# What is a reasonable upper bound on the performance of a daily trading strategy?

I am backtesting an equity trading strategy which trades only once per day. Is there a general rule of thumb for the reasonable upper bound on the rate of return of such a strategy? For example, a 2000% return over a week might be unrealistic, but a 20% return is possible. Identifying a reasonable limit may help me identify faulty strategies.

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I am sorry but your question doesn't really have a sense, sure if 20x is impossible then it will not happen. If there is a fault it's not your strategy that is wrong, it's your backtester or your market data, in that case it's no use putting a limit, your 1.2x return will be faulty too. –  Lliane Oct 6 '11 at 12:37
Please pay attention to formatting a little bit. It was hard to simply read the question at first. –  SRKX Oct 6 '11 at 13:20
@Lliane I disagree. Sometimes your signals make use of forward-looking information and you don't even realize it. Establishing what is a reasonable upper bound may help identify some of the most egregious cases of look-ahead bias, but it is nothing but an initial filter, as many pernicious forms of look-ahead bias have a way of sneaking into your backtest. –  Tal Fishman Oct 6 '11 at 13:58
@lliane If you're looking at OTCCB trades, its quite easy to get even 80x in a year [assuming the company never goes under], but in a week... thats not very likely. –  monksy Oct 6 '11 at 14:22
@TalFishman: you literally rewrote the whole question haha ;) Id' still separate it on several lines though... –  SRKX Oct 6 '11 at 14:22

I believe the concept you are looking for without really knowing it is the information coefficient (IC). IC is the correlation between your forecast and actual subsequent returns. If your IC is 1 (perfect correlation, also known in this context as perfect foresight), then your maximum return is the compounded sum of the greatest daily return of any stock in your universe (or of the difference between the greatest and lowest return, in case of a long-short strategy). For a lower IC, you can simulate what returns are realistic by artificially constructing a signal starting with realized returns and adding noise to get the desired IC.

A separate question is what is a realistic IC. I'm not sure, but I doubt any strategies can achieve higher than 0.1.

For more details, see Active Portfolio Management by Grinold and Kahn.

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Quite simply, no, you can't bound returns.

Assuming you can invest in several assets, and that you can short-sell, you could quite easily make a huge return by simply getting (maybe even just by pure luck) the right directions on an especially volatile way.

You can't bound complex strategies daily return.

If you consider buying only a single asset, the is no bound either.

What you might be willing to do is to look at the distribution of past return, and take some quantile (99% for example) which would give you your limit, or basically some kind of confidence interval (and it would basically correspond to the VaR for losses). But this would be wrong anyway in my opinion, since you basically assume that all the data available right now fully characterizes the distributions of future returns, which has been proved wrong every time there has been a major crisis.

Keep in mind, seeing one billion white swans is not enough to prove that all swans are white, whereas seeing only one black swan is sufficient to prove that all of them aren't white.

But my main concern is: why on earth would you discard a strategy because it makes large returns or losses? I mean, how could your strategy be "faulty"???? Are you trying to detect fraud?

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If you are getting a strategy that is averaging 8000% in one week I'm fairly sure the SEC will lock you up for something, however in a year it might be possible. In any manner, you know what your lower bounds for the amount (-1*Commission) –  monksy Oct 6 '11 at 14:29
Sorry but, I don't get your last sentence... –  SRKX Oct 6 '11 at 15:28
So if the trade commission is $8 the minimum result of the trade is: -$8 [you lost all of your original capital + the commission] (in my system a buy is treated as "you don't have access to the capital anymore) –  monksy Oct 6 '11 at 16:40