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How advanced mathematics and gaming theory can help you as a trader
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How advanced mathematics and gaming theory can help you as a trader

  #91 (permalink)
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worldwary View Post
To push the thought experiment a bit further, let's assume you have a system with an overall positive expectancy of $50 per trade and an overall success rate of 60%.

If you break the data down further, however, let's say you can classify this as two different systems. Sometimes the system is actually a loser, with an expectancy of ($100) per trade and a success rate of 50%. During successful periods, the system has an expectancy of $200 per trade and a success rate of 70%. The difference is whether market conditions favor the system's approach on a given day.

The key question for the trader is whether, right now on any given day, you're trading the losing system or the winning system. One thing that is clear is that you would expect there to be more (and longer) strings of winners under the winning system than under the losing system. In fact, a sizeable cluster of wins over any given period would be the primary evidence you'd use to determine which system had been in place over that period. If wins are occurring more frequently (or perhaps more accurately, if expectancy is higher), this is what tells you that conditions were favorable for your trading approach over that period.

Might it therefore make sense to increase bet size when you've noticed more winners, or higher expectancy, across the most recent sample of trades?

I don't expect a definitive answer, just raising this as a thought to mull over. I think the answer really depends on your view of how frequently market conditions change. If conditions can be expected to change constantly, so it's basically random whether or not the system will be favored on a given day, then that would be one thing. If conditions can be expected to linger for weeks or months at a time, that would be another. These are empirical questions that you can't really answer with a thought experiment, but that may be worth thinking about.

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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  #92 (permalink)
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whatnext View Post
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 11:03 AM.
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  #93 (permalink)
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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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  #94 (permalink)
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worldwary View Post
...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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  #95 (permalink)
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whatnext View Post
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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  #96 (permalink)
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What is progressive betting?

We have now discussed it over and over. Let me just state again the essential point to understand progressive betting.


Essentials

(1) A progressive betting system uses the outcome of the prior trade to establish the position size of the following trade. This is the definition of progressive betting.

(2) If the outcome of the following trade does not depend on the prior trade(s), this does not make sense.

(3) If there is a dependency, progressive betting can have a positive or negative impact.


Side Effect

A progressive betting system always has an impact on position size. If you increase position size, you increase the returns for profitable bets, but increase the losses for non-profitable bets. Your returns will be better but your risk of ruin will be higher as well. The side effect can also be observed for non-correlated bets.


Martingale and Anti-Martingale systems

A Martingale system increases the bet size after a loss. It can be used when the outcomes of consecutive bets are negatively correlated. Example: Black Jack.

An Anti-Martingale system increases the bet size after a win. It can be used when the outcome of consecutive bets are positively correlated. Example: Pyramiding Trades

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  #97 (permalink)
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it depends on your trading system


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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  #98 (permalink)
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Grid Martingale Expert Advisor

Just by chance, I noticed a new thread here, which is referring to a Grid Martingale Expert Advisor.

https://futures.io/commodities-futures-trading/9438-cl-crude-oil-futures-contract-currency-broker.html

This sounds very impressive, but is the simplest of all progressive betting systems. You will know this from Roulette:

You start wit $ 1 and put it on black. If you win you get another $1. If you lose, you double up and bet $2. You continue doubling up until you win. This way you will always win. For example if you experience 10 consecutive losses (probability is around 1:784) and then win, your profit is Profit = $ - 1 - 2 - 4 - 8 - 16 - 32 -64 - 128 - 256 - 512 + 1024 = $ 1.

The problem of such bets is the asymmetric risk profile. Every casino has a limit, and let us assume that the limit of the casino is $ 50,000. With 16 consecutive losses (probability around 1: 42,777) you cannot continue to play. Statistically you will have 42,776 winning strings with a profit of 1$ and one losing string, which comes at a combined cost of $ 65.535. The difference is the edge of the casino.

Now, if you want to apply that wonderful system to trading, you can get yourself a Grid Martingale Expert Advisor. It has different levels for averaging down, so you can play it in the way you can play Roulette. Now, if the bets are uncorrelated, your account will prosper for some time, before experiencing a sudden death.

The only way to make money with a Martingale System would be to find a system that produces bets, which are negatively correlated. Does anybody have some evidence that such a negative correlation can be exploited?


Last edited by Fat Tails; April 15th, 2011 at 06:56 AM.
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  #99 (permalink)
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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 04:00 AM. Reason: post # was wrong
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  #100 (permalink)
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Fat Tails View Post
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 11:57 AM. Reason: typo and improve clarity
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