Model risk is the risk that a model is, or will become, unable to perform the tasks it was designed to do. In terms of trading, this can be the risk that a set-up stops working, the risk that a variable loses its predictive power, etc. Ever-changing market conditions mean that model risk is a significant issue for most systematic traders: managing it is an integral part of adapting to new market environments.

Two heuristic rules are commonly used to handle this risk: drawdown-based position sizing, and a maximum drawdown cutoff. The former involves reducing exposure depending on drawdown (e.g. position sizes will be halved below 10% drawdown); the latter technique simply stops the strategy if it ever reaches a specified drawdown cutoff.

To investigate the efficacy of these rules, I’m going to use a simple Monte Carlo approach. The basic strategy has returns drawn from a normal distribution with mean 0.20% and  standard deviation 1.5%. Model risk is represented by a small chance (0.05% per cycle) that the returns distribution will permanently change to having a mean of -0.05%.

Equity curves for 100 simulations, no model risk.

Equity curves for 100 simulations, with model risk. Bold equity curves show simulations in which the model switched to the “failed” state.

The rules for dealing with the risk are as follows: equity curve-based position sizing will decrease positions by 25% if the drawdown is below 5%, and by 50% if the drawdown is below 10%. The cutoff simply stops trading if the drawdown ever reaches 25%.

Equity curves for 100 simulations, with model risk and a drawdown limit of 25%.

Running 10,000 simulations with 1,000 steps each, the results are shown below:

The first thing to note is the obvious fact that, without model risk, these heuristics have a negative effect on risk-adjusted returns. Yes, maximum drawdowns are decreased on average, but at an unacceptable cost to returns. In the case of equity curve-based position sizing, the average drawdown is deeper and longer as well. The lesson should be obvious a priori but deserves to be stated anyway: if you are confident that a strategy will continue to work well in the future, you should abandon such rules.

Note that these results assume that the returns distribution remains constant; some real-world strategies such as trend following futures exhibit higher than average returns after drawdowns, so decreasing exposure at those times would be even more hurtful. The inverse may be true of other strategies.

Things change when we look at the results after including model risk. Both heuristics improve risk-adjusted returns, with the drawdown cutoff being particularly effective. While equity curve-based sizing improves on the vanilla case, it actually harms returns when combining it with the cutoff. This is presumably because the cutoff already takes care of all the failed strategies (and even more: while 38.5% of strategies failed, 42.6% of them hit the drawdown limit) and the variable sizing only serves to hurt the healthy ones.

Setting the drawdown limit for each particular strategy is a bit trickier. The maximum drawdown of a backtest should serve as a guide. This can be augmented either by assuming normal returns and using the results in On the Maximum Drawdown of a Brownian Motion, or through Monte Carlo simulation.

In the real world there are, of course, infinite states between the model working perfectly and it not working at all, so one must leave some room for deterioration and temporary changes by widening the cutoff point a bit. Finally, a more rigorous approach would perhaps use some sort of regime change detection and stop trading when the mean of the returns is determined to be below a hurdle, at a particular level of confidence.