Most mechanical or system traders are familiar with the concept of R or risk per trade as a percent of equity – I believe that Van Tharp did a great deal to popularize the usage of R. When dealing with many such systems, R can pretty easily be varied by increasing leverage. The question arises, what is the optimum bet size R for a given system? The math-turbational answer might involve the Kelly Criterion, and indeed, for a hedge fund manager, it might be the right answer, because playing with other people’s money provides them the luxury of viewing risk differently than a retail trader can. For the retail schlump, however, assuming that one has some backtested system data, such as equity curves at various R, and a Monte Carlo simulator, I don’t think that the RIGHT answer has anything to do with Kelly. Even without sophisticated software, the RIGHT answer for a retail trader can be approximated without talking to Kelly about it – at all.

Just remember, an examination of bet size in isolation presupposes that the other variables in your system, such as choice of instrument, entry rules, and exit rules (including initial and other stops), are already set. Obviously, this post if aimed at the more active system traders …

Using the test data, assemble some basic information at various bet sizes (R), such as the backtested cumulative annualized growth rate (CAGR), maximum drawdown (DD), and Monte Carlo simulated 90% confidence DD and Monte Carlo simulated risk of a trading-ending margin call.

Start at the highest R and look at the Monte Carlo risks of going bust. Do you want to go bust? If not, cross out any options that have non-zero numbers here. If you don’t mind some risk of going back to live in your parents’ basement, cross out only those non-zero numbers that seem “too high” to you (masochist!).

Start at the highest remaining R. Picture in your mind the amount of trading equity you will commit to the system. Now imagine you start trading this thing, and by the end of 2008 you have lost that Monte Carlo simulated 90% confidence DD amount! Would that give you an ulcer? Would a loss of that particular amount make you stop trading your system? Would that loss amount cause bitter arguments with you and your spouse? Then maybe that R level should be crossed off of your list. Continue this process until a DD level is reached that you find tolerable. Now check the CAGR against your predetermined absolute benchmark, and decide if this system is worth pursuing.

Remember, trading is not an arena where you should be concerned with how you think others view you, or to be deluded about how you view yourself. It’s not “manly” or commendable to try to trade a system that’s beyond your own gut-level risk tolerance; the courageous and smart thing is to know what you can tolerate, and what you cannot tolerate.

The answer to what you should do is inside you.

Even if you don’t have access to software that spits out Monte Carlo simulations and equity curves, if you have enough backtested system trades in a spreadsheet, you can get somewhere near the same process. Grab your data and some of the statistics links from my links page, and get cracking. Take your number of trades and percentage of losing trades from test, and assemble a table of confidence intervals around what the system’s percentage of losing trades might be. Use 90%, 95%, 99%, or whatever else you think is appropriate, but using those three will give you a start. Take the “worst case” or highest percentage estimate from each interval, and bring it to another table.

In this second table, use the losing percentage estimates to calculate the number of consecutive losses that might occur with 50%, 90%, 95%, and 99% odds against. Lay out the different confidence interval odds on the left column, the odds against consecutive losses on the top row, and fill the table with results.

For example, suppose my system has 99% confidence of a loss rate no worse than 65%. I want to fill the table cell for my 99% odds against number of trades. Using Excel’s Log function, I take Log(1-0.99,0.65) as equal to 10.69. In other words, with this 99% confidence estimate of my system’s loss rate, I should expect a losing streak of 10-11 consecutive trades to happen about 1% of the time.

When this table is assembled, you’ll have a rough idea of what kind of losing streaks are common and uncommon, and what kind of losing streaks you might expect at an extreme – which you’re certainly GOING to see if you trade for any length of time! Take this data, and multiply those consecutive loss counts by your prospective candidate R amounts, and give ‘em the old stomach test!

Stepping up a bit in complication, if you know the frequency of trades per unit time that your system yields, you could do your own calculation of maximum losing streak over the next ten years of trades, or assemble a spreadsheet Monte Carlo of your own.

Regardless of the math used to see the results, the answer to what you should do is inside you.

Kelly Criterion gives a very incomplete picture of the results, and one that’s not intuitive to a retail trader following the system. For example, a long-term trend-following (LTTF) system may pay winners average twice losers and win 35% of its trades, yielding a Kelly Bet optimum of 2.5% of equity per trade. The volatility of results at that level could be bone-chilling! A money manager can bail on a fund if it draws down too much, losing its investors, but the same drawdown might make the retail trader demotivated, or drive them out of the game if they’re dependent on their trading for income. Much better in my opinion to rely on simpler math that produces intuitive results like drawdown odds, and use those intuitive results and gut feel to determine if a given system is “for you” or not.

There’s one final thing that needs to be said about Monte Carlo simulations and statistical treatments of test data. Monte Carlo is only as accurate as the input data – it’s stringing trades or segments of equity into random orders. There could be, in the next ten years, some event that occurs naturally but just wasn’t in your test data, that blows your system past those parameters. That event could be good for you, or bad for you. You should think about whether you can live with the worst of it. Even using the less sophisticated method from “per trade” data, you should accept the inaccuracy of all backtested results and data derived from them as part and parcel of viewing only a SAMPLE of all potential price action.

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To view my actual trades and model portfolios for the different systems I track, visit The Rempel Report. If you’d like to become of member of The Rempel Report, you can register here. At The Rempel Report, I track model portfolios for four different mechanical trading systems, disclosing all results (good and bad) at regular intervals. I also track my personal portfolio, and disclose all trades before I make them. Members receive email notification of new posts and can contribute to the site through comments. Registration is still free!