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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?

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Both are valid, but in terms of what is "commonly accepted," probably better to go with sum of squares. –  Tal Fishman Sep 22 '11 at 20:29
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Tal, why is the sum of squares used in particular? Why not take the sum of absolute values multiplied by two? I'm not disagreeing with you, I just am trying to understand why using the sum of squares in particular is preferred. –  sooprise Sep 22 '11 at 20:35
    
Because risk models are typically evaluated in terms of $R^2$, which corresponds in your case to sum of squared hedging errors. –  Tal Fishman Sep 22 '11 at 21:20

2 Answers 2

up vote 4 down vote accepted

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. :)

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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?

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