How advanced mathematics and gaming theory can help you as a trader - Psychology and Money Management | futures io social day trading

 Updated: February 5th, 2016 (02:10 AM) Views / Replies: 35,486 / 203 Created: March 19th, 2011 (02:00 PM) by RM99 Attachments: 16

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worldwary

You are talking about a winning and a losing system. If the both the winning system and the losing system persists over a longer period of time, this simply means

- that you have streaks of bets with a higher expectancy, and streaks of bets with a lower expectancy
- or otherwise put that the trades a positively correlated

Now assuming that the bets of the winning and the losing system taken my themselves do not show any correlation, the overall system will show positively correlated bets. This can be exploited by adapting position sizing via progressive betting.

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whatnext
 Fat Tails and anyone else who doesn't buy the system- Do you feel that Nickemp's charts don't represent typical results or that their formula is flawed?

I have not checked them, but I think that @Nickemp's results are genuine. So what he clearly showed is that his progressive betting approach increased the returns relative to the win rates.

The point is not the (correct) result, but the explanation.

By using the progressive betting system, he also doubled position size. For any system with a positive expectancy, if you double your position size, you will double your returns. If you trade 1 contract over a year and get a return of \$ 30,000, you will possibly earn \$ 60,000 when trading 2 contracts. This also implies higher risk.

When you apply a progressive betting system to uncorrelated bets (which makes no sense), you may still benefit from the side effect of increased position size. But then you do not need the system, you can simply double your position size and leave it that way, which would even reduce the dispersion of the cloud shown on the graph presented by Nickemp.

Last edited by Fat Tails; April 14th, 2011 at 10:03 AM.
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 April 14th, 2011, 07:34 AM #93 (permalink) Elite Member Rockland county , New York   Futures Experience: Intermediate Platform: NT 7 Favorite Futures: CL, 6E, SI, ZC     Posts: 235 since Mar 2011 Thanks: 340 given, 80 received I thought the strings would equal out because they are based on a 50% chance. It doesn't intuitively make sense to me either and you explained the reasons why much better than I could have. Most of my "thanks" have been to you btw for taking the time to be helpful so often. Here's where I am now.. If the expectancy of extended strings to occur regularly is valid and the loser at the end doesn't wipe out the profit margin - increasing the position size accordingly is no longer an uncorrelated bet. I bet others will eventually tinker with and replicate Nickemp's work and that might be more convincing.

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worldwary
 ...the profits posted in those charts would be higher if you used a larger bet on all trades than if you used a larger bet only during strings of wins. To see this clearly you'd need another chart showing the results of a fixed position size using a larger bet. Increasing bet size after a win would make sense if the odds of a win increased with each win, but the assumption in these examples is that the odds of a win are fixed. In that case what you want to do is find the optimal bet size and use it on each trade since each trade is equally likely to give you a profit.

Maybe it's just over my head - I can't calculate what the results would be for a larger fixed position size on all trades in my head - but it doesn't make sense to me.

If raising the wager 50% at the start of a string is the optimal betting size; the success of isn't because you have any better chance on that next flip. Rather the combination of strings occurring naturally, compounded with the continual increase in leverage, would make the average return greater on whatever the likely hood of having long enough strings or/and enough of them.

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whatnext
 Maybe it's just over my head - I can't calculate what the results would be for a larger fixed position size on all trades in my head - but it doesn't make sense to me. If raising the wager 50% at the start of a string is the optimal betting size; the success of isn't because you have any better chance on that next flip. Rather the combination of strings occurring naturally, compounded with the continual increase in leverage, would make the average return greater on whatever the likely hood of having long enough strings or/and enough of them.

If you look at nickemp's chart in post # 75, the red dots represent the expected return using a fixed bet of \$500.

For instance, the chart shows that the expected return is about \$75,000 if you have a 55% success rate and bet \$500 each time. If you were to double that bet to \$1000 rather than \$500, the expected return would double to \$150,000. The distribution of blue dots suggests that the string betting system with a \$500 starting bet might give you a \$150,000 return, or it might not, depending on how the strings play out.

So here's the question: assuming you want to target that \$150,000 return, what's the best way to do it:

1. Use a default \$500 bet size, and increase it after each win, so that some bets are \$500 and others are \$4000 or more depending on the outcome of the preceding bets; or

2. Use a default \$1000 bet size and don't alter it based on the outcome of the preceding bets.

I would expect choice 2 to give you a more predictable and stable equity curve, without those gut-wrenching large losses that occur at the end of each string of wins under the progressive system. So if you can afford to make your default bet \$1000, in most cases I'd see this as preferable to the string system. Unless, that is, the results of your trades are correlated, which is a question I'm personally still grappling with.

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Fat Tails
 If there is a dependency, progressive betting can have a positive or negative impact.

This is a crucial point. It really depends on your trading system and whether it is the type of trading system where the result of one trade is influenced by the previous trade or not.

For example, a few types of systems that usually will have dependencies include: always-in systems, trend-following systems that take every trade without skipping any (winners are more likely after a series of losers and vice versa), and mean reversion systems that take repeated entries on the same MR setup even if the previous entries have failed (each consecutive attempt to catch the same falling knife will have higher probability of success, and if you keep trying, eventually you will catch that falling knife)

If, however, your trading system is the type that is not usually in the market and waits for a certain setup to occur, then the chances are smaller that there will be a dependency between the trades.

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 April 14th, 2011, 08:54 PM #99 (permalink) Elite Member Rockland county , New York   Futures Experience: Intermediate Platform: NT 7 Favorite Futures: CL, 6E, SI, ZC     Posts: 235 since Mar 2011 Thanks: 340 given, 80 received I completely misread the chart of returns - thought he was starting out with 10,000 not 50,000 in post 65. Last edited by whatnext; April 15th, 2011 at 03:00 AM. Reason: post # was wrong

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Fat Tails
 Correct. We need to differentiate between progressive betting and position sizing: Progressive Betting The bet size depends on the outcome of the prior bet or the outcome of strings of prior bets. Position Sizing The bet size depends on expectancy and win rate. The bet size is regularly adjusted to match account equity (see fixed fractional position sizing as suggested by Ralph Vince or Kelly criterion). The Difference Position Sizing is a money management technique, progressive betting can be used to increase the expectancy of a bet, but only if the bets are correlated. The expectancy can now be calculated as a conditional probability as opposed to an absolute probability.

I spent weeks studying Vince 8 years ago and setting up excell files of a 35+ year trading history to calculate optimum f on my personal trading history.

Well worth the effort, and it uncovered that my bet sizes were often way too big. It also reduced my overall market exposure, and confirmed a kind of anti-Martingale approach of the type Vince discusses in his "Leveraged Trading Space"

But even @ optimum f, I still didn't like the drawdowns, and the potential drawdowns, especially when trading in highly correlated assets in leveraged positions, although the run ups were exciting.

Then I found that adjusting optimum f for the biggest drawdown /size of loss I'm willing to suffer helped both my trading and my disposition.

Thus, I now use Optimum f % x total equity bet size/largest loss % =bet size/1% of equity. Such sizing also permitted more reliance on trading signals for exits rather than stops.

Then I increased the number of systems I traded and expanded the asset classes involved in an effort to reduce the overall correlation of the different bets in the portfolio.

Seems to work OK and add consistency, but there is more effort to time and monitor many more asset classes/positions, plus be worried about how everything seems to be correlated these days. A lot of work for a lone trader.

Indeed, a resource on correlation coefficients would be most helpful.

Geo

Last edited by Geomean; April 16th, 2011 at 10:57 AM. Reason: typo and improve clarity
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