I didn’t read Pedro’s post as a kind of marketing. It was a counter example. Matthew didn’t make the same point: He wrote that closing and opening wouldn’t affect the Sharpe ratio, while the point of Pedro is that big winners do not necessarily spoil the Sharpe ratio. It is good to have counter examples and it is only natural that someone has a little preoccupation with his own systems.
Jules
I would like to correct something. My second example was a wrong one (looks like nobody noticed) because that was actually evidence for Hans’ theory.
The correct comparison would be between Pannonia and Bender, and goes like this: Pannonia has a higher Sharpe ratio even that it has bigger wins then Bender, thus Hans theory of “big wins screw up the Sharpe ratio” doesn’t apply. And Matt might have made the same point earlier, but sure he didn’t provide examples…
Chris, I don’t want to interrupt your academic discussion of Sharpe ratios and such, but people should realize something:
C2 is only a wonderful piece of software without:
1. Vendors with profitable and followable systems AND integrity.
2. People who are willing to subscribe to those systems.
I think we already have enough people from the #2 group, what C2 needs is not another 10 statistical indicators and extra columns on the main board, but more consistently reliable,profitable and followable systems.
Honestly, if you take away Sharpe ratio, winning % and anything else, except the equity curve and the trades, I still can decide which system is good and which one is bad. And there are only a handful of good ones…
But please continue the academic discussion and sorry for interrupting…
I also have been thinking about something Pal said, that the periods over which the Sharpe gets calculated differ when the system gets older. Weekly, Monthly, Quarterly… Is this true? If so, then I would vote to scrap Sharpe Ratio completely. From what I read and saw by doing a few trial runs in Excel, Sharpe Ratio results differ drastically depending on the period it is calculated on. That would not be fair then to compare a system with a year of trade history and Sharpe Ratio calculated over Quarterly periods, against a new system with Sharpe Ratio calculated over weekly periods. A new system with a good month, will almost always have better sharpe ratio than a decent system with a good year, but a case can be made that the system with longer history is more reliable since it has proven itself already.
>On the same token, this will also not be fair to compare all systems with Sharpe Ratio calculated over weekly periods when weekly period calculation will favor more active and short term systems over long term systems.
The annualized values should be about the same regardless of the sampling period (yearly, quarterly, monthly, weekly, daily, etc.) if the distribution is “normal”. In actual fact, it isn’t quite “normal” so the standard deviations calculated for shorter periods tends to be somewhat larger than for longer periods.
ps: If you are compounding your returns, that is, investing in the next
period, the value of your account at the end of the previous period,
you need to use logarithmic returns to account for the compounding
but this is a small refinement.
If you use logarithmic monthly return samples, then the monthly return would be multiplied by 12 to get the annualized return.
The monthly standard deviation is multiplied by the square root of 12 to get the annualized standard deviation. (Actually, the monthly variance is multiplied by 12 but the standard deviation is the square root of the variance.)
Sharpe Ratio= 12 mo_return / (SQRT(12) mo_standard_deviation) [for futures]
so
Sharpe Ratio = SQRT(12) mo_return / mo_standard_deviation; [for futures]
If you are trading stocks or mutual funds that require using money (as opposed to margin) to buy the positions, then you need to use the “excess return” (in excess of the risk-free rate) in the above equations in order to substract the interest one would have received if invested in a money market instrument.
I just noticed that the Sharpe Ratio has been modified for all systems. Particularly, the Sharpe Ratio for newer systems is not being calculated. This makes it very difficult to compare two similar systems, whether newer or older.
The Sharpe Ratio is independent of the sampling interval if the returns are normally distributed. Returns are typically not strictly normally distributed so the sampling interval will affect the results somewhat. There should be atleast about 30 samples to get reasonable accuracy, so I would use daily samples for 2 to 9 months (40 to 180 days or 8 weeks to 36 weeks) of trades, weekly samples for 9 to 36 months (36 to 144 weeks of trades), monthly samples for 36 to 360 months (144 weeks to 1440 weeks) etc. to compute the Sharpe Ratio. That should cover almost all systems/methods at C2. The relevant formulas would be:
Sharpe Ratio= 253 X daily_return / (SQRT(253) X daily_standard_deviation) [for futures or forex or stocks traded with margin]
or
Sharpe Ratio = SQRT(253) X daily_return / daily_standard_deviation; [for futures or forex or stocks traded with margin]
or
Sharpe Ratio= 52 X weekly_return / (SQRT(52) X weekly_standard_deviation) [for futures or forex or stocks traded with margin]
or
Sharpe Ratio = SQRT(52) X weekly_return / weekly_standard_deviation; [for futures or forex or stocks traded with margin]
or
Sharpe Ratio= 12 X weekly_return / (SQRT(12) X weekly_standard_deviation) [for futures or forex or stocks traded with margin]
or
Sharpe Ratio = SQRT(12) X weekly_return / weekly_standard_deviation; [for futures or forex or stocks traded with margin]
ps: If one is compounding returns, that is, investing in the nextperiod, the value of your account at the end of the previous period, one needs to use logarithmic returns to account for the compounding but this is a small refinement, nevertheless an important one.
The annualized values should be about the same no matter how frequently one takes the samples. In theory, they will be independent of how frequently one take the samples, if the returns have a “normal” (Gaussian) distribution. In practice, returns tend to be not quite “normal” but are a little narrower in the middle and have fatter than normal “tails”, but this is not a reason to discard Sharpe Ratio calculations for newer systems/methods.
I would also, for stocks (without margin) assume a constant value of 4.75% for the risk-free return (T-Bill interest rate). This is a good assumption for recent times but may be incorrect for the distant past.
I guess this is quite easy to figure out, but the formula mentioned above is not accurate. Here is the corrected version:
Sharpe Ratio= 12 X month_return / (SQRT(12) X monthly_standard_deviation) [for futures or forex or stocks traded with margin]
or
Sharpe Ratio = SQRT(12) X monthly_return / monthly_standard_deviation; [for futures or forex or stocks traded with margin]
