The following ârandom equity curve generatorâ has been referred to many times on ET: http://www.hquotes.com/tradehard/simulator.html IMHO, it provides various insights for the systematic trader. For example, I would propose the following two: Insight #1 â âItâs folly to compare two strategies based on the âshapeâ of their equity curves (e.g. âI like this strategy more than that one because its equity curve has a nice, upward-sloping shape without any big kinksâ ... I too have been guilty of such statements here on ET!). As the above generator shows, equity curve âshapeâ is largely the result of how random sequences of winners and losers play out. The same strategy could produce many different alternative equity curves, depending on how these sequences play out in practice.â Insight #2 â In building a resilient systematic strategy, it shows how important is the relationship between a) the ratio-of-average- winner-to-average-loser, and b) % winners. Any thoughts on the above? What other lessons does the random equity curve generator teach?

It's not so much that the shape of the equity curve doesn't matter so much that it is making an investment decision after the fact based on something which may not continue into the future. Nice smooth upward equity curves come from having evenly distributed losses. If it is an HFT system with 1000 trades a day, there may be a reason to think that this will continue. If this is a positional system with 100 trades where the trades happen to be alternating win/loss, then one is just cherry-picking systems based on assumed serial-correlation of trading profits. At CSI, we had a tool Trading System Performance Evaluator which does Monte Carlo analysis of the capital requirements for a trading system based on some termination conditions. It generates equity curves based on random drawings of trade profits/losses from an input trading record. From tens of thousands of these samples, it generates a graph showing the probability of various outcomes depending upon the initial risk capital. For example, the result might be that with $200k in the account, there is 0% risk of complete depletion of the account within the first 10 trades, 75% chance of at least breaking even, and a 50% of hitting a profit target of $20k. Not an absolute guarantee, but it gives one some odds on the assumption of zero-serial correlation of returns.

This is the typical monte carlo simulation. While I'm sure it's interesting for some, you can't simply randomize the trade order as the market also move in a not-so-clearly defined order. I disagree that the win rate is important and even profit factor (total profit vs total loss) is overrated - if you can guarantee near zero slippage then the only thing matters is curve smoothness and total return.

Thanks. I believe you are stating that Monte Carlo simulations arenât useful for timing trades. If I have interpreted this correctly, then I don't have any grounds to disagree with you; as far as I can tell, the âRandom Equity Curve Generatorâ doesnât provide any insights into when to take (or not take) a specific trading set up. Rather, (IMHO) its value is educative in warning that an equity curveâs shape is not a function solely of the systematic strategyâs performance metrics (e.g. itâs Sharpe Ratio, average trade, % winners, etc), since random chance also plays a very significant part (under the assumption of zero-serial correlation of returns, to borrow the terminology introduced above by Steven.Davis). Therefore clear, certain conclusions about the relative merits of two systematic strategies cannot be reached solely by comparing the equity curves they generate; further information is required... What the âGeneratorâ does make clear though is that if a systematic strategy has a âWin/Loss Ratioâ (which for the "Generator" is defined as average winner divided by average loser) = X, then it needs to have a Win Probability > P if you are to have a, say, <1% chance of incurring a net loss after N trades. For a concrete example, take: Win/Loss Ratio = 0.5 (i.e. average winner is 50% of average loser) Lines Qty = 100 Trial and error suggests Win Prob > 0.71 to be sure of a <1% chance of not being positive after â453 barsâ. Note, this is a completely different calculation to saying Win Prob must be > 0.66... to give a PF > 1.

@abattia, monte carlo simulation stress tests are used to get better feeling for possible chances (profits) and draw downs (losses). Input data is a typical system test report of your system. Another way to use MCS methods is to generate "artificial" data (based on your original data) for use in your system tests. All this is described on my website - see this free article: http://www.zentrader.de/mcs_article_traders2007.pdf bye, zentrader

Rather, (IMHO) its value is educative in warning that an equity curveâs shape is not a function solely of the systematic strategyâs performance metrics (e.g. itâs Sharpe Ratio, average trade, % winners, etc), since random chance also plays a very significant part (under the assumption of zero-serial correlation of returns, to borrow the terminology introduced above by Steven.Davis). Therefore clear, certain conclusions about the relative merits of two systematic strategies cannot be reached solely by comparing the equity curves they generate; further information is required... ____ +1 to the above observation. One thing i can add is; once one observes thus and the fact that chance plays a huge role sink in, there comes a point in system comparison where too good is bad; and good enough is probably the best - giving chance a chance to work itself out. And the most important thing is to have a set of good enough systems that you feel comfortable trading with; which hopefully complement each other in philosophy. Secret sauce then becomes the simple act of nature/chance playing out (survival of the fittest); and all that is left for a system designer/trader to do is to grind his teeth if he has to and shoot for perfect execution. Then add diversification across instruments and viola - there's about 10years worth of work - carved out for the entrepreneur.

The assumption in MC simulations is that when the null hypothesis is true, all of the n! possible permutations, including the original trade sequence, have an equal chance of appearing. This assumption is violated for many different types of trading systems including those that rely on trends, S&R, overbought/oversold levels, you name it. Serial dependence violates MC simulation assumptions. MC simulation tells you nothing for most systems other than the fact that it is a good mental masturbation. The person who developed that silly java knows nothing about real trading systems and MC simulation.

Thanks. Why is the assumption of zero-serial correlation violated in the system case examples you identify (i.e. trend-based systems, Support&Resistance, overbought/oversold levels)?