Skip to content
All library documents

Comparing Statistical Evidence Across Trading Strategy Horizons

Article Quant Q&A · Author: Tal Fishman
Read the original

Summary

The discussion asks whether a strategy with a shorter average holding period deserves preference when two strategies otherwise have similar performance statistics and costs. The question raises a key inference issue: serial correlation in strategy P&L can affect standard errors and the apparent confidence in expected returns, but short-horizon strategies may also have autocorrelation beyond their holding periods.

The answer argues that long-horizon predictability can show higher t-statistics and fit measures when predictor persistence and overlapping returns create common sampling error. It cites prior research on this phenomenon and suggests that equal information ratios may not mean the strategies are equally attractive. The response further proposes that shorter-horizon strategies may offer optionality, but does not define or measure that advantage. The exchange is conceptual rather than a complete comparison method; it does not provide a worked adjustment for serial dependence or a general test for choosing between horizons.

Key ideas

  • Serial correlation in strategy returns can affect standard errors and inference about expected performance.
  • Persistent predictors and overlapping returns can raise long-horizon fit statistics through shared sampling error.
  • Similar reported information ratios do not by themselves settle which strategy horizon is preferable.
  • The answer suggests shorter horizons may offer optionality, but does not quantify that benefit.

Tags

StatisticsBacktestingRisk management
Full text
# Are shorter holding period strategies better?


# Are shorter holding period strategies better?












Consider two statistically identical strategies (identical information ratios, sample size, ratio of transaction costs to total profit, etc.) except that one has a much shorter average holding period. Is there a statistical reason to favor one over the other?

At first blush, it would appear the statistical confidence in the expected return to the two strategies is identical. One way to measure statistical confidence is to regress the P&L time-series on a constant and examine the t-statistic. Using OLS, these two strategies would yield identical t-stats. However, the longer holding period strategy may be expected to have greater serial correlation, and so perhaps we should adjust the standard errors. Of course, even short horizon strategies can display autocorrelation in P&L beyond the holding period, so perhaps this is not a reason to prefer one over another.

My intuition says I should prefer the short holding period strategy, but I have been unable to find a solid reason why, and in particular how I would measure the strength of this preference.

Note: This question is a follow-up to my previous question: How much data is needed to validate a short-horizon trading strategy?

## Answer by Ram Ahluwalia (score 7, accepted)

https://quant.stackexchange.com/a/1930

This is a partial explanation in that trading strategies with longer horizons have higher information ratios, t-statistics, slope coefficients, and R^2 in general.

In other words, if information ratios for both strategies are identical then the longer-term trading strategy is already worse.

John Cochrane illustrates how longer horizons have higher t-stats and information ratios in various lectures including "Discount Rates" -- a fantastic read for its other ideas as well.

Fama and French (1998) initially documented the fact that long-horizon models have higher fits. This spawned a slew of statistical research to understand why this peculiar feature would hold.

This research is summarized in Boudoukh, Richardson, and Whitelaw (2006) who find that it is not the case that predictability somehow "emerges" at long-horizons but rather higher R^2 occurs when you have i) persistency (auto-correlation) of the predictive variable and ii) overlapping returns, and therefore iii) common sampling error in the coefficient estimates.

If you can contrive a scenario where these effects do not hold or are controlled for then your question stands. On that front, I would argue that shorter-term horizon trading strategies generate optionality and so should be preferred to longer-horizon models.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.