# A Few Spins Of The Wheel

Last week we talked about the casino’s edge which in the trading world is called expectancy, but all that expectancy tells us is whether or not our trading strategy is likely to be profitable or not—but not how much money we might make.  How profitable depends on how often we have a chance to trade our system—will it be a few times a year, a few times a week, or many times per day.

And this is also how our casino makes money—calculating the edge is easy, but the number of hands dealt or spins of the wheel in an hour start to tell us the profit potential.  Going back to the statistics from a real casino in Las Vegas, let’s look at how profitable a few games are when we combine their edge with hands (spins) per hour—let’s assume a \$10 average bet, and ten bettors per table, except for Black Jack where we assume five bettors per table:

 Game House Edge Hands Per Hour Revenue Per Hour Per Bettor Revenue Per Hour Baccarat 1.2% 72 \$8.64 \$86.40 Black Jack 0.8% 70 \$5.60 \$28.00 Craps 1.6% 48 \$7.68 \$76.80 Roulette 5.3% 38 \$20.14 \$201.40

Ever wonder why so many people play Black Jack??  They can play for a very long time before losing all their money.  For example, if a bettor came in with \$200 and was placing \$10 bets, he could still be playing at the Black Jack tables 35 hours later, but the odds are he would have blown everything in just ten hours at the Roulette table.

And of course the house likes someone with a hot hand since it draws more and more people to the table which increases the total number of bettors and the total amount bet.  It’s a numbers game, and while it is impossible to predict the house take for any given day, it is quite simple to predict it for longer timeframes.

And so it is with a trading system that has been thoroughly vetted.  Total profit potential is the expectancy times the number of trades per day—sometimes called opportunity.  And of course we have to account for commissions and slippage, which have a minimal impact on positions held for days or even months, but which can destroy the returns on an otherwise profitable system that trades several times per day.

1)      We will assume the same trading system is used for each timeframe, and that it generates a trade on average every 20 bars.  If it is applied to a weekly chart, there would be a trade every 20 weeks, or about 2.6 times per year.  With a daily chart, it would be every 20 days, or about 12.5 trades per year, and so on.

2)      Let’s assume that the expectancy is based on an average position size of \$10,000.

3)      We will also assume friction to be \$0.03 per trade, where friction is defined as commissions plus slippage.

4)      Return on capital assumes no leverage—return on buying power would be higher in all timeframes, and much higher at the lower timeframes.

 Periodicity Expectancy After Friction Trades Per Day Gross \$\$ Per Day Gross \$\$ Per year Return On Capital Weekly \$500.00 \$499.97 0.01 \$5.00 \$1249.92 12.5% Daily \$125.00 \$124.97 0.05 \$6.25 \$1562.13 15.6% Hourly \$30.00 \$29.97 0.35 \$10.49 \$2622.38 26.2% 15 Minutes \$15.00 \$14.47 1.3 \$18.81 \$4702.75 47.0% 3 Minutes \$4.00 \$3.97 6.5 \$25.81 \$6451.25 64.5% 1 Minute \$2.00 \$1.97 19.5 \$38.42 \$9603.75 96.0%

And this is where systems trading starts to really shine—at the lower timeframes where we can trade tens or hundreds or even thousands of different stocks concurrently.

The high frequency and ultra high frequency strategies are an extreme example of this where they make hundreds of thousands of trades per day—even millions of trades per day–often with a gross return of a fraction of a penny per trade. Even at \$0.001 expectancy per trade (net of friction), 100,000 trades would yield \$100, and assuming the same \$10,000 position size, that is \$25,000 per year which is about 250% return on capital unleveraged—not too shabby—and of course the machines make many more trades than that and the position sizes are much larger—do the arithmetic and you will see why high frequency trading has become the new best thing.

There are really three basic approaches to systems trading:

1)      The algorithms generate signals that a discretionary trader uses in conjunction with his normal strategies.

2)      The system is traded as a gray box where a human trader decides whether or not to take each signal.

3)      And as a black box where the computer takes every signal.

This mirrors the number of trades that can be executed per day.

1)      If a discretionary trader uses the signals in conjunction with his other strategies, hopefully his returns per trade will improve, but it is unlikely he will see a significant increase in the number of trades per day that he can handle.

2)      If a trader operates with a gray box, there not only is the possibility of higher returns per trade, but significantly more trades per day, so the return on capital or buying power can be significantly improved.

3)      And of course a black box can handle an unlimited number of trades, so the only question is what is the lowest timeframe in which the algorithms will deliver a positive expectancy net of all friction, and what is the total number of stocks, FX pairs, commodities and so forth that can be traded at the modeled expectancy.  For example, some strategies might be better using high beta stocks while others are better with low beta stocks, and of course if the strategy trades long/short, it might not always have an ample list of easy to borrow shares depending on market conditions.

Next time we will look at how you can lose all your money even with a trading system that has a high expectancy

Author:  Rick Martin

Hypothetical computer simulated performance results are believed to be accurately presented. However, they are not guaranteed as to accuracy or completeness and are subject to change without any notice. Hypothetical or simulated performance results have certain inherent limitations. Unlike an actual performance record, simulated results do not represent actual trading. Since, also, the trades have not actually been executed; the results may have been under or over compensated for the impact, if any, of certain market factors such as liquidity. Simulated trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any portfolio will, or is likely to achieve profits or losses similar to those shown. All investments and trades carry risks.