Short-term trading has no ironclad definition, though there are some fairly clear differentiating properties between short-term traders and their more common, long-term counterparts. Typically, short-term trading is defined by strategies that hold positions for 10 days or less. More recently, some short-term trading systems have begun to consist partially or entirely of intra-day strategies.

We want to point out that short-term trading has not, historically, included the so-called high-frequency strategies that recently have gained attention (most notably in the context of the May 2010 "flash crash"). High-frequency strategies, in our view, are those employed by electronic market-makers, and consist primarily of quasi-arbitrage strategies that allow someone to profit off the bid/ask spread. Moreover, while there well may be significant strategy development underlying such strategies, an additional and necessary condition for their success is speed of execution — so much so, in fact, that it appears to be more of a technological arms race than a search for new and profitable trading patterns. Hence, for this discussion we will exclude high-frequency trading and focus on strategies that do not depend primarily on ultra-low-latency execution to be profitable.

**The case for short-term traders**

The goal of short-term systems is simple: Provide diversification. Specifically, short-term traders try to provide diversification to the dominant managed futures strategy of trend-following.

The following thought experiment makes clear the potential benefit of such diversification. Imagine a bucket of systems, each with equal risk-adjusted performance. For simplicity, as the measure of risk-adjusted performance, we can use the annualized Sharpe ratio (S_{Y}) as the corresponding metric and ignore the effect of higher-order statistics such as skewness, kurtosis, etc. The annualized Sharpe ratio of each of the systems will be denoted simply as S. Further, assume that each of these systems has a correlation of C to each system in the bucket. In other words, for any two systems that we might pick out of the bucket, we find that their mutual correlation is C.

This would at first appear to be an oversimplification. But some numerical experimentation can show that the following conclusions still are valid for real-world portfolio construction as long as the chosen value of C equals the average value that would be obtained by picking many such pairs from the bucket, thus relaxing the condition that each value need be equal to C. What we find is that, if we are allowed to populate the bucket with as many systems as we want, with the goal of maximizing the risk-adjusted performance (i.e., Sharpe ratio) of our ensemble, our diversification factor will asymptote as 1/. Mathematically:

where is our diversification factor and N is the number of systems chosen from the bucket. In terms of our overall portfolio, its Sharpe ratio S_{P} is given as:

A quick check using our minimum and maximum values of C shows that these equations make sense. (Note that the equation holds only for 0 ≤ C ≤ 1; if C is negative, then in theory we can generate an infinite Sharpe ratio with a finite number of systems.) If C=0, then all strategies are uncorrelated to all others, and our diversification ratio approaches infinity as we add more and more strategies. In this case, our portfolio Sharpe ratio S_{P} continues to increase without bound. If this generally were the case, it would make the lives of allocators and fund-of-funds managers much easier.

The other extreme, and one closer to reality, is when all strategies are completely correlated and C=1. In this case, no matter how many strategies we add, the pure overlap between them gives us an asymptotic diversification factor of =1, which is to say we haven’t added any additional risk-adjusted performance to the portfolio by adding more strategies.

More realistically, what we see with a typical basket of long-term strategies is that the average cross-correlation between strategies is between 0.7 and 0.8. This suggests that we can achieve diversification factors between 1.12 and 1.20. In other words, if each system can achieve a Sharpe ratio of 0.75, then by adding a bunch of these systems, we can achieve a Sharpe ratio between 0.84 and 0.90. This is certainly a net benefit, but the somewhat-sobering conclusion is that it is a mathematical certainty that we can’t improve on this unless we can pick a basket of programs with better baseline Sharpe ratios. Otherwise, at some point more is not better. Diversification may be the only proverbial free lunch, but even in this case it’s not an all-you-can-eat buffet.