simple money management...

Discussions about Money Management and Risk Control.
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mpok8
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simple money management...

Post by mpok8 » Mon Mar 23, 2009 7:56 am

Here is a quote posted on this forum earlier...

"The idea that money management is a mysterious and complex issue is proliferated by books like this. I can sum up effective money management in two steps: First take your worst case loss scenario, which will be based on a run of lossses with a less than one percent probability of occurring, as calculated by your expected win/loss ratio. For example, if you reasonably expect to win 40% of the time and lose 60% of the time, there is a less than 1% or "worst case" probability, that you will see ten losses in a row at some point in your trading (this may look like hard math but the calculations are actually grade school level). Next, determine your max desired drawdown. What's the biggest hit you could possibly stand? Ten percent down? Twenty five? Fifty? Let's say you are moderately aggressive and able to deal with a twenty percent drawdown without losing your nerve. Divide twenty percent by ten, and you see that your max allowable risk is 2% of your account balance, including calculated slippage and commissions per trade. If you can stomach a 40% drawdown you don't risk more than 4%, and so forth. Simple, straightforward, no hidden gimmicks, gizmos or geekspeak. The only other bogey you have to deal with is the once in a blue moon nasty price shock that blows your stop to kingdom come (a simple and emphatic argument for less risk per trade, not more). "

Can someone help me then calculate the risk per trade I should take given that I have a system with the following characteristics:


%win = 42%
%lose = 58%
avgwin/avgloss = 1.64

If I have a less than 1% chance of incurring 9 losses in a row (i.e. 0.58^9) and I can stand a maximum DD of 20% then does that mean I should risk 20/9= 2.22% per trade? I'm not using the avgwin/avglose statistic as is mentioned above though... can someone help? THanks

nzbryant
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Post by nzbryant » Mon Mar 23, 2009 9:03 am

Dont use this system. You could have 8 losses in a row, one win, then another 8 losses.

Just use testing.

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Post by DeanoT » Mon Mar 23, 2009 9:32 am

Like many areas of trading, traders often hold many different, and sometimes conflicting opinions on optimal money management methods. I, for example, disagree with the author of the quote you provided.

In my opinion, too much emphasis is placed on estimating the consecutive number of losses a system might generate, and using this as a benchmark to calculate potential drawdown. The problem with this method is that drawdowns can also result from a number of non-consecutive losses. For example, having 35 losing trades out of 40 might be more damaging to a portfolio than 9 consecutive losses. How do we calculate the probability of 35 losses out of 40 ? It isn't difficult, but do you really want to calculate every conceivable possibility out there ?

Additionally, my own experience has demonstrated that, at least for longer term systems, the largest drawdowns in a simulation are often the result of significant trend reversals in very profitable positions, as opposed to consecutive losses. And in my subjective opinion, losses derived from give back of profits are much less "dangerous" to the portfolio than a series of consecutive losing trades. As a result, I do not use drawdown indicators heavily in my own evaluation of trading systems.

As a start, I would suggest experimenting heavily with stop placement, from very tight to very wide, and everything in between, and noticing the effect on your Win %, and your Average Win/Average Loss ratio. You may also begin to notice some correlation between Win % and risk-adjusted return measures such as MAR.

As for your question of how much to risk per trade, you can derive the mathematical answer by using the Kelly formula, but that is going to give you a result which will push your drawdown levels to close to 100%, since the optimal position size for maximum profit will always be the size which pushes you closest to the edge of the cliff, without falling off (in backtesting at least).

It might be better to simply run the simulations in Trading Blox for various position sizes and notice its effect on profits and drawdowns, and then choose the one that gives you satisfactory profit for satisfactory risk.

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Post by sluggo » Mon Mar 23, 2009 9:36 am

Roundtable member Ghostrider wrote that: viewtopic.php?p=4147&highlight=mysterio ... speak#4147 She was quoting a review of Ralph Vince's book "Portfolio Management Formulas" found on Amazon.com's website http://www.amazon.ca/Mathematics-Money- ... ingblox-20 (see picture).

