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High Returns From Math Models Should Be Taken With A Grain Of Salt

Apart from the trend-followers of the 1980s who used simple math models and exploited a real market anomaly, any other claims of high trading returns from the use of math models should be taken with a grain of salt. There are cases where math is used to conceal luck, or even illegal trading activity.

Trend followers of the 1980s, and especially CTAs, realized high returns by exploiting a real market inefficiency that has since diminished. Their high returns were based on simple math models, for example moving average crossovers, price series momentum and channel breakouts.  However, when the space got crowded, it was reasonable that these returns diminished. In the last 13 years trend-following CTA performance has been disappointing. Below is a chart from a recent article with average annual returns of top 20 systematic CTAs. Most of those are trend-followers.

In the last 13 years, annualized return of the above group is about 2.5%. However, the large returns of the 1980s were real, regardless of whether they were achieved by luck or skill.

Other hedge funds, apart from High Frequency Trading (HFT) operations, have claimed high returns from the use of math models. Anyone who has been in this area for a few years knows that high returns from math models are either random or not possible in a consistent manner. The signal to noise ratio in financial series is just too low and behavior is non-stationary. Certain funds could be using math as a cover to justify certain other edges that may be legal, or even illegal.

We will not mention anyone in particular here but there is evidence that certain claims of success due to use of math are used to obscure illegal trading activity. For example, the fund of a high profile trader was involved in illegal but lucrative transactions in the past but the public thinks he was profitable because he was a math genius. This is what articles in mainstream media claim. The operation of another high profile trader was involved in insider trading.

Real returns from math models rarely beat buy and hold of S&P 500 total return over the longer term unless there is luck or high risk. One thing math models can do is to provide better risk-adjusted returns where the annualized return is lower than buy and hold but drawdown is much lower. Then, traders can possibly leverage these models to gain an edge above buy and hold but not by much. This is the reality of the markets. Obviously, there are always lucky traders who realize high returns but they are never consistent and at some point they even get ruined because of excessive risk. This is shown in a simulation of coin toss SPY traders discussed in this article.

Although buy and hold for 2016 was 13.6%, some random traders made close to 50%. They may of course claim use of math models and the financial media may get excited. But the truth in most cases of high returns involves these two: luck or illegal activity. We exclude returns of trend-followers and HFT market making.

Everyone should be skeptical of claims of high returns via the use of math models. Math is useful in managing risk and developing strategies with high risk-adjusted returns. But high absolute returns are not possible because they have to come from some other pockets, usually those of small account retail traders.

The financial media should carefully investigate claims of math geniuses and high absolute returns via the use of math models. Math is a tool, not a license to print money. Journalists should always keep in mind that math can play the role of a cover of either luck or illegal trading activities. There is always possibility that a math genius can beat the market but this is a highly unlikely tail event that is indistinguishable from luck because the market always responds to winning math models by arbitraging them out. The market will always be there but all ambitious math models will be broken. Otherwise, someone with a genius model would own the market in a few years. Obviously there are trading limitations. Everyone should understand this and take claims of high returns via the use of math models with a grain of salt.

If you have any questions or comments, happy to connect on Twitter: @mikeharrisNY

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