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Do you evaluate a strategy in a backtest based on the cumulative returns generated by the strategy (i.e. looking at the cumulative returns of the trades that occur) or do you start with a certain dollar amount and look at the cash at end to compute the annualized return. The reason I ask is because things like position sizing and adding position to a certain trade are much easier to do when starting out with a dollar amount in a portfolio.

I tend to look at a strategy as a collection of trades with particular entry and exit points. If using multiple entry & exit points are used for each signal (adding positions or taking off positions for each signal) it is much easier to calculate returns per trade if looking at a dollar amount that was invested due to each signal.

I have seen both approaches being used and personally prefer using returns rather than starting with a dollar amount. Just curious to see how people approach this and why.

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    $\begingroup$ In what sense are position sizing and adding positions easier with dollar amounts? $\endgroup$ – Tal Fishman Dec 4 '11 at 21:49
  • $\begingroup$ This is what I mean...I tend to look at a strategy as a collection of trades with particular entry and exit points. If using multiple entry & exit points are used for each signal (adding positions or taking off positions for each signal) its is much easier to calculate returns per trade if looking at a dollar amount that was invested due to each signal. $\endgroup$ – silencer Dec 4 '11 at 23:32
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    $\begingroup$ Now we are getting at the rub of your problem. Calculating returns "per trade" is a flawed measure. It is too easily skewed by a refusal to close out losing trades. Better to simply look at daily P&L or some other time horizon. $\endgroup$ – Tal Fishman Dec 5 '11 at 15:10
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I'd say it depends on how close you want to be to reality and what the strategy entails.

For instance one scenario when actual currency makes sense is when you want to take contract sizes and position limits into account, for instance agricultural futures contracts nearly always impose a position limit for one party in one or all contracts. If your strategy on the other hand wants to invest, say, all returns in one or more such contracts the strategy will either fail, well, not in the backtest but in the real world.

Representing hard limits like contracts sizes, position limits, minimum tick movement, etc. in terms of returns is impossible or at best questionable.

I'm sure this scenario doesn't apply to you as you can obviously go with either approach, I just want to point this out to other people that may have a similar question in a different context.

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http://www.portfolioprobe.com/2010/11/05/backtesting-almost-wordless/ shows an example of how the results from a backtest can be deceiving. This would be true with either returns or value.

The main issue is that the portfolio you start with can have an impact on what "good" means.

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We don't give strategies a dollar amount during backtesting, rather backtesting shows how much capital would be required to successfully deploy a strategy. We also don't look just at returns but many different metrics including but not limited to, max drawdown, variance of draw downs, number of trades, holding period, correlation (or lack of) with various indexes, Sharpe ratio, commissions paid, share turnover, and numerous other measures of variance. I view position sizing as a somewhat separate problem that we currently don't completely tackle at backtesting time. There may be max position sizes that a strategy can use for a given opportunity but often this is somewhat dependent on security being traded.

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I think your question may be getting at the difference between time weighted returns and dollar weighted returns. The only advantage I see to using a dollar amount is to simplify drawdown calculations. Both dollar weighted and time weighted returns are necessary to evaluate a strategy particularly when benchmarking against a competing strategy. Ignoring drawdowns by looking at a starting dollar amount and ending dollar amount will become problematic when you want to leverage the strategy and margin calls may occur.

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@hroptatyr, @Steve, @Tal Fishman, and others here have alluded to the main problem of evaluating backtests. First we have to define what constitutes a backtest, which is simply an ability to simulate market activity and how specific instructions (algo) would perform in that environment. The simulation is supposed to best reconstruct how the market would have behaved at the time. Tick level simulation is the most precise way to do this, but ms, second, and minute data is increasingly less precise, but faster to process. A strategy where intraday timing may be able to get away with minute backtesting, but more than likely you would have to at least use seconds interval as minimum to properly simulate what would have happened.

Then you need to know what the algo system is supposed to do. In other words, What category of speculation is it? (e.g. news trading, arbitrage, value trading, dealer, etc) did the algo actually perform (execute its functions) as advertised. A lot of investors who are not actually owners of the algo (black box) or have insight as to how the inputs work (grey box) will only have the usual results from the backtest (equity, total trades, sharpe ratios, etc). There is a structural conflict of interest there; you are just hoping that the live results will be similar without knowing why you were profitable. Easy to succumb to sample selection bias without covering the basics.

Then you can determine the adequate starting capital and see if the returns net of estimated trading costs make it worthwhile.

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