Notice that the review was written in 2001 -- back in the bad old days when "Money Management" books (and reviews of such books) assumed you were using only one system trading only one market. This is silly; most traders trade several markets simultaneously, and many of them trade several systems (each with its own portfolio of markets) simultaneously. My IRA, for example, has got 38 positions on today; trades that have been entered but not yet exited. That's 38 simultaneous trades.

In a multiple-simultaneous-trades reality, the account equity at the end of trade number N is not the account equity at the beginning of trade number N+1. Yet that is the basic assumption in Justice Litle's calculation. Conclusions that proceed from incorrect assumptions are questionable at best; financially disastrous at worst.

I suggest that a safer route is to put your system(s) into modern backtesting software -- software that can simulate portfolio trading and dynamic positionsizing -- then simulate your system(s) behavior with lots of different betsizes. When you find a betsize that you think you like, turn on your software's "Monte Carlo" feature and have a look at the statistics of "What might happen to this system" and the probabilities of those various happy and unhappy scenarios.
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Post by mpok8 » Mon Mar 23, 2009 11:35 am

Ok -- thanks for the replies... I understand that thinking in terms of consecutive losses is flawed...

Just out of interest, given the aforementioned stats (i.e. P(win) = 0.42 and avgwin/avgloss = 1.64) then is the kelly fraction found as follows:

k = P(w) - (1-p(w))/[avgwin/avgloss] =

= 0.42 - (1-0.42)/1.64

= 0.066

I.e. the Kelly fraction of capital is 6.6%??

Is this correct?

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Post by sluggo » Mon Mar 23, 2009 12:23 pm

mpok8 wrote:I.e. the Kelly fraction of capital is 6.6%??

Is this correct?
Just now I queried an internet search engine, to find web pages that calculate the Kelly optimal betsize using input values you provide. The search returned quite a few different websites that do the Kelly calculations. You could type in your example problem and see whether they get the same answer as you.

A good "test case" is the one in Ralph Vince's book (also repeated in the Druz/Seykota "Heat" article): You bet a fraction "f" of your bankroll (0 <= f <= 1.00). A fair coin is flipped. If it comes up Tails, you lose your bet. If it comes up Heads, you keep your bet AND the counterparty pays you a profit of 2x your bet. (i.e. your profit is 2*f*B where B is your bankroll before the flip). What is the Kelly optimal value of "f"? Answer: 0.2500

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Post by mpok8 » Mon Mar 23, 2009 1:24 pm

Sluggo

I did as you said and looked it up on the tinternet... here is a simple article explaining kelly criterion:

The Formula

The Kelly formula itself is rather simple to understand, the formula is:

Kelly % = W - (1 - W) / R

Where:

Kelly % = the percentage of capital to risk on the trade for maximum gains.
W = Historical winning percentage of all trades.
R = Historical average Win/Loss ratio.

To understand the Kelly % statistic a little better, it's important to follow an example. Consider the following ten trades, or, if you wish you might like to follow this example by using your own set of closed trades.

Trade 1 - Win $250
Trade 2 - Loss $500
Trade 3 - Loss $80
Trade 4 - Win $250
Trade 5 - Win $670
Trade 6 - Loss $45
Trade 7 - Loss $110
Trade 8 - Win $210
Trade 9 - Win $105
Trade 10 - Loss $50

From this set of trades we can obtain the inputs into the Kelly formula:

W = Winning Trades (5) / Total Trades (10) = 50%
R = Average Winning Dollar = $297 / Average Loss Dollar = $157 = 1.89

Substituting these values into the Kelly formula we can calculate the Kelly % result:

Kelly % = 0.5 - (1 - 0.5) / 1.89 = 0.23544

What does this figure mean?

The next step to the analysis process is to evaluate this figure and determine exactly what it means. As we previously mentioned, the Kelly % calculates the optimal amount of capital to risk on the next trade in order to maximise your gains.

