THE ONLY CERTAINTY IN TRADING. FIRST PRIORITY IS TO BOUND LOSSES WITH THE KELLY CRITERION.
The wrong exposure management and over-exposure is probably the number one cause of failure and margin call bankruptcy, to all the accounts of small initial funds. But this means it is the case to the majority of small individual traders. Huge funds accounts trading managers, are not so much threatened by the over-exposure, because as a rule (although it is non-optimal) they apply systematic under-exposure. But with small and very small initial funds accounts, systematic under-exposure is not something very practical.
Once I watched during 2002 a Russian Physics Scientist (that we were working in Brussels in the same University) now in Switzerland to perform a manual and semi-automated very succesful intraday trading for 100 days online. He doubled 100 K $ in 100 days. His maximum exposure rule was simple: To reserve for each contract so much funds that it becames of leverage=1, in other words without leverage. He started with under-exposure compared to the exposure corresponding to Leverage=1 and increased it gradually till the maximum exposure corresponding to leverage=1. It is probably not an exact optimal rule but it is for sure a safe tactic.
We can call it the rule of Leverage=1
Alexander Elder in his books and many other older and celebrated traders recommend a fixed exposure of 2% of the available funds. We may call it the rule of 2 %
It seems that for Alexander Elder it might have been his "holy grail" that transformed his losing trading in to winning trading. And indeed just correcting the over-exposure is enough to make the trading from losing in to profitable for a majority of traders.
Ralph Vince in his book "The mathematics of Money Management" explains that the optimal exposure is to be found by computer iterative optimization based only on the information of all the trades their gain or loss, and their percentage of succesful-unsuccesful when trading with fixed position size. In other words it is a variable parameter depending on the system's backtest. He furthermore suggest a composite empirical formula, including the optimal f, the margin and the maximum draw-dawn of the system's backtest.
Other experts (like Keith Fitshen) insist that using the maximum drawdown is an oversestimation of the risk, as the maximum drawdown will increase indefinetly as the backtest horizon increases. He suggests using the
average starting or absolute draw-down and the standard deviation of the average draw-down.
It can even be derived a formula for the average starting or absolute draw down under general hypotheses of the Equity curve growth. (See post 33, the formula is s^2/|r| , where s^2 is the variance of the equity curve, (without reinestment money mamagement) and r is the drift (slope) of the equity curve.In fact the histogram of the absolute draw downs follows the exponential distribution, see http://en.wikipedia.org/wiki/Exponential_distribution)
So he suggest estimating an accumulative histogram of draw-downs to calculate all that. His remarks are certainly correct, amd his methods, better from a statistical point of view. This is what I am using myself. I always calculate the histogram of draw-downs on any backtest, or historic performace of any system. After calculating the accumulative histogram of draw-downs we may apply a value at risk analysis and estimate what is the frequency or probability of a particular draw down. In addition what is the probability of crashing the account if a particular exposure is folowed, after this particular histogram of draw-downs. As a rule while starting with little funds we tend to apply under-exposure, compared to the optimal exposure; if we survive, and have accumulated significant ammount of gained funds, we may increase the exposure but still systematic under-exposure compared to the optimal exposure. Besides the larger size of the funds makes a small percentage of profits, a significant absolute ammount of money, adequate for normal consumtion needs.
Other traders prefer a fixed exposure (e.g. a rule of 6%) and then apply it to trade by trade, calculating the exposure based on the stop loss of each trade.
There are therefore mathematical-statistical laws of optimal exposure.
There is also subjective "feeling comfortable" exposure management conduction.
In general the final result is as smart as the dumpiest trade. (Ralph Vince)
Multiplying a large profit with zero makes always zero. (Warren Buffett)
"While reinvesting can turn a profitable system in to losing one,no reinvesting can turn a losing system in to profitable system." (Ralph Vince)
Focusing to make every single trade the best quality trade possible, it can always work, while it will not work if you focus to make every single trade profitable. So in conduction quality goes first and money afterwards.
Over-exposure above the optimal exposure will lead with almost certainty to crashing the account. Under-exposure falling in arithmetic progression, leads average return falling with geometric progression.
Instead of analysing further the exposure management I recommend reading the book by Ralph Vince : The Mathematics of Money Management.
