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Money Management 101

  • #81
  • Edited 6:54am Jul 21, 2007 6:51am | Edited 6:54am
Quoting mmeimandi
The point is although equity could be constant for a couple of runs SMA is not and it will cross again.
Yes equity is constant and the SMA converges with it but never actually crosses back. I tried to come up with a mathematical proof for this but was unable (it's been a few years since I've done any proofs ). I did, however do a quick Excel sheet that illustrates my point (see attached .zip file). You can play with the numbers as much as you want, but at the end of the day, if you stop trading, the SMA will never cross back to the other side of the equity curve.

Here is an article that discusses the idea. Unfortunately the author also uses the word "crosses" instead of "converges with". If we actually look at his last chart though, we do see that as long as he is not trading, the curves only converge and never actually cross.

Semantics aside however, I do think we can consider convergence of the 2 curves (i.e. SMA = Equity) as a cross, so "when the SMA moves down to meet the equity curve, we can begin to trade again."
Attached File(s)
File Type: zip Equity-SMA.zip   4 KB | 483 downloads
  • #82
  • Jul 22, 2007 12:31am Jul 22, 2007 12:31am
Quoting fierceman
Semantics aside however, I do think we can consider convergence of the 2 curves (i.e. SMA = Equity) as a cross, so "when the SMA moves down to meet the equity curve, we can begin to trade again."
Agreed,

Recently someone asked me to develop an EA for him based on this method. Actually we used the second way of trading equity curve.We tailored the size of the trades based on crosses. I mean we didn't stop trading just increased and reduced the sizes and to be honest the system worked quite well on backtesting and I guess he is live trading it now.

Anyways thanks for the illumination.

Moh
  • #83
  • Jul 22, 2007 2:04am Jul 22, 2007 2:04am
Quoting mmeimandi
We tailored the size of the trades based on crosses. I mean we didn't stop trading just increased and reduced the sizes and to be honest the system worked quite well on backtesting and I guess he is live trading it now.
Yes I agree that's a better way to approach the equity MA cross-over method.

BTW, has anyone here tried MM software to do the calculations for you (PipItUp you might be interested in this) such as the "Adaptrade Market System Analyzer" or something similar? I just came across it while researching that link in my last post and it seems like it may be quite relevant to this thread (Just for the record, I'm not in any way affiliated with the company, I'm just looking for an honest opinion). Any thoughts are appreciated.

I should also caution that it is still important to understand what the software is doing, so don't stop reading this thread just because you've found software that will "do it all for you", even if it does in fact do it all for you.
  • #84
  • Jul 24, 2007 9:18am Jul 24, 2007 9:18am
Quoting fierceman
Yes I agree that's a better way to approach the equity MA cross-over method.

BTW, has anyone here tried MM software to do the calculations for you (PipItUp you might be interested in this) such as the "Adaptrade Market System Analyzer" or something similar? I just came across it while researching that link in my last post and it seems like it may be quite relevant to this thread (Just for the record, I'm not in any way affiliated with the company, I'm just looking for an honest opinion). Any thoughts are appreciated.

I should also caution that it is still important to understand what the software is doing, so don't stop reading this thread just because you've found software that will "do it all for you", even if it does in fact do it all for you.
Hi fierceman,

Thanks for the research and contribution.

I went over and checked it and I have to say you are completely right about convergence and crossing on the chart.

As per your question about the software, well over the course of years I have developed my own routines and "software" to do the job for me. I haven't tried this or any other MM software myself so I cannot comment on it but I believe this kind of software if they can do the job well they can off load the burden of implementing all these math and calculations and techniques from the trader's shoulder to a great extent.

It doesn't mean that we shouldn't try to learn concepts and develop skills but I don't see any problems to get help with the implementation. In this way we can focus more on the trading itself.

Thanks,

Moh
  • #85
  • Jul 25, 2007 9:00pm Jul 25, 2007 9:00pm
Quoting mmeimandi
Hi fierceman,

I believe this kind of software if they can do the job well they can off load the burden of implementing all these math and calculations and techniques from the trader's shoulder to a great extent.
Hey Moh frankly speaking i was thinking of giving one sucha software a shot. Im not very good at math and not so fund of doing things in spreadsheets. Any specific thing i should look for while searching? Any piece of advice would be appreciated.

