Question on Kelly Formula : Positive Expectancy But...

[choubix 10]

Hello everyone,

 

I am currently reading about the Kelly formula on various website.

I now understand better that money management is a powerful tool to use when trading.

 

However something escapes me:

Assuming one has a trading system tat delivers a positive expectancy BUT there are fewer winning trades than losing trades, how to use the kelly formula??

 

e.g:

 

winning trades : 45%

losing trades : 55%

 

average win: 2,000

average loss: 1,000

 

expectancy is positive with : 0.45 * 2,000 - 0.55 * 1,000 = 350

 

Yet the K% would be negative because there are only 45% winning trades.

 

K% = (0.45 - 0.55) / 2 (where 2 is derived from 2,000 / 1,000)

 

Is there a more "refined/updated" Kelly formula that addresses this issue or this kind of bet should be considered a bad trade and should be avoided ?

 

Thanks!

[equtrader 10]

K% = Expectancy/average winner = 350/2000 = 0.175 or 17.5%

 

This is the best paper on Kelly I have been able to find:

 

http://www.priceactionlab.com/Literature/Kelly.pdf

 

Read the examples at the end.

[choubix 10]

Thank you for your post Equtrader.

 

I've printed the document and will read it in a short while!

 

Happy new year to you.

 

+++

[choubix 10]

actually I also made a mistake as I wrote : K% = (0.45 - 0.55) / 2 (where 2 is derived from 2,000 / 1,000)

 

when actually it should be:

 

K% = 0.45 - ( 0.55 / 2 )

 

which returns a positive result (17.5% as you mentioned equtrader)

 

Tks!

[equtrader 10]

actually I also made a mistake as I wrote : K% = (0.45 - 0.55) / 2 (where 2 is derived from 2,000 / 1,000)

 

when actually it should be:

 

K% = 0.45 - ( 0.55 / 2 )

 

which returns a positive result (17.5% as you mentioned equtrader)

 

Tks!

 

ur welcome with a delay:)

[silentdud 10]

Hello everyone,

 

I am currently reading about the Kelly formula on various website.

I now understand better that money management is a powerful tool to use when trading.

 

However something escapes me:

Assuming one has a trading system tat delivers a positive expectancy BUT there are fewer winning trades than losing trades, how to use the kelly formula??

 

e.g:

 

winning trades : 45%

losing trades : 55%

 

average win: 2,000

average loss: 1,000

 

expectancy is positive with : 0.45 * 2,000 - 0.55 * 1,000 = 350

 

Yet the K% would be negative because there are only 45% winning trades.

 

K% = (0.45 - 0.55) / 2 (where 2 is derived from 2,000 / 1,000)

 

Is there a more "refined/updated" Kelly formula that addresses this issue or this kind of bet should be considered a bad trade and should be avoided ?

 

Thanks!

 

The Kelly formula is only useful if you are taking on a single trade at once. You will not make money if you play a single trade of the same strategy at one time unless you are highly leveraged or you have a substantial cash reserve. Also you will take larger hits to your cash reserve. It's a good lesson for making basic trades, but it is really poor in terms of actual risk management. I know for a fact that Edward Thorpe used to use it, but he was old school and there have been so many innovations since then.

 

For example, if you play 5 games of poker that are within your bankroll instead of one you are diversifying away some of the risk. On the other hand, when you try to do this with stocks there is a correlation of every single security to every single other security and you need to acknowledge this other wise you will loose a lot of money.

 

It's also important to pay attention to skewness in return distributions (not accounted for in the kelly criteria) and Kurtosis (which Long Term Capital Management ignored and caused them to be ruined).

 

Here are two popular books on portfolio management:

 

Managing Investment Portfolios: A Dynamic Process (CFA Institute Investment Series)

 

The CFA institute publications are usually very good but this book includes extra types of portfolio management which you might not need.

 

You may want to look at this one which is cheaper and its highly rated:

The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk

 

 

You should realize that a lot of the theory that is in these can actually be applied to modern portfolio theory. I also highly recommend that you look at some of Edward Thorp's papers, although they are highly outdated.

 

[http://edwardothorp.com/id10.html]Edward Thorps publications[/url]

 

 

Hopefully that helps!

 

-Silentdud

Edited May 30, 2011 by silentdud

[SunnyJHarris 10]

I have a modified Ralph Vince optimal-f that I call Ultimate-F, because it avoids the high risk of ruin. It is much better than the Kelly formula and still compounds your results dramatically. YES, it works great with 45% or even 40% as long as your CPC Index is greater than 1.2.

 

 

Hello everyone,

 

I am currently reading about the Kelly formula on various website.

I now understand better that money management is a powerful tool to use when trading.

