N = 0.5 * [(1 + 8 * P/delta)^0.5 + 1]

This is as close to the grail as I will ever get. Where most of my profits come from.

liquidcci 

N = 0.5 * [(1 + 8 * P/delta)^0.5 + 1] This is as close to the grail as I will ever get. Where most of my profits come from.

This is probably one of the shortest statements that I have ever seen to start a thread.


Could you elaborate why you prefer the fixed ratio position sizing to fixed fractional position sizing?

I do not understand how I would ever use a formula for position sizing, which does neither take into account the risk of ruin nor the size of my account.

Let us take a simple example, assuming that my account is $ 20,000 and that I wish to increase the number of contracts from 1 to 2 once I have reached an equity of $ 30,000. this corresponds to a delta of $ 10,000. If I use your formula I will trade

cumulated profit = $ 10,000 -> N = 0.5 * [sqrt(1 + 8* $ 10,000/$ 10,000) + 1] = 2 contracts
cumulated profit = $ 30,000 -> N = 0.5 * [sqrt(1 + 8* $ 30,000/$ 10,000) + 1] = 3 contracts
cumulated profit = $ 60,000 -> N = 0.5 * [sqrt(1 + 8* $ 60,000/$ 10,000) + 1] = 4 contracts
cumulated profit = $ 100,000 -> N = 0.5 * [sqrt(1 + 8* $ 100,000/$ 10,000) + 1] = 5 contracts
cumulated profit = $ 150,000 -> N = 0.5 * [sqrt(1 + 8* $ 100,000/$ 10,000) + 1] = 6 contracts

If I look how much equity is required for each additional contract, this is the result

first contract: margin used = $ 20,000 -> average margin per contract = $ 20,000
second contract: margin used = $ 10,000 -> average margin per contract = $ 15,000 (increased risk)
third contract: margin used = $ 20,000 -> average margin per contract = $ 16,666 (risk still higher compared to the beginning)
fourth contract: margin used = $ 30,000 -> average margin per contract = $ 20,000 (base risk)
fifth contract: margin used = $ 50,000 -> average margin per contract = $ 24,000 (reduced risk)
sixth contract: margin used = $ 50,000 -> average margin per contract = $ 28,333 (risk further reduced)

This shows that the system allows me to take an excessive risk when increasing the position size from 1 to 2 and 3 contracts, but then reduces the risk of ruin each time the number of contracts is increased. Or otherwise put

- when increasing from 1 to 2 or 3 contracts, you may take excessive risks
- in the long term this approach to money management suffers from risk aversion as it does not increase position sizing in a similar way as a fixed fractional betting system


Summary

The formula does neither consider account equity nor the risk of ruin. In the end you will need to find a formula for delta which is based on account equity and the trade expectancy based on 1 contract.

The leitmotif of this approach is to avoid any risks after a few profits have been booked.

If you have a profitable approach to trading, relying on fixed fractional betting - with a reasonable Kelly factor - will lead to results that are by far superior.

liquidcci 

N = 0.5 * [(1 + 8 * P/delta)^0.5 + 1] This is as close to the grail as I will ever get. Where most of my profits come from.

Correct me if I am wrong, but this is the money management technique put forth by Ryan Jones in his book "The Trading Game."

This approach works wonders when winning trades are made, but can be disastrous when a drawdown is hit (which can be said for most money management approaches).

The book author used this approach to do great in a trading contest, tripling his money in 3 months (or something like that), but a few months later he had blown out his account with the fixed ratio technique.

I don't doubt OP's success with the method, but it may not be appropriate for everyone...