Thanks man your opinion means alot to me.
  • #86
  • Jul 26, 2007 12:46pm Jul 26, 2007 12:46pm
Quoting PipItUp
Hey Moh frankly speaking i was thinking of giving one sucha software a shot. Im not very good at math and not so fund of doing things in spreadsheets. Any specific thing i should look for while searching? Any piece of advice would be appreciated.

Thanks man your opinion means alot to me.
Hi PipItUp,

As I mentioned in my previous post I haven't personally used any MM software so I really cannot recommend any. Maybe some of the guys here can help you with that.

Quote
Any specific thing i should look for while searching? Any piece of advice would be appreciated.

Basically I look at money management as an incremental process. Any software you choose should give you the ability to use it on your historical trades as well as your more recent trades. So it should have some sort of recording facility. In fact recording your trading results could be beneficial to you when it comes to monitoring your performance as well.

Another issue is, before you go about using any software you need to know what type MM techniques you want to follow and check how that software addresses your requirements.

Thanks for asking my opinion dude.
  • #87
  • Jul 27, 2007 5:28pm Jul 27, 2007 5:28pm
Quoting mmeimandi
Hi PipItUp,

As I mentioned in my previous post I haven't personally used any MM software so I really cannot recommend any. Maybe some of the guys here can help you with that.



Basically I look at money management as an incremental process. Any software you choose should give you the ability to use it on your historical trades as well as your more recent trades. So it should have some sort of recording facility. In fact recording your trading results could be beneficial to you when it comes to monitoring your performance as well.

Another issue is, before you go about using any software you need to know what type MM techniques you want to follow and check how that software addresses your requirements.

Thanks for asking my opinion dude.
Thanks man very informative.
  • #88
  • Jul 30, 2007 3:02pm Jul 30, 2007 3:02pm
Quoting PipItUp
Thanks man very informative.
Where is everybody here? Hey Moh im waiting for rest of position sizing stuff. where are ya man.
  • #89
  • Jul 30, 2007 7:57pm Jul 30, 2007 7:57pm
Quoting PipItUp
Where is everybody here? Hey Moh im waiting for rest of position sizing stuff. where are ya man.
Sorry PipItUp. Blame it on makrets

Anyways here it comes.

Thanks,

Moh
  • #90
  • Jul 30, 2007 8:04pm Jul 30, 2007 8:04pm
This method is explained extensively by Ralph Vince in his amazing book, “Portfolio Management Formulas”, and here I will try to give you a very brief abstract.

Fixed Fractional method is based on reinvestment of returns. Basically it helps you answer this question: “How best to reinvest?”

One thing to clarify is that the relationship between potential gain and quantity risked is not a straight line, it is curved and there is a peak to this curve and it is at this peak that we maximize potential gain per quantity at risk.

This method helps you to involve risk in your position sizing decision. It is argued that position sizing is whether knowingly or un-knowingly the result of the trader’s perceived “worst-case” loss on the next trade.

In fixed fractional method we state that there is a divisor of this perceived biggest loss, a number between 0 and 1 that you will use in determining your position size.

If you figured that there is a positive mathematical expectation, however small, the next step is to exploit this positive ME to its fullest potential. For an independent trials process (e.g. Trading), this is achieved by reinvesting a fixed fraction of your total stake.

Traders often use Kelly formulas to calculate this fixed fraction. The first equation here is:

F = 2 * P - Q

Where f = The optimal fixed fraction, P = The probability of a winning trade, and Q = The probability of a losing trade.

This equation will yield the correct answer for optimal f provided the quantities are the same for both wins and losses.

Thanks,

Moh
  • #91
  • Jul 31, 2007 8:11am Jul 31, 2007 8:11am
Quoting mmeimandi
Thanks for the research and contribution.

You're very welcome. I currently use a very simple MM strategy based on fixed fractional (although it's not entirely 'fixed'). It has worked well for me, but I am always interested in learning more, particularly if it helps my trading. A more efficient MM strategy seems like my next logical step, so I'll keep this thread in my favorites .
  • #92
  • Jul 31, 2007 9:18am Jul 31, 2007 9:18am
I'd like to add my two cents here.

Suppose you have a method (or EA) that you believe will make tons of money in certain years. Perhaps some years it makes 2000%, and some years it loses 75%.

How can you work this toward your advantage?

