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Testing Whether Equity Factors Affect a Trading Strategy

Article Quant Q&A · Author: CyberQuant
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Summary

The document asks how to determine whether a factor such as size changes a strategy’s performance, using backtests on large- and small-cap stock groups as an example. Comparing returns or Sharpe ratios alone does not establish that the difference reflects a persistent factor effect rather than sampling noise.

The reply suggests regressing strategy returns on market factor returns, following a mutual-fund performance framework. The intercept estimates return beyond the modeled factor exposures, while the factor loadings indicate the strategy’s associated risks; statistical tests can assess whether these estimates differ meaningfully from zero. This approach helps distinguish apparent skill from returns explained by risk exposure, but the exchange does not specify a direct test of the difference between the two portfolio backtests, nor address dependence, multiple testing, or selection bias. Its final caveat is that conclusions from a backtest may not persist as markets change.

Key ideas

  • Differences in backtested returns or Sharpe ratios alone do not show that a factor caused a performance difference.
  • A multivariate regression can estimate a strategy’s intercept and its exposures to market factors.
  • The intercept’s significance assesses returns beyond the modeled factor exposures.
  • Factor loadings help identify whether performance reflects risk exposure rather than excess return.
  • Backtest results may not persist as market conditions change.

Tags

Factor investingEquitiesStatisticsBacktesting
Full text
# How to conduct statistical test to see if certain factors impact trading streategy


# How to conduct statistical test to see if certain factors impact trading streategy












Since the seminal paper by Fama and French(1993) that uses size, market, and value factors to explain extra market returns on the equity market, people have conducted tons of research on equity factor investing. Many factors such as growth, quality, ROE, etc., were discovered and used in actual trading.

I want to test whether certain factors (for example, size, value, growth, etc.,) will have an impact on a trading strategy. For example, for size factor, I implemented a trading strategy, and I backtested the strategy with stocks in the top 30% by market valuation and holding everything else unchanged, I backtested the same trading strategy but traded with stocks in the lowest 30% by market valuation. Of course, I will get two different investment returns, sharpe ratios, etc., Looking at the two investment returns(for example, 37% and 23%), how can I conduct a statistical test so that I can argue that, statistically, with 95% or 99% confidence, the size factor is making a difference in the trading strategy and the difference in the two investment returns is not due to random noise?

Thank you in advance.

## Answer by Si Chen (score 1)

https://quant.stackexchange.com/a/68175

The Carhart 1997 paper, "On Persistence in Mutual Fund Performance", is probably a good reference for doing exactly what you're looking to do. I think you would want to do a multivariate regression of your returns against the market's factor returns. Then the regression will give you both an intercept and the loadings (betas) to each risk factor. The statistical significance of the intercept is whether you earned excess returns. The loadings will tell you how much risk you took to get your total returns. Taken together, they'll tell you if you were really good (statistically significant intercept) or just lucky (high risk loadings.)

Remember, of course, this is just a back test. Markets change.

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.