Fat Tails 

This is probably one of the shortest statements that I have ever seen to start a thread. Could you elaborate why you prefer the fixed ratio position sizing to fixed fractional position sizing? I do not understand how I would ever use a formula for position sizing, which does neither take into account the risk of ruin nor the size of my account. Let us take a simple example, assuming that my account is $ 20,000 and that I wish to increase the number of contracts from 1 to 2 once I have reached an equity of $ 30,000. this corresponds to a delta of $ 10,000. If I use your formula I will trade cumulated profit = $ 10,000 -> N = 0.5 * [sqrt(1 + 8* $ 10,000/$ 10,000) + 1] = 2 contracts cumulated profit = $ 30,000 -> N = 0.5 * [sqrt(1 + 8* $ 30,000/$ 10,000) + 1] = 3 contracts cumulated profit = $ 60,000 -> N = 0.5 * [sqrt(1 + 8* $ 60,000/$ 10,000) + 1] = 4 contracts cumulated profit = $ 100,000 -> N = 0.5 * [sqrt(1 + 8* $ 100,000/$ 10,000) + 1] = 5 contracts cumulated profit = $ 150,000 -> N = 0.5 * [sqrt(1 + 8* $ 100,000/$ 10,000) + 1] = 6 contracts If I look how much equity is required for each additional contract, this is the result first contract: margin used = $ 20,000 -> average margin per contract = $ 20,000 second contract: margin used = $ 10,000 -> average margin per contract = $ 15,000 (increased risk) third contract: margin used = $ 20,000 -> average margin per contract = $ 16,666 (risk still higher compared to the beginning) fourth contract: margin used = $ 30,000 -> average margin per contract = $ 20,000 (base risk) fifth contract: margin used = $ 50,000 -> average margin per contract = $ 24,000 (reduced risk) sixth contract: margin used = $ 50,000 -> average margin per contract = $ 28,333 (risk further reduced) This shows that the system allows me to take an excessive risk when increasing the position size from 1 to 2 and 3 contracts, but then reduces the risk of ruin each time the number of contracts is increased. Or otherwise put - when increasing from 1 to 2 or 3 contracts, you may take excessive risks - in the long term this approach to money management suffers from risk aversion as it does not increase position sizing in a similar way as a fixed fractional betting system Summary The formula does neither consider account equity nor the risk of ruin. In the end you will need to find a formula for delta which is based on account equity and the trade expectancy based on 1 contract. The leitmotif of this approach is to avoid any risks after a few profits have been booked. If you have a profitable approach to trading, relying on fixed fractional betting - with a reasonable Kelly factor - will lead to results that are by far superior.

@Fat Tails it was a short way to start a thread Appreciate your post and elaborating more on the subject. In regards to this approach. The biggest strength for me with fixed ratio is more you scale the less you risk on a per contract basis. But like you pointed out that does create a higher risk on the front end. Idea here is if I start with just for example 15k and scale to 1 million. My 1 million is much safer than my 15k. But I can live with out 15k but if I hit $1,000,000 I really want to make sure I keep it. If I was up to 20 contracts on a system I want to be more risk adverse and can afford to be because those 20 contracts can produce a nice yearly return.

That being said the way I overcome the front end is to essentially have pad of a much greater amount so I can live to trade another day if the system had problems in the front. I also am very careful in how I set my deltas. I don't set them by margin available. I set them at a higher level and run everything including fixed ratio calculations through back test that help me set what I consider safe but still allow me to scale at an acceptable rate.

I am by no means anti fixed fractional. Ryan Jones the guy who developed Fixed Ratio gets into the strengths and weakness of both and developed fixed ratio to deal with the slow increase on the front and the fast increase on the back that can happen with fixed fractional. He has a good book on the subject called "The Trading Game". Will not make sense for everyone to use but it is worth exploring. Ryan initially convinced me but then my own systems just run smoother using Fixed Ratio.

I also back test my systems through Fixed Fractional and I just prefer the equity curve Fixed Ratio produces. But would never tell someone fixed fractional is a bad way to go.

kevinkdog 

Correct me if I am wrong, but this is the money management technique put forth by Ryan Jones in his book "The Trading Game." This approach works wonders when winning trades are made, but can be disastrous when a drawdown is hit (which can be said for most money management approaches). The book author used this approach to do great in a trading contest, tripling his money in 3 months (or something like that), but a few months later he had blown out his account with the fixed ratio technique. I don't doubt OP's success with the method, but it may not be appropriate for everyone...