For example, with total capital of $10,000 you would risk 23.54% on the next trade. Sometimes you may have to exercise due care and reduce your risk to remain in line with other trading constraints that you might have in place. For example, you might have a constraint which limits the maximum risk on each trade to a total of 2% total capital. In this instance the Kelly % optimal risk of 23.54% exceeds your constraint and cannot be adhered to.

But what does this Kelly % mean for your trading performance?

The Kelly % is purely an optimal growth strategy, it provides a means to trade based upon the maximum expected rate of wealth growth calculated from your existing trade history. By analysing the probability of past events, the Kelly % statistic provides a guide for trades in the future, the movement of Kelly % can be summarised as follows:

1. Kelly % increases as R increases
2. Kelly % increases as W increases

This movement correlates to a position sizing strategy known as "Anti-Martingale" whereby the risk defined on each bet is increased based upon the success of previous results. The main difference between the two strategies is that "Anti-martingale" only assesses the outcome of the previous trade to influence the size of the next, while Kelly % takes into consideration an entire set of trade data.

Kelly % dictates that more money can be risked if historical probabilities indicate the chance of success is high, the higher the chances of success the more money that can be risked.

As previously mentioned, exercise caution when using Kelly % and make sure you don't breach any existing risk constraints already in your trading plan.


Using my stats for my method I have the following:

Kelly % = W - (1 - W) / R

= 0.42 - 0.58/1.64 = 6.6% as previously stated....

Does anyone disagree with any of this?

Thanks

Mike

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Post by sluggo » Mon Mar 23, 2009 1:51 pm

I recommend you type the details of your problem, into one of the websites that performs the Kelly Calculations on a web server. See whether the answer you get, matches the website's answer. After all, the website was created by someone who was very interested in Kelly calculations. So interested that he or she went to a lot of trouble, building a web page, writing software to do the calculations, and presenting it to the world for free.

Here are some "look and feel" screen images of a few web pages that I found using internet searches
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Post by RedRock » Mon Mar 23, 2009 5:16 pm

mpok8 wrote: Kelly % dictates that more money can be risked if historical probabilities indicate the chance of success is high, the higher the chances of success the more money that can be risked.
this presumes that the next trade "knows" that it is the chosen one, which will break the string of losers. Sort of like.. What are the odds of a coin coming up heads after a run of ten tails in a row. Better than 50/50?

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Post by babelproofreader » Mon Mar 23, 2009 6:31 pm

The following link has some interesting stuff about the Kelly formula as well as freely down-loadable spreadsheets.

http://www.gummy-stuff.org/kelly-ratio.htm

Personally I would not use Kelly to calculate optimal trade risk but, taking on board what Sluggo said about multiple, simultaneous positions, I would simulate my trading system to obtain a figure for draw down for the multiple positions and then using the average win, average loss and winning % for all the trades used in the simulation calculate the optimal draw down for the system and thus arrive at a minimum account size to trade such a diversified system.

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Post by Asamat » Tue Mar 24, 2009 4:30 am

I don't understand why Kelly is mentioned time and again in the context of money management. Let's make it totally clear: sizing according to Kelly is a guaranteed way to go broke. The Kelly formula gives a by far too big and optimistic results, and amplifies the tendencies of most private traders to trade too agressive anyway.

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Post by DeanoT » Tue Mar 24, 2009 6:49 am

Asamat

I don't see anyone advocating trading with position sizes equal to the results driven by the use of the Kelly formula. But to dismiss the Kelly formula as irrelevant to money management is to miss the point entirely.

Lets look at an example:

System A has the following trade characteristics:

Wins 10%
Losses 90%
Avg Winner 17%
Avg Loser 1%

Expectation per Trade = ( (10% x 17%) - (90% x 1%) / 1% )
Expectation per Trade = 0.8

System B has the following trade characteristics:

Wins 90%
Losses 10%
Avg Winner 1%
Avg Loser 1%

Expectation per Trade = ( (90% x 1%) - (10% x 1%) / 1% )
Expectation per Trade = 0.8

Both systems have the same expectancy, and for the sake of simplicity, let's assume they also have the same trade frequency. Since expectancy and frequency for both systems are equal, then they will make the same amount of money right ???

