“Paul,” (not his real name), a former floor trader, has a problem. This didn’t used to be a problem when he simply traded corn, but now he trades markets in several different sectors. It is safer that way, or so he thought.
“When I was on the floor, I traded one thing at a time. I didn’t have to worry about who was correlated to what,” states our trader. “If I’m trading corn and every damn market in Christendom drops like a rock what do I care? I care if I’m long corn, but otherwise no. Now, I’m upstairs and if everything starts going in the same direction I’m in big fat trouble.”
He also can see some big profits, which is the ideal time to adjust his position sizing to move in step with the new reality. Many managers were able to do that in the second part of 2008 when they realized that their outsized profits in nearly every sector they traded could be turned against them in a hurry. Several of the Top Traders of 2008 (see March 2009), many of whom earned in excess of 100%, reported reducing position sizes due to this correlation. This helped reduce the effect of the inevitable correction that came in the first quarter of 2009.
The big fat trouble “Paul” could be in is being on the wrong side of almost everything. Most of the time, most markets move more or less independently. There are, of course, higher correlations within sectors and soybean prices may respond to changes in the price for gasoline, but they respond to a lot of other things, too. Anyone trading both soybeans and gasoline futures, for example, is making two more or less independent bets and that’s a good thing. But every now and then much of the economy will be dominated by just one thing: the collapse of the banking sector, a plane crashing into the World Trade Center, a natural disaster. When something like that happens, price correlations spike and most prices move up or down together (see “So you are diversified,” right). When that happens a fund manager is no longer trading a portfolio. He is no longer making lots of independent bets. He is making one bet and if he loses, he loses big.
These days, most commodity trading advisors (CTA) and fund managers trade a lot of different markets simultaneously. So do most sophisticated traders. Many funds and the majority of CTAs trade in as many different markets as they can and use the powerful tools of portfolio theory to manage their risks. All of this works reasonably well most of the time and sometimes it works wonderfully — as long as most of the trades are not highly correlated and as long as the correlations remain fairly stable.
There are a lot of different measures of correlation and all of them measure things a little bit differently. The measure most fund managers use is called the Pearson correlation coefficient and it measures correlation on a scale from one to minus one inclusive (See “The Pearson method,” page 54). A correlation of one, also called a perfect correlation, means that every movement of market A is accompanied by a similar movement of market B. If there is a 5% rise in market A, it will be accompanied by a 5% rise in market B. Strictly speaking, every movement in market A doesn’t have to be duplicated by market B. The correlation can be perfect if every movement in market A is, say, exactly doubled by market B. The correlation is also perfect if, say, every movement in market A is matched by three and a half times the movement in market B plus an extra percent.
In a perfect negative correlation, every movement in market A is matched by an equal opposite movement in market B. Every rise in market A is accompanied by a drop in market B and vice versa.
No correlation means that markets A and B move independently; they have nothing in common.
Market correlations are almost never negative and never perfect and almost never close to being perfect. In the real world, as long as correlations remain fairly stable; that is, a correlation of, say, 0.4 in 2008 remains fairly close to 0.4 in 2009, diversification works reasonably well. But while correlations are often reasonably stable, they vary over time. And sometimes correlations wander far from their historical norms. So, two markets whose correlation coefficient was 0.5 in 2008 might suddenly have a correlation coefficient of 0.15 or 0.93 in 2009. Drops don’t matter. But when everything or almost everything is headed in the same direction the portfolio is suddenly much riskier than its owner designed it to be. In which case, the fund manager might well make or lose much more money than he expected.
So, what can a trader do?
