One major weakness of quantitative trading is that it’s based on the concept of how correlated various instruments and instrument classes are. Today I’m planning to rant about this, thanks to a reader who suggested I should. By the way, I do not suggest that anything in today’s post is new- I’m just providing a public service by explaining this stuff to people who may not know about it.
Correlation between two things indicates how related they are. The maximum is 1 and the minimum is -1; in other words, correlation ignores the scale of the two things and concentrates only on the de-scaled relationship. Uncorrelated things have correlation 0.
All of the major financial models (for example Modern Portfolio Theory) depend crucially on the concept of correlation, and although it’s known that, at a point in time, correlation can be measured in many different ways, and even given a choice, the statistic itself is noisy, most of the the models assume it’s an exact answer and never bother to compute the sensitivity to error. Similar complaints can just as well be made to the statistic “beta”, for example in the CAPM model.
To compute the correlation between two instruments X and Y, we list their returns, defined in a certain way, for a certain amount of time for a given horizon, and then throw those two series into the sample correlation formula. For example we could choose log or percent returns, or even difference returns, and we could look back at 3 months or 30 years, or have an exponential downweighting scheme with a choice of decay (explained in this post), and we could be talking about hourly, daily, or weekly return horizons (or “secondly” if you are a high frequency trader).
All of those choices matter, and you’ll end up with a different answer depending on what you decide. This is essentially never mentioned in basic quantitative modeling texts but (obviously) does matter when you put cash money on the line.
But in some sense the biggest problem is the opposite one. Namely, that people in finance all make the same choices when they compute correlation, which leads to crowded trades.
Think about it. Everyone shares the same information about what the daily closes are on the various things they trade on. Correlation is often computed using log returns, at a daily return horizon, with an exponential decay weighting typically 0.94 or 0.97. People in the industry thus usually agree more or less on the correlation of, say, the S&P and crude.
[I'm going to put aside the issue that, in fact, most people don't go to the trouble of figuring out time zone problems, which is to say that even though the Asian markets close earlier in the day than the European or U.S. markets, that fact is ignored in computing correlations, say between country indices, and this leads to a systematic miscalculation of that correlation, which I'm sure sufficiently many quantitative traders are busy arbing.]
Why is this general agreement a problem? Because the models, which are widely used, tell you how to diversify, or what have you, based on their presumably perfect correlations. In fact they are especially widely used by money managers, so those guys who move around pension funds (so have $6 trillion to play with in this country and $20 trillion worldwide), with enough money involved that bad assumptions really matter.
It comes down to a herd mentality thing, as well as cascading consequences. This system breaks down at exactly the wrong time, because after everyone has piled into essentially the same trades in the name of diversification, if there is a jolt on the market, those guys will pull back at the same time, liquidating their portfolios, and cause other managers to lose money, which results in that second tier of managers to pull back and liquidate, and it keeps going. In other words, the movements among various instruments become perfectly aligned in these moments of panic, which means their correlation approaches 1 (or perfectly unaligned, so their correlations approach -1).
The same is true of hedge funds. They don’t rely on the CAPM models, because they are by mandate trying to be market neutral, but they certainly rely on a factor-model based risk model, in equities but also in other instrument classes, and that translates into the fact that they tend to think certain trades will offset others because the correlation matrix tells them so.
These hedge fund quants move around from firm to firm, sharing their correlation matrix expertise, which means they all have basically the same model, and since it’s considered to be in the realm of risk management rather than prop trading, and thus unsexy, nobody really spends too much time trying to make it better.
But the end result is the same: just when there’s a huge market jolt, the correlations, which everyone happily computed to be protecting their trades, turn out to be unreliable.
One especially tricky thing about this is that, since correlations are long-term statistics, and can’t be estimated in short order (unless you look at very very small horizons but then you can’t assume those correlations generalize to daily returns), even if “the market is completely correlated” on one day doesn’t mean people abandon their models. Everyone has been trained to believe that correlations need time to bear themselves out.
In this time of enormous political risk, with the Eurozone at risk of toppling daily, I am not sure how anyone can be using the old models which depend on correlations and sleep well at night. I’m pretty sure they still are though.
I think the best argument I’ve heard for why we saw crude futures prices go so extremely high in the summer of 2008 is that, at the time, crude was believed to be uncorrelated to the market, and since the market was going to hell, everyone wanted “exposure” to crude as a hedge against market losses.
What’s a solution to this correlation problem?
One step towards a solution would be to stop trusting models that use greek letters to denote correlation. Seriously, I know that sounds ridiculous, but I’ve noticed a correlation between such models and blind faith (I haven’t computed the error on my internal estimate though).
Another step: anticipate how much overcrowding there is in the system. Assume everyone is relying on the same exact estimates of correlations and betas, take away 3% for good measure, and then anticipate how much reaction there will be the next time the Euroleaders announce a new economic solution and then promptly fail to deliver, causing correlations to spike.
I’m sure there are quants out there who have mastered this model, by the way. That’s what quants do.
At a higher perspective, I’m saying that we need to stop relying on correlations as fixed over time, and start treating them as volatile as prices. We already have markets in volatility; maybe we need markets in correlations. Or maybe they already exist formally and I just don’t know about them.
At an even higher perspective, we should just figure out a better system altogether which doesn’t put people’s pensions at risk.