Here is my example of what I could do:

With a 100K account, you can cap your risk each year to 10% of the entire account. Your upside is 2000%, or actually a 200K increase on your 10K. So the entire account will grow to 300K in a great year. In a losing year, your account could shrink as low as 90K.

After a 10% losing year, your risk shrinks to 9K (10% of 90K.) So a great year (2000%) moves the account up to 270K (90K + 180K.)

The example paints broad strokes, but conveys that a high risk/high reward system can be very profitable over the long term.
  • #93
  • Jul 31, 2007 10:18am Jul 31, 2007 10:18am
tdion, as soon as you start talking about percentages of your account, you are already pre-supposing some sort of money management technique. A trading system alone, without MM, cannot earn any % of any account because it doesn't take into account position sizing. Every trader in the world is involved in MM, whether they know it or not. Whatever thought process dictates to you how much risk to take on with every trade is your MM. What we are trying to accomplish in this thread is to optimize this thought process by using the mathematics of probability. The only thing your trading strategy provides for your MM calculations is the expectancy value. Hope that helps
  • #94
  • Jul 31, 2007 10:22am Jul 31, 2007 10:22am
I leave specific lot sizes to the system in play. That will be dependent on the trading strategy. For example, grid trades lot sizes will not apply to a crossover MA system like Cornflower, or trendfollowing like Jacko.

What I have presented is a yearly MM technique for systems that perform very well some years, and very poorly others. -Regards
  • #95
  • Aug 1, 2007 12:48pm Aug 1, 2007 12:48pm
Quoting fierceman
You're very welcome. I currently use a very simple MM strategy based on fixed fractional (although it's not entirely 'fixed'). It has worked well for me, but I am always interested in learning more, particularly if it helps my trading. A more efficient MM strategy seems like my next logical step, so I'll keep this thread in my favorites .
It is great that you already have something in place that works for you. Maybe by getting more exposure to the math behind some of these techniques you can back your system with some facts and feel more comfortable with it.

Thanks,

Moh
  • #96
  • Aug 1, 2007 12:49pm Aug 1, 2007 12:49pm
Quoting tdion
I'd like to add my two cents here.

Suppose you have a method (or EA) that you believe will make tons of money in certain years. Perhaps some years it makes 2000%, and some years it loses 75%.

How can you work this toward your advantage?

Here is my example of what I could do:

With a 100K account, you can cap your risk each year to 10% of the entire account. Your upside is 2000%, or actually a 200K increase on your 10K. So the entire account will grow to 300K in a great year. In a losing year, your account could shrink as low as 90K.

After a 10% losing year, your risk shrinks to 9K (10% of 90K.) So a great year (2000%) moves the account up to 270K (90K + 180K.)

The example paints broad strokes, but conveys that a high risk/high reward system can be very profitable over the long term.
Thanks for you contribution.

In my opinion you are somehow (maybe without knowing) using fixed fractional method.

As I mentioned fixed fractional allows you take risk into account when deciding on your position sizing. The only difference here is finding that optimal percentage. In your example you used 10%. Fixed Fractional helps you to make this decision mathematically correct.

If you have $1000 account obviously your risk is a bit high if you spend $500 on a trade. Likewise, if you have a $10 million account don’t you think you’d be a little light if you spend $50 on a trade?

We need to found a way to find this percentage correctly.

Thanks,

Moh
  • #97
  • Aug 1, 2007 2:52pm Aug 1, 2007 2:52pm
All right so we mentioned if the winners and losers are not the same size, the first Kelly formula would not yield the correct answer. Consider a coin-toss example, where all of the winners are for 2 units and all of the losers for 1 unit. For such a situation that wins and losses are for different amounts the Kelly formula is:

F = ((B + 1)*P-1)/B

Where f = The optimal fixed fraction, P = The probability of a winning trade, and B = The ratio of amount won on a winning bet to amount lost on a losing bet.

Applying this formula to our example:

f = ((2 + 1) * 0.5 – 1)/2 = (3 * 0.5 -1)/2 = 0.25

There is still a shortcoming here. This formula will yield the correct answer for optimal f provided all wins are always for the same amount and all loses always for the same amount. If your take profit and stop loss limits are not always the same size, which probability it is not most of the cases, then this formula will not yield the correct answer.

To apply the Kelly formulas to a non-Bernoulli distribution of outcomes (A Bernoulli distribution is one with two possible, discrete outcomes.) like trading is a mistake.