@kevinkdog I don't see it as necessarily a quicker way to blow out your account. You have to set your deltas correctly on the front end and be capitalized adequately. Just like you scale up you also scale down based on the formula. So once contracts start to bump up you could come back down and end up at 1 contract. If you are not under capitalized on that first contract you are just back to square one. Point being you are not just going to suddenly blow out an account you will scale down. If you do get up to higher contract level your draw downs even become more muted.

I also believe it is important to use something like Market System Analyzer to run all back test data through to see how something like Fixed Ratio or any other money management technique affects profit and draw downs. When setting my deltas I take a hard look at how a particular delta draws.

liquidcci 

@Fat Tails it was a short way to start a thread Appreciate your post and elaborating more on the subject. In regards to this approach. The biggest strength for me with fixed ratio is more you scale the less you risk on a per contract basis. But like you pointed out that does create a higher risk on the front end. Idea here is if I start with just for example 15k and scale to 1 million. My 1 million is much safer than my 15k. But I can live with out 15k but if I hit $1,000,000 I really want to make sure I keep it. If I was up to 20 contracts on a system I want to be more risk adverse and can afford to be because those 20 contracts can produce a nice yearly return. That being said the way I overcome the front end is to essentially have pad of a much greater amount so I can live to trade another day if the system had problems in the front. I also am very careful in how I set my deltas. I don't set them by margin available. I set them at a higher level and run everything including fixed ratio calculations through back test that help me set what I consider safe but still allow me to scale at an acceptable rate. I am by no means anti fixed fractional. Ryan Jones the guy who developed Fixed Ratio gets into the strengths and weakness of both and developed fixed ratio to deal with the slow increase on the front and the fast increase on the back that can happen with fixed fractional. He has a good book on the subject called "The Trading Game". Will not make sense for everyone to use but it is worth exploring. Ryan initially convinced me but then my own systems just run smoother using Fixed Ratio. I also back test my systems through Fixed Fractional and I just prefer the equity curve Fixed Ratio produces. But would never tell someone fixed fractional is a bad way to go.

@liquidcci: The discussion now shifts from mathematics to psychology.

Mathematically, if you follow a fixed-fractional approach your relative risk of ruin remains constant, while the absolute risk of ruin decreases. The definition of risk of ruin is based on a percentage (such as 50%) lost of your account equity. If you lose 50% of 1 million, than it seems (at least from today's perspective) that this is a higher loss than 50% of 15k. But in fact, if you lose 50% of 1 million, you still have 500k and enough money to recover, whereas with 7.5 K you are out of the game.

Also I doubt that the Fixed Ratio approach will ever lead you to an account of 1 million. The more you make the more you will try to keep your "precious ...." and settle for bets that are too low.

However, I do understand that the utility function of your account is non-linear, that is the first million is worth more than the second one. The Fixed Ratio approach could be explained by a different utility function, if - and that is the problem - it would not cut short profits too much.

Fat Tails 

@liquidcci: The discussion now shifts from mathematics to psychology. Mathematically, if you follow a fixed-fractional approach your relative risk of ruin remains constant, while the absolute risk of ruin decreases. The definition of risk of ruin is based on a percentage (such as 50%) lost of your account equity. If you lose 50% of 1 million, than it seems (at least from today's perspective) that this is a higher loss than 50% of 15k. But in fact, if you lose 50% of 1 million, you still have 500k and enough money to recover, whereas with 7.5 K you are out of the game. Also I doubt that the Fixed Ratio approach will ever lead you to an account of 1 million. The more you make the more you will try to keep your "precious ...." and settle for bets that are too low. However, I do understand that the utility function of your account is non-linear, that is the first million is worth more than the second one. The Fixed Ratio approach could be explained by a different utility function, if - and that is the problem - it would not cut short profits too much.

While psychology plays into it for me my real reason for using it may be more philosophical. Just fits what I am doing from back test to forward test. It can definite mathematically lead to a million of course that is contingent on what market gives. I have run it against fixed fractional and for what I am doing fixed ratio just behaves better. I also run it on a portfolio so every market adds against the delta pushing contracts on all markets higher. At some point in the process each market I trade will hit level where slippage will keep me from increasing contracts. So at some point betting more at higher levels becomes moot. While Fixed fractional on backend can increase contracts very rapidly compared to Fixed ratio at some point they both hit the slippage wall. So I don't view it as cutting profits short just slows down the journey to that wall on the backend. I like the the way Fixed ratio behaves on back end and it gets me to where I want to go plenty fast on front. When I say fits me comes down to my trading philosophy. I would rather take more risk on the front end when account is smaller and take less risk on the back end as my account matures and I have the kind of money you can actually do something with.

