# Should Sharpe ratio be computed using log returns or relative returns?

I am trying to reconcile some research with some published values of 'Sharpe ratio', and would like to know the 'standard' method for computing the same:

1. Based on daily returns? Monthly? Weekly?
2. Computed based on log returns or relative returns?
3. How should the result be annualized (I can think of a wrong way to do it for relative returns, and hope it is not the standard)?
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In long-short equities, it's common to use daily returns in $\frac{\mu}{\sigma}$ and then multiply by $\sqrt{252}$ to annualize.

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daily returns as percents or in log returns? –  shabbychef Jul 22 '11 at 16:41
@shabbychef Neither. Just use the dollar returns. –  chrisaycock Jul 22 '11 at 18:21
what exactly do you mean? returns with dollar units? –  shabbychef Jul 22 '11 at 18:47
@shabbychef Correct. Just use the daily P&L in dollars. –  chrisaycock Jul 22 '11 at 20:20
that really makes no sense to me. If the AUM of the fund changes (investments/disbursements), or there is a split in the stock, or a large change in nominal value, you cannot compare dollar returns from one time period to another. Did I misunderstand your comment? –  shabbychef Sep 7 '11 at 4:20
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I don't feel I can give you an authoritative answer on what the "standard" approach is, maybe someone with more hands-on experience will be able to help. But my quick thoughts.

As to the period, I've seen both daily and monthly returns being used. Weekly probably not that often. But in the end you annualize them either way to make them comparable.

The method I know is to multiply by $\sqrt{12}$ (for monthly data) - as can be seen in Kestner, 2003.

I would go with log returns, but it's rather gut instinct. I haven't really thought about it, so feel free to correct me/validate this statement.

There's one implication to arbitrarily changing your measurement interval - it can (should) alter the deviation. See Spurgin, 2002 for details.

And all this has to be done under the assumption that you can define your performance using only two first moments of the distribution. But the pitfalls of using Sharpe ratio - that's another issue to discuss.

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Yes, daily log (excess) returns are most often used in scholar articles to calculate Sharpe ratio, which then can be annualized. –  Dmitrii I. May 2 '11 at 13:49
Note that annualizing with square root of time implies that the asset returns are i.i.d. –  Quant Guy Jul 20 '11 at 1:00
Nowadays most quantitative researchers choose to use Information Ratio, developed and popularized by Grinold and Kahn (1999), as the gold standard for performance evaluation. Generally, though, it is called a Sharpe Ratio if returns are measured relative to the risk-free rate and an Information Ratio if returns are measured relative to some benchmark. Calculations may be done on daily, weekly, or monthly data, but results are always annualized (and typically by a factor of $\sqrt{252}$ for daily equities, $\sqrt{260}$ for daily FX, or $\sqrt{12}$ for any monthly series).