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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

  #61 (permalink)
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Progressive Betting versus Position Sizing


GoldStandard View Post
Betting 2, or even 200 units per roll (assuming you have a system with positive expectancy) will similarly yield more than simply wagering 1 unit over all rolls. This does not mean you improved your odds. All you did was increase your position size.

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.

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  #62 (permalink)
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I ran some numbers through my spreadsheet and gave this a bit more thought. I find myself agreeing more with Fat Tails now.

If your system has a winning percentage greater than 50%, then the progressive betting technique will improve profitability. However, this isn't due to the concept of capitalizing on "winning streaks" but rather, more accurately, to the simple fact that under the progressive system, you're using an increased bet size at least some portion of the time. If it's a winning system (which we're assuming by definition here), then larger bets equals larger expected profits. Presumably a similar improvement could be achieved by increasing the bet size at random intervals, regardless of the outcome of the preceding bets. And of course profitability could be improved more by increasing the bet size on all trades (assuming you can afford to do so).

When trading in the real world rather than a thought exercise, however, there does still seem to be some value to the notion of varying bet size based on recent experience, particularly when it comes to decreasing bets during a drawdown. That's because you don't really know that your system will maintain the same success rate you've observed in the past. If recent results are giving you evidence that your method isn't working at the moment, it still may be wise to scale back until proven otherwise. Or maybe this is just "wimping out."

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  #63 (permalink)
Fortitudo et Honor
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I give up.

You guys are right.

All I'll close with is saying that it's a similar concept as performance enhancing drugs in baseball.

There are idiots out there that say "taking steroids won't help you to hit a baseball." and the intuitive logic tells you that if it didn't help, they wouldn't do it. Steroids helps to increase production in a number of ways, namely extending careers (which increases overall career numbers) allowing a player to recover faster from injury (thus improving seasonal and career numbers) and it also helps to improve a players average distance on their hits and also allows them to put on additional muscle mass through more intense workouts, which in turn, helps them to use a heavier bat with the same swing speed or increase their swing speed using the same weight bat. In just about any aspect, it DOES help with homerun production, but there's always an idiot who goes "taking steroids won't help you to hit homeruns."

If it didn't help, then they wouldn't do it. You don't see baseball players all on a vegetarian diet....you know why? Cause there's no evidence that it helps them perform. If it did, then they'd do it.

The same concept is true here, why do you think virtually every performance report gives string and winning/losing sequence stats? Because it is an effective way to reduce drawdown and manage risk.

If you don't believe me, try it yourself. Take your own winning strategy, apply a 50% positionsize increase (or take 50% of your previous profits) following winning trades and then return to the original positionsize following a loser. Plot the equity curves and compare. It's not that difficult.

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  #64 (permalink)
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worldwary View Post
I ran some numbers through my spreadsheet and gave this a bit more thought. I find myself agreeing more with Fat Tails now.

If your system has a winning percentage greater than 50%, then the progressive betting technique will improve profitability. However, this isn't due to the concept of capitalizing on "winning streaks" but rather, more accurately, to the simple fact that under the progressive system, you're using an increased bet size at least some portion of the time. If it's a winning system (which we're assuming by definition here), then larger bets equals larger expected profits. Presumably a similar improvement could be achieved by increasing the bet size at random intervals, regardless of the outcome of the preceding bets. And of course profitability could be improved more by increasing the bet size on all trades (assuming you can afford to do so).

When trading in the real world rather than a thought exercise, however, there does still seem to be some value to the notion of varying bet size based on recent experience, particularly when it comes to decreasing bets during a drawdown. That's because you don't really know that your system will maintain the same success rate you've observed in the past. If recent results are giving you evidence that your method isn't working at the moment, it still may be wise to scale back until proven otherwise. Or maybe this is just "wimping out."

So now we're getting somewhere...if you develop a "random" strategy, that improves upon the simple progressive strategy, then fill me in I'm all ears.

But "random" isn't very comforting to me, I need a setup that I can employ with consistency and predictability.

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  #65 (permalink)
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I read thread this yesterday and found it very interesting. I used to have discussions like his with a programmer buddy who was a Math PHD. He hated TA and insisted markets were random so no prediction could work then got sick of modelling passenger queues for Airlines and decided to make a living selling options. My argument was always along the lines that TA is not about prediction but that even random events have trends and all you are doing is finding and riding them.

Anyhow I digress. I happen to believe in changing R size in accordance with wins in row even though up until now I have never bothered to prove or disprove the theory.

It seems to make sense that it should work given that even at a 50% win rate you can expect a string of 14 wins in a row at some stage. The down side is that the 1st loser after that is a doozy.