Have a plan
The first thing is to have a plan. If you built your system skillfully, it may respond to the market reasonably most of the time. But it can’t respond to correlation spikes reasonably because no matter how thoughtful you are and how large your sample size is, it is impossible or almost impossible to get a meaningful sample; correlation spikes are rare. So, it probably isn’t in the system. The history of the market is, to some extent, a history of non-recurring events. How, exactly, are you going to plan for that? If you are extremely alert and know what an unexpected event looks like when you see one, you may need to do nothing more than constantly scan the horizon for danger, condescending to act once every decade or so. If the correlation between wheat and corn goes above 0.9, what are you going to do? Are you going to close all of your corn positions and keep a little bit of your wheat? Close out all of your positions? Close some of both and see what happens? You need to know what you are going to do before the market hits the fan.
Not incidentally, deciding you are never, ever going to override your system is a plan and for some fund managers it may be the right plan. But that plan means that every now and then you are going to lose on just about every trade you have. The rest of your money management system has to be built so it can withstand those kinds of shocks. In which case, your best bet may be to reduce your leverage and take your hits like a man. Correlations shift and like all elements of a trading plan, it is good to design a strategy for it in the calm during the system building process rather than in the heat of a fast market.
Watch the markets
When correlations rise, lower your commitment. With the right software, watching the market is a lot easier than it sounds. Unfortunately, all of the commercial software I know does it wrong. Here’s the problem: most correlation measures measure the relationship between data pairs. Which means that if you are following N markets you have to follow N(N-1)/2 pair wise correlations. For 10 markets this means 10(10-1)/2 = 45 pair wise correlations. This can be done by watching half of a matrix (the top left to diagonal right values are all ones and the bottom of the matrix is a mirror image of the top) but it can’t be done well. Unless the matrix is tiny, it is impossible to keep everything in mind. But the world comes in natural groups (interest rates, stock market indexes, grains, metals, oils, etc). By using a measure such as Kendall’s W, you can measure the correlation of a group of markets. In which case, the number of correlations the trader has to watch may well be in the middle single digits. Kendall’s W, also know as Kendall’s coefficient of concordance, can be found in most books on non-parametric statistics. It’s not that hard to program.
Find non-correlated trades
If possible, look for trades that are not correlated. Obviously this goes beyond our normal markets that have become correlated. Bizarrely, trading profits are not always dependent on changes in the price of the underlying investment. Bertrand Savatier of Numbers Alternative Management, a French CTA, trades calendar spreads, among other things. Mr. Savatier says “calendar spreads aren’t correlated with anything, including the underlying investment.” Savatier also suggests using fundamental filters such as seasonal approaches because they necessarily differ for each investment.
Don’t overfit
If you use software to allocate your trades, don’t overfit. Money management software bases its allocations on estimates of return, risk and correlation. Change a couple of those estimates even a little bit and your optimal money allocations can change in radical and unobvious ways. Worse, professional money management software is usually based on systems that are almost impossible not to overfit. So, for N markets, most such systems demand 2N + N(N-1)/2 estimates. For 10 markets a system based on quadratic programming, for example, demands 65 estimates. How much do you want to bet that a few of those estimates aren’t going to be a bit squirrelly?
Understand correlations
Make sure you understand how your markets correlate. Start by finding out what the baseline correlations are. The futures markets for wheat and corn, for example, are more than a century old. Are wheat/corn price correlations stable or do they cycle over years or decades? When correlations depart from their historical norms how long does it take them to go back to their norms? Hilary Till, who runs a private trading firm, argues, in effect, that the recent history is not necessarily relevant. In Till’s opinion, there are types of markets. Forecasting price behavior and risk properly depends upon finding similar past markets.
When we last spoke to “Paul,” we hadn’t listed all these ways to avoid the risk of rising correlations. “Paul” looked over at me and said, “Saw this James Caan movie a couple years back. Caan says, ‘If you can afford to lose, you’re not gambling. I’m a gambler.’ You see that movie? Anyway, I’ve done my share of gambling over the years. I think I would rather just keep some of
my money.”
Fred Gehm is a consultant to CTAs and the publisher of FredGehm.com. He is the author of “Quantitative Trading and Money Management” and the forthcoming “Trust is not an Option: Evaluating and Selecting Investment Managers.”
