Assessing Plausible Returns with Information Coefficient and Tail Risk
Summary
The document asks whether daily trading strategy returns have a reasonable upper bound as a way to detect faulty backtests. One answer frames the issue through information coefficient, the correlation between forecasts and subsequent returns. Under perfect foresight, returns would be bounded by the compounded best daily asset returns available in the universe, or by the best long-short spread. For weaker forecasts, the answer suggests constructing noisy signals with a target information coefficient to examine implied performance.
A second answer cautions that there is no general bound for complex strategies: leverage, shorting, volatile assets, and luck can produce very large outcomes. Historical return quantiles or confidence intervals may serve as rough diagnostics, but rely on past data representing future distributions and can fail during crises. The exchange offers conceptual guidance rather than a validated screening threshold, and it does not settle what information coefficient is realistically attainable. Large backtest returns should prompt scrutiny, not automatic rejection.
Key ideas
- Information coefficient links forecast quality to subsequent returns and can help assess implied strategy performance.
- A perfect forecast would select the best available daily return, or the widest long-short spread, in the stated universe.
- No universal upper bound applies across strategies, particularly when shorting and volatile assets are involved.
- Historical quantiles can provide a rough reference but may fail when future conditions differ from past data.
- The discussion gives no validated return cutoff or definitive realistic information coefficient.
Tags
Full text
# What is a reasonable upper bound on the performance of a daily trading strategy? # What is a reasonable upper bound on the performance of a daily trading strategy? I am backtesting an equity trading strategy which trades only once per day. Is there a general rule of thumb for the reasonable upper bound on the rate of return of such a strategy? For example, a 2000% return over a week might be unrealistic, but a 20% return is possible. Identifying a reasonable limit may help me identify faulty strategies. ## Answer by Tal Fishman (score 7, accepted) https://quant.stackexchange.com/a/2119 I believe the concept you are looking for without really knowing it is the information coefficient (IC). IC is the correlation between your forecast and actual subsequent returns. If your IC is 1 (perfect correlation, also known in this context as perfect foresight), then your maximum return is the compounded sum of the greatest daily return of any stock in your universe (or of the difference between the greatest and lowest return, in case of a long-short strategy). For a lower IC, you can simulate what returns are realistic by artificially constructing a signal starting with realized returns and adding noise to get the desired IC. A separate question is what is a realistic IC. I'm not sure, but I doubt any strategies can achieve higher than 0.1. For more details, see Active Portfolio Management by Grinold and Kahn. ## Answer by SRKX (score 2) https://quant.stackexchange.com/a/2118 Quite simply, no, you can't bound returns. Assuming you can invest in several assets, and that you can short-sell, you could quite easily make a huge return by simply getting (maybe even just by pure luck) the right directions on an especially volatile way. You can't bound complex strategies daily return. If you consider buying only a single asset, the is no bound either. What you might be willing to do is to look at the distribution of past return, and take some quantile (99% for example) which would give you your limit, or basically some kind of confidence interval (and it would basically correspond to the VaR for losses). But this would be wrong anyway in my opinion, since you basically assume that all the data available right now fully characterizes the distributions of future returns, which has been proved wrong every time there has been a major crisis. Keep in mind, seeing one billion white swans is not enough to prove that all swans are white, whereas seeing only one black swan is sufficient to prove that all of them aren't white. But my main concern is: why on earth would you discard a strategy because it makes large returns or losses? I mean, how could your strategy be "faulty"???? Are you trying to detect fraud?
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