Thanks,

Moh
  • #98
  • Aug 1, 2007 2:54pm Aug 1, 2007 2:54pm
Quoting mmeimandi
To apply the Kelly formulas to a non-Bernoulli distribution of outcomes (A Bernoulli distribution is one with two possible, discrete outcomes.) like trading is a mistake.
In order to fix this problem so many traders mistakenly take the averages of wins and losses to calculate B.

Consider the following sequence of trades:

+9, +18, +7, +1, +10, -5, -3, -17, -7

As you can see this is not a Bernoulli distribution (the wins and losses are of different amount). Since 5 of the 9 events are profitable, the P = 0.555. Now take the average of the wins and losses to calculate B.

Average win is = 9
Average loss is = 8

Therefore B = 1.125

By plugging this B into the Kelly formula:

f = ((1.125 + 1) * 0.555 – 1) / 1.125
= (2.125 * 0.555 – 1) /1.125
= 0.179375/1.125
= 0.159444444

If we round this number we reach at 0.16 for optimal f.

Actually this is not correct. The optimal f for this sequence of trades is 0.24. In the next post I will explain how Ralph uses Geometric Mean for finding the correct optimal f for a non-Bernoulli distribution like trading.

Thanks,

Moh
  • #99
  • Aug 1, 2007 6:58pm Aug 1, 2007 6:58pm
  •  tazmet
  • | Joined Jun 2007 | Status: Gold Member - Solid Gold Baby! | 47 Posts
Looking forward to the next post. I just finished reading all 7 pages - not an easy read - but well worth it. I might just have to dig up my old statistics text. This is a fascinating application of statistics to money management.

I wanted to summarize a couple of things you talked about just to clarify my own thinking and in case I completely got it wrong:

A) What I got from the initial discussion on dependency (i.e. correlation method) is that it makes no sense to increase your position size thinking because you had so many losers in a row that you are bound to have a winner or if you're winning, you're likely to keep on winning. There is no correlation except in rare cases.

B)The equity curve seems very valuable for trading in that unlike the gambler's method of position sizing, it would allow a trader to decrease position size or stay out of the trade all together until the cross in the positive direction. FYI, I still have no idea how to calculate this and need to study this more. Is this essentially looking at your trade log over a 2 year period and saying, ok, I tend to have 4 successful trades on average before a loser, so I will take a break or decrease my position on the 5th trade?

C)Finally, the fixed fractional method gives you an idea of what position size you should use that goes beyond a simple 2% based on the probability of wins and losses. I hope you're going to explain how to calculate this probability.

Thanks for the great info!
My business model Get pips => Keep Pips => Repeat
  • #100
  • Aug 3, 2007 9:43am Aug 3, 2007 9:43am
Hi tazmet,

I’m glad you found this thread useful and thanks for devoting time to read through all the pages. As you said it’s not an easy read. I tried to keep it really simple though.

As per your questions please find my answers below:


Quoting tazmet
A) What I got from the initial discussion on dependency (i.e. correlation method) is that it makes no sense to increase your position size thinking because you had so many losers in a row that you are bound to have a winner or if you're winning, you're likely to keep on winning. There is no correlation except in rare cases.
You got this one right. Serial Correlation helps you to measure the dependency between trades mathematically and just based on guts and as I mentioned there are some rare case that the result of a trade is dependent on the previous ones.

Quoting tazmet
B)The equity curve seems very valuable for trading in that unlike the gambler's method of position sizing, it would allow a trader to decrease position size or stay out of the trade all together until the cross in the positive direction. FYI, I still have no idea how to calculate this and need to study this more. Is this essentially looking at your trade log over a 2 year period and saying, ok, I tend to have 4 successful trades on average before a loser, so I will take a break or decrease my position on the 5th trade?
As you mentioned by looking at your trade log over a period of two or three years you get a feel of your systems’ behavior and you can exploit this using the equity curve position sizing method.


Quoting tazmet
C)Finally, the fixed fractional method gives you an idea of what position size you should use that goes beyond a simple 2% based on the probability of wins and losses. I hope you're going to explain how to calculate this probability.

Yes. Basically Ralph believes that the risk/reward is not a straight a line, meaning that the more you risk the higher your rewards. It is a curved line and has only one peak called optimal f. Fixed Fractional method is all about finding this optimal f.

I will write about calculation and pros and cons of this method. Make sure you stay tuned.

Thanks,

Moh
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