The previous considerations lead to a withdrwal rule that e.g. has been applied for many years by professor Michael LeBoeuf in his investments (see https://en.wikipedia.org/wiki/Michael_LeBoeuf and http://www.nightingale.com/beat-time-money-trap-mp3.html )
CONSTANT RATIO WITHDRAWAL RULE . We may divide the funds to 2/3 of them that we trade, and 1/3 that we do not trade. The exact percentage should be defined by the ratio (f=R/a^2) (that we mention above from the book "Stochastic Differential equations" by B. K. Oksendal (Springer editions) page 223, example 11.5) where R is the average per period rate o return of the trading on the used funds, measured on a sample of periods and a^2 is the variance of this rate of return on this sample of periods. E.g. of the rate of return is 10% per period and the standard deviation a of it is 34%, then the percentage f is 2/3. Each period we re-adjust the total funds so that this ratio f applies as division of the funds. As the sample of measurement of this ratio is not small, usually it remains rather constant. We withdraw e.g. from the 1/3 non-trading funds ,each period never more than half of the average profits per period of the other 2/3 of the funds that are traded.
The wrong exposure management and over-exposure is probably the number one cause of failure and margin call bankruptcy, to all the accounts of small initial funds. But this means it is the case to the majority of small individual traders. Huge funds accounts trading managers, are not so much threatened by the over-exposure, because as a rule (although it is non-optimal) they apply systematic under-exposure. But with small and very small initial funds accounts, systematic under-exposure is not something very practical.
Once I watched during 2002 a Russian Physics Scientist (that we were working in Brussels in the same University) now in Switzerland to perform a manual and semi-automated very succesful intraday trading for 100 days online. He doubled 100 K $ in 100 days. His maximum exposure rule was simple: To reserve for each contract so much funds that it becames of leverage=1, in other words without leverage. He started with under-exposure compared to the exposure corresponding to Leverage=1 and increased it gradually till the maximum exposure corresponding to leverage=1. It is probably not an exact optimal rule but it is for sure a safe tactic.
We can call it the rule of Leverage=1
Alexander Elder in his books and many other older and celebrated traders recommend a fixed exposure of 2% of the available funds. We may call it the rule of 2 %
It seems that for Alexander Elder it might have been his "holy grail" that transformed his losing trading in to winning trading. And indeed just correcting the over-exposure is enough to make the trading from losing in to profitable for a majority of traders.
Ralph Vince in his book "The mathematics of Money Management" explains that the optimal exposure is to be found by computer iterative optimization based only on the information of all the trades their gain or loss, and their percentage of succesful-unsuccesful when trading with fixed position size. In other words it is a variable parameter depending on the system's backtest. He furthermore suggest a composite empirical formula, including the optimal f, the margin and the maximum draw-dawn of the system's backtest.
Other experts (like Keith Fitshen) insist that using the maximum drawdown is an oversestimation of the risk, as the maximum drawdown will increase indefinetly as the backtest horizon increases. He suggests using the
average starting or absolute draw-down and the standard deviation of the average draw-down.
It can even be derived a formula for the average starting or absolute draw down under general hypotheses of the Equity curve growth. (See post 33, the formula is s^2/|r| , where s^2 is the variance of the equity curve, (without reinestment money mamagement) and r is the drift (slope) of the equity curve.In fact the histogram of the absolute draw downs follows the exponential distribution, see http://en.wikipedia.org/wiki/Exponential_distribution)
So he suggest estimating an accumulative histogram of draw-downs to calculate all that. His remarks are certainly correct, amd his methods, better from a statistical point of view. This is what I am using myself. I always calculate the histogram of draw-downs on any backtest, or historic performace of any system. After calculating the accumulative histogram of draw-downs we may apply a value at risk analysis and estimate what is the frequency or probability of a particular draw down. In addition what is the probability of crashing the account if a particular exposure is folowed, after this particular histogram of draw-downs. As a rule while starting with little funds we tend to apply under-exposure, compared to the optimal exposure; if we survive, and have accumulated significant ammount of gained funds, we may increase the exposure but still systematic under-exposure compared to the optimal exposure. Besides the larger size of the funds makes a small percentage of profits, a significant absolute ammount of money, adequate for normal consumtion needs.
Other traders prefer a fixed exposure (e.g. a rule of 6%) and then apply it to trade by trade, calculating the exposure based on the stop loss of each trade.
