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Choosing Absolute or Squared Hedging Errors for Risk Evaluation

Article Quant Q&A · Author: sooprise
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Summary

The document asks whether hedging strategies should be compared using the absolute values of their errors or the squared errors. One response favors squared-error summability, noting that it is a weaker requirement than absolute summability and that squaring makes larger deviations contribute more heavily to the score. This makes the metric more sensitive to sizable hedge misses, which may matter when evaluating risk control.

A second response disagrees, preferring absolute errors in many practical settings and pointing to price volatility that can register as apparent hedging error, especially around closing prices. The exchange therefore highlights a trade-off: squared loss emphasizes large errors, while absolute loss is less dominated by outliers. It does not settle which metric is generally superior or analyze the example sequences quantitatively. The choice depends on the evaluation objective, error distribution, and how observed price noise relates to the hedge being assessed.

Key ideas

  • Absolute and squared error measures assign different relative importance to large hedging misses.
  • Squared errors give larger deviations more influence on the total score.
  • The responses disagree about which measure is preferable in practical hedging evaluation.
  • Observed price volatility can complicate the interpretation of measured hedging errors.

Tags

Risk managementDerivatives pricingStatistics
Full text
# Is it better to grade hedging strategies based on the sum of absolute or squared hedging errors?


# Is it better to grade hedging strategies based on the sum of absolute or squared hedging errors?












Let's say I have one strategy that has a hedging error of:

2, 2, -2, -2

Let's say I have another strategy that has a hedging error of

.5, .5, 3, 3

Would it be a better idea to grade the hedging strategies based on the sum of hedging errors (absolute value) or the sum of squares of hedging errors? Why?

## Answer by dangiankit (score 5, accepted)

https://quant.stackexchange.com/a/2009

In practice, absolute summability of hedging errors may not be applicable. Mostly, for the sequences of hedging errors, one relaxes the absolute convergence criteria and uses the squared summability of hedging errors. Note: Absolute summability is a stricter condition than squared summability. Some sequences may not be absolute summable but are only squared summable.

Also, to notice the significant impact of the error and to make it visible is one of the prime reasons for using sum of squares for hedging errors. Remember, we're talking about managing or controlling risks, the finer we notice the errors, the useful it shall be. :)

## Answer by Michael WS (score 0)

https://quant.stackexchange.com/a/2038

Honstly, I have to disagree. I would almost always prefer sum of errors instead of squared sum of errors unless my holding periods were very short.

There is a good amount of vol in (especially closing) prices that would be real hedging errors . Imagine a trading strategy that is a near perfect hedge. Say trade SPY versus SH. Would you rather have sum of squared errors or sum of hedging?

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.