So maybe for me at least the difference between using one over the other fits into my world view. We move from Mathematics to Psychology and now to Philosophy.

Also just looking at your example because of my approach that first profits are not as valuable as the latter my deltas are usually set at under 3k. I also use an Equity Curve switch to control draw downs which mitigates some of the front end issues and allows for a more aggressive delta.

Appreciate your comments @Fat Tails I am always open to explore all angles. Strengths and Weakness of everything I am doing.

liquidcci 

Also just looking at your example because of my approach that first profits are not as valuable as the latter my deltas are usually set at under 3k. I also use an Equity Curve switch to control draw downs which mitigates some of the front end issues and allows for a more aggressive delta. Appreciate your comments @Fat Tails I am always open to explore all angles. Strengths and Weakness of everything I am doing.

Thanks for a very informative thread fellas. May I ask what is an equity curve switch and how it is used in this scenario?

@Fat Tails

I got curious about what you said on adding or taking into account the risk of ruin. Obviously newbie here, could you explain this a little bit further or point me into something where i can learn more from risk please?.

Thanks in advance.
Rhuz.

Fat Tails 

This is probably one of the shortest statements that I have ever seen to start a thread. Could you elaborate why you prefer the fixed ratio position sizing to fixed fractional position sizing? I do not understand how I would ever use a formula for position sizing, which does neither take into account the risk of ruin nor the size of my account. Let us take a simple example, assuming that my account is $ 20,000 and that I wish to increase the number of contracts from 1 to 2 once I have reached an equity of $ 30,000. this corresponds to a delta of $ 10,000. If I use your formula I will trade cumulated profit = $ 10,000 -> N = 0.5 * [sqrt(1 + 8* $ 10,000/$ 10,000) + 1] = 2 contracts cumulated profit = $ 30,000 -> N = 0.5 * [sqrt(1 + 8* $ 30,000/$ 10,000) + 1] = 3 contracts cumulated profit = $ 60,000 -> N = 0.5 * [sqrt(1 + 8* $ 60,000/$ 10,000) + 1] = 4 contracts cumulated profit = $ 100,000 -> N = 0.5 * [sqrt(1 + 8* $ 100,000/$ 10,000) + 1] = 5 contracts cumulated profit = $ 150,000 -> N = 0.5 * [sqrt(1 + 8* $ 100,000/$ 10,000) + 1] = 6 contracts If I look how much equity is required for each additional contract, this is the result first contract: margin used = $ 20,000 -> average margin per contract = $ 20,000 second contract: margin used = $ 10,000 -> average margin per contract = $ 15,000 (increased risk) third contract: margin used = $ 20,000 -> average margin per contract = $ 16,666 (risk still higher compared to the beginning) fourth contract: margin used = $ 30,000 -> average margin per contract = $ 20,000 (base risk) fifth contract: margin used = $ 50,000 -> average margin per contract = $ 24,000 (reduced risk) sixth contract: margin used = $ 50,000 -> average margin per contract = $ 28,333 (risk further reduced) This shows that the system allows me to take an excessive risk when increasing the position size from 1 to 2 and 3 contracts, but then reduces the risk of ruin each time the number of contracts is increased. Or otherwise put - when increasing from 1 to 2 or 3 contracts, you may take excessive risks - in the long term this approach to money management suffers from risk aversion as it does not increase position sizing in a similar way as a fixed fractional betting system Summary The formula does neither consider account equity nor the risk of ruin. In the end you will need to find a formula for delta which is based on account equity and the trade expectancy based on 1 contract. The leitmotif of this approach is to avoid any risks after a few profits have been booked. If you have a profitable approach to trading, relying on fixed fractional betting - with a reasonable Kelly factor - will lead to results that are by far superior.