There are therefore mathematical-statistical laws of optimal exposure.
There is also subjective "feeling comfortable" exposure management conduction.
In general the final result is as smart as the dumpiest trade. (Ralph Vince)
Multiplying a large profit with zero makes always zero. (Warren Buffett)
"While reinvesting can turn a profitable system in to losing one,no reinvesting can turn a losing system in to profitable system." (Ralph Vince)
Focusing to make every single trade the best quality trade possible, it can always work, while it will not work if you focus to make every single trade profitable. So in conduction quality goes first and money afterwards.
Over-exposure above the optimal exposure will lead with almost certainty to crashing the account. Under-exposure falling in arithmetic progression, leads average return falling with geometric progression.
Once we have a trading system good enough to be successful with trades where StopLoss<=TakeProfit we may apply a reinvestment technique based on the Kelly formula:
f=(bp-(1-p))/b=p-(1-p)/b . where f=optimal percentage of funds to risk, b=TakeProfit/StopLoss (it has to be >=1) and p=probability of success of the trade. (see http://en.wikipedia.org/wiki/Kelly_criterion)
For example let us say that we have an account of 1000$, and our trading system has a general success rate of 66% (after back-tests with constant lot size). Let us assume that we take a signal for a trade, that its stop-loss SL=20 and take-profit TP=30 have ratio TP/SL=1.5
Then the Kelly formula can be used to define the lot size: The optimal percentage to risk is f=(1.5*0.66-0.33)/1.5=0.44 or 44%. In other words we may risk 440$, and for the 20 pips stop loss this is converted in to 440/20=22$/pip or 2.2 standard lots! Seems quite a big number indeed.In practice we should trade with smaller lot size, (e.g. a fixed percentage of what the kelly formula gives; my experients show that 5%-25% of the Kelly percentage is a safer choice) because the Kelly formula is derived with the assumption of continous subdivision of the funds and constant success rate of the trades, while in practice, the minimum lot size,and rather variable winning rate of the trades, does not permit such a procedure.If we continue to apply this formula, if the account grows, larger, more lots are opened so it is both a de-investment (when the results go bad) and re-investment (when the results go well) money management system.
We may also derive directly the optimal leverage from the above Kelly formula and the SL, as
OptimalLeverage=((f*Equity)/SL*10)*100=(((((TP/SL)*p-(1-p))/TP/SL)*Equity)/SL*10)*100 or
OptimalLeverage=(((((TP/SL)*p-(1-p))/TP/SL)*Equity)/SL*10)*100
In practice, my backtests show that one should take a constant smaller percentage over the Kelly variable percentage.
OptimalLeverage=((f*Equity)/SL*10)*100=(((((TP/SL)*p-(1-p))/TP/SL)*Equity)/SL*10)*100 or
OptimalLeverage=(((((TP/SL)*p-(1-p))/TP/SL)*Equity)/SL*10)*100
In practice, my backtests show that one should take a constant smaller percentage over the Kelly variable percentage.
Upon this money management system we may superimpose the optimal adjustment management system, described in another post that somehow does the reverse.
Instead of analysing further the exposure management I recommend reading the book by Ralph Vince : The Mathematics of Money Management.
The previous considerations lead to a withdrwal rule that e.g. has been applied for many years by professor Michael LeBoeuf in his investments (see https://en.wikipedia.org/wiki/Michael_LeBoeuf and http://www.nightingale.com/beat-time-money-trap-mp3.html )
CONSTANT RATIO WITHDRAWAL RULE . We may divide the funds to 2/3 of them that we trade, and 1/3 that we do not trade. The exact percentage should be defined by the ratio (f=R/a^2) (that we mention above from the book "Stochastic Differential equations" by B. K. Oksendal (Springer editions) page 223, example 11.5) where R is the average per period rate o return of the trading on the used funds, measured on a sample of periods and a^2 is the variance of this rate of return on this sample of periods. E.g. of the rate of return is 10% per period and the standard deviation a of it is 34%, then the percentage f is 2/3. Each period we re-adjust the total funds so that this ratio f applies as division of the funds. As the sample of measurement of this ratio is not small, usually it remains rather constant. We withdraw e.g. from the 1/3 non-trading funds ,each period never more than half of the average profits per period of the other 2/3 of the funds that are traded.
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