Anyhow I did a little Monte Carlo to see what would happen. Starting at $50,000 and risking 1% of capital I increased R by 0.1% every time there was a win and went back to 1% as soon as a loss came along. I did this for 1,000 random trades and then took the results for 1,000 of these and stuck them into a chart.

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  #66 (permalink)
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Here is the same deal except increasing R by 0.5% each time.

From these two I would say this is worthwhile as long as you win rate is better than 50%. It doesn't seem to rescue a 50% win rate

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  #67 (permalink)
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Just in case you were wanting to give up on this method of position sizing. Have a look at what happens if your win rate is 55% - Hint. Look at the scale along the bottom

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  #68 (permalink)
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Nickemp View Post
Anyhow I did a little Monte Carlo to see what would happen. Starting at $50,000 and risking 1% of capital I increased R by 0.1% every time there was a win and went back to 1% as soon as a loss came along. I did this for 1,000 random trades and then took the results for 1,000 of these and stuck them into a chart.

If you do this with a win rate of 50%, increasing and decreasing R cancel out in the longer run.

If your win rate is 55% always assuming that the average profit equals the average loss, this does not cancel out, as the results are biased to the upside. So you are gradually increasing the bet size knowing that your bet is favorable.

Actually you get 11 wins for 9 losses, so after 20 runs you will typically have increased your bet size from 1% to 1.2%. After hundred runs your betsize should be close to 2%, after 1000 runs close to 11% of the original equity.

This is similar to fixed-fraction position sizing, as you add to your bet for every winner. It is part of the anti-Martingale strategies an can be applied to uncorrelated bets. It has nothing to do with strings though, as strings rely on correlation between consecutive bets.

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  #69 (permalink)
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Fat Tails View Post
If you do this with a win rate of 50%, increasing and decreasing R cancel out in the longer run.

If your win rate is 55% always assuming that the average profit equals the average loss, this does not cancel out, as the results are biased to the upside. So you are gradually increasing the bet size knowing that your bet is favorable.

Actually you get 11 wins for 9 losses, so after 20 runs you will typically have increased your bet size from 1% to 1.2%. After hundred runs your betsize should be close to 2%, after 1000 runs close to 11% of the original equity.

This is similar to fixed-fraction position sizing, as you add to your bet for every winner. It is part of the anti-Martingale strategies an can be applied to uncorrelated bets. It has nothing to do with strings though, as strings rely on correlation between consecutive bets.

You're still not getting it. Call it semantics, chicken or the egg, whatever...but you cannot observe an outcome rate different than 50% and not observe an uneven distribution of both wins/losses and the strings of those outcomes.

Whether you attribute the phenomenon to the rate or to the strings, the phenomenon stands, that if you approach the wager amount consistently and methodically ACCORDING TO STRINGS, it has an effect on the overall yield of the strategy.

As I stated earlier, the real world yield isn't always optimal though. In order for the phenomenon to be optimal, the wager sizes have to be fairly equal and the wager has to be large with respect to the account size (or the instrument has to have very continuous compounding).

When you try to evaluate this type of strategy modification with futures, you'll find that in many instances, you'd have been better off just wagering the maximum amount every time. (i.e. if your marginal reserve is $5k, then holding that extra $5k in reserve and putting it into play only after a certain outcome increases the yield, but not with respect to overall account size).

It works best for instruments like stock where you can compound/rollover much smaller amounts from a previous win.

It also works best when dealing with win rates that are larger (but not too much) than 50%. I.e. a 90% win rate would be better served to just rollover as much as you can, because the strings are much longer. (and the losers much less common).

It's simply A TOOL (singular) that you can try and see how it effects your particular strategy. It doesn't always result in a desired effect....but in some situations it can help to reduce risk/drawdown and/or increase profits.

Again, you keep fixating on this concept of expectation and I fully conceded that for the most part, trades are independent and mutually exclusive.

HOWEVER, if you have a "side heavy" strategy that does well in bull or bear markets (and not as well in sideways markets) then a win may have some indication as to the expectation of the next win....(i.e. if you're winning 3 in a row, you can do the analysis to see what the odds are on the very next trade following a 3 win series).

Regardless, if you approach the strategy as groups of strings (rather than individual outcomes) it can and does have an effect by consistently and deliberately altering your wage amount.

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  #70 (permalink)
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@RM99 Your statement is not clear and confuses different subjects.

You really would need to differentiate between uncorrelated and correlated bets.

Strings have no meaning, if consecutive bets are uncorrelated, such as for a coin tosses.

If you apply any progressive betting system to uncorrelated bets, it just becomes a tool for position sizing.

For uncorrelated bets the progressive betting produces a similar result as fixed fractional position sizing, as you increase your bet size, when your equity has grown. However, this has nothing to do with strings, but simply follows from the positive expectancy.


Last edited by Fat Tails; April 9th, 2011 at 06:51 PM.
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