar, and gold should be high occurs in times like these, but we never see these correlations in the statistics used to describe markets (which are a non-linear system).
So why do we use them? Right now, they are the best we have. I use the Black-Scholes model (and its derivations) to price options, but it is only a guide, something that tells me how to price an option when an asset is trading nicely around its mean. When it is useless is when it is the most important time to be right, tail events.
The darker view as to why we use correlations has to do with politics. Wall Street is the greatest money making machine that has been granted monopoly status. It is 99% sales and that sales machine must have "reasons" for you to do things. Wall Street backs up all its recommendations with very faulty statistics. A simple example, not related to statistics, is the fallacy created by Wall Street types (financial advisors, etc.) that having a mortgage is essential for a tax write-off.
The fact is, having a mortgage, from a purely economic and risk standpoint, makes little sense unless future income is expected to rise and if one wants to quickly increase their standard of living today, in lieu of tomorrow. When you have a mortgage; you pay interest. The proper way to analyze a mortgage is to ask "can I get a better or worse rate of return after-tax, risk-free or not"? You must use the risk-free rate. Otherwise, you are assuming superfluous risk. But of course, Wall Street wants everyone to have a mortgage so that they have more money to buy stocks. When you have a mortgage and you own stocks, you are basically borrowing money in order to buy stocks. Just know, this is superfluous risk.
I have learned one thing over 35 years of studying markets (I started, in earnest, at 15 learning from my grandfather): I really don't know anything. I only know that I am a trader who must exchange value for value.
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