This conclusion would be wrong, and the proper use of Kelly formula can guide you as to why it would be wrong.

System A will encounter many strings of losing trades resulting in punishing drawdowns, and occasionally strike gold and erase all previous losses in one fell swoop. A winning system overall, but once which will be highly volatile. Trade this system with large position size, and astronomical drawdowns will inevitably result.

System B will plod along posting constant, but small profits, very frequently making new equity highs. This system will highly unlikely encounter a series of severe drawdowns, unless traded with close to 100% position size.

Do you have a preference yet for which system you think is likely to produce better absolute, or risk-adjusted returns ?

Throw the Kelly formula into the mix, and you get the following results:

System A 4.7%
System B 80.0%

Again, no-one is advocating trading at these supposed optimum levels, however, it should strike you as interesting that two systems with the same expectancy, and same frequency, derive very different results when input into the Kelly formula. Additionally, the results confirm our analysis above, that systems with a high probability of loss should be traded much more conservatively than more accurate systems.

All trading is about finding a meaningful edge (expectancy), exploiting this edge as often as possible (frequency), and then using money management (position size) to protect and maximise our edge. I find that the true value of the Kelly formula is its ability to assist the trader to distinguish between competing systems which, through the sole analysis of expectancy and frequency, and the absence of any money management formulae, such as the Kelly formula, can be indistinguishable.

Hence I always evaluate potential trading systems with the following formula:

Frequency x Expectancy x Kelly

Like all trading performance measures, it is not perfect, but it does account for all of the factors that are important to me in trading system evaluation.

As you rightly point out, its true value is not in determining optimal position size for traders trading multiple markets, or multiple systems, simultaneously.

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Post by RedRock » Tue Mar 24, 2009 9:05 am

DeanoT wrote:
Frequency x Expectancy x Kelly

Like all trading performance measures, it is not perfect, but it does account for all of the factors that are important to me in trading system evaluation.

.
Creative use as a system Quality measure!

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Post by stopsareforwimps » Sun Feb 27, 2011 9:35 pm

Asamat wrote:I don't understand why Kelly is mentioned time and again in the context of money management. Let's make it totally clear: sizing according to Kelly is a guaranteed way to go broke. The Kelly formula gives a by far too big and optimistic results, and amplifies the tendencies of most private traders to trade too agressive anyway.
The Kelly formula only applies when

a) You have certainty as to the probabilities and the payoffs.
b) There are only two outcomes per bet.
c) You only have one bet on at a time (implied by (b)).

So anyone who uses standard Kelly for trade sizing is misusing it.

Kelly does make an important point, which is that there is an optimal bet and it is often very counter-intuitive what it is. Ralph Vince's books have a lot of material on generalizing Kelly to more realistic situations eg where there is a range of possible returns, or a distribution. (I like Vince's books because they are very fruitful and full of interesting ideas. I would not say that he crosses all the 't's and dots all the 'i's so you should double check his formulas and recommendations before using them, as always.)

He demonstrates at length how to use Monte Carlo analysis to work out an approximation of the optimal bet size. You can also use Monte Carlo analysis to test the sensitivity of your outcomes to wrong estimates of the distribution of returns ie model error and uncertainty.

Kelly and its generalizations do not tell you where your "vomit point" is - the level of volatility, drawdowns and 'action' that your stomach cannot handle. You need to work that out for yourself. In my case the "vomit point" is usually the limiting factor not the "Kelly level".

All of this assumes that you want to maximize compound returns in the long run. That is not what I want to do. I want to maximize my lifetime utility of wealth. This takes into account my expected lifespan, required spending, different usefulness of money at different ages, and the non-linear utility of money. $1b is not 1000X as good as $1m, it is worth less than that. With sufficient effort you can also take this into account using Monte Carlo analysis. I did this a while back for myself but the code is not publishable quality.

Tim Josling

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