 

However something escapes me:

Assuming one has a trading system tat delivers a positive expectancy BUT there are fewer winning trades than losing trades, how to use the kelly formula??

 

e.g:

 

winning trades : 45%

losing trades : 55%

 

average win: 2,000

average loss: 1,000

 

expectancy is positive with : 0.45 * 2,000 - 0.55 * 1,000 = 350

 

Yet the K% would be negative because there are only 45% winning trades.

 

K% = (0.45 - 0.55) / 2 (where 2 is derived from 2,000 / 1,000)

 

Is there a more "refined/updated" Kelly formula that addresses this issue or this kind of bet should be considered a bad trade and should be avoided ?

 

Thanks!

Edited June 1, 2011 by MadMarketScientist
removed marketing

[silentdud 10]

I can see a few problems with optimal-f from just a quick look at it though. It is guilty of the same problem that problem that the Kelly criterion is, i.e. not looking at the instances around the mean, only at the estimated values. Does the modified version fix this?? Do you have any links describing its calculation?

 

As far as I can tell it is only useful for ball parking and quick, on the spot math.

 

I looked at this for information on calculating the original "optimal" f.

Contango: Optimal f

 

Thank you.

Silentdud

[SunnyJHarris 10]

I have a chart of the results ... I can't reveal the calculations, as, unlike Vince, mine is proprietary and I offer it to my students without revealing the code. My code uses the actual trade values and calculates the number of shares to put on for the next trade. To use the code you must have a minimum of 30 actual trades to put into the spreadhseet.

Sunny

 

I can see a few problems with optimal-f from just a quick look at it though. It is guilty of the same problem that problem that the Kelly criterion is, i.e. not looking at the instances around the mean, only at the estimated values. Does the modified version fix this?? Do you have any links describing its calculation?

 

As far as I can tell it is only useful for ball parking and quick, on the spot math.

 

I looked at this for information on calculating the original "optimal" f.

Contango: Optimal f

 

Thank you.

Silentdud

Edited June 1, 2011 by MadMarketScientist
removed marketing

[pashag81 10]

I used Kelly for strategy which trades by single instrument, I see that perfomance became better only on 10%-20%. is it normal?, or it should gives better upgrates for perfomance?

[silentdud 10]

I used Kelly for strategy which trades by single instrument, I see that perfomance became better only on 10%-20%. is it normal?, or it should gives better upgrates for perfomance?

It's not really improving your returns, i.e. your immediate ones, it should be improving them over time, but the idea is the same as controlling and making sure your capital reserve isnt depleted so much that you can't regrow it.

You may want to look at the Safety first criteria. If you are looking for simple management that could be up your alley. It depends on how much money that you are managing.

[eqsys 10]

The problem with using the Kelly formula, or any other formula that considers closed trades is that there is no consideration of what happens DURING the trade - in other words, the drawdown that can and does occur while waiting for the system to close out of the position.

 

Not only is there the drawdown that happens during one trade, but there is the accumulated drawdown from a series of trades. Even if your system produced 100% profitable trades on a closed trade basis, if the intra-trade drawdown is large, it is going to cause you much grief and it is likely you will bail on your trade and system well before your system pulls you out.

 

I use TradeStation to backtest my systems, and always look at the Strategy Performance Report. Then I look at the Max Drawdown Intra-day Peak to Valley calculation.

 

I then allocate 10x this number to trade 1 futures contract. This way, when this drawdown occurs again (and it WILL) I will only be down 10% in my account equity - a number I have found I can handle without getting extremely upset. If your account is small, you might be able to handle up to 30% drawdown before you panic, but as your account size increases, it becomes increasingly more difficult to take drawdown of this magnitude.

 

If you get extremely upset, and everyone has a different point where this occurs - but it does and will occur, you will 1) exit your trade at the wrong time, 2) be unable to sleep, 3) stop trading your system, or 4) some other irrational behavior. Have you ever just said, "I can't take this anymore", and just sold everything?

 

If you are overleveraged and trading futures, you may just run out of equity and get a margin call - and that's the end of your trading either permanently or temporarily.

 

The trouble with a system that shows a 2:1 profit factor, that is, winning trades make double the losing trades, but you have fewer than 50% winning trades, is that you have a lot of losing trades - tough to handle emotionally. Also, the winning trades come from a subset of the whole universe of closed trades, and this might mean that the winners were based on some unusual price behavior not llikely to occur in the future.

 

The ideal system has maximum gains and minimum drawdown, and ideally, seldom has a losing day.

 

The simplest example of a system that is almost impossible to trade, yet looks great on paper (compute the Kelly formula) , is a buy and hold. It may have 1 profitable trade,and no losing trades. However, the intra-day drawdown peak to valley might be HUGE. That's what will bury you as a trader.

[SunnyJHarris 10]

As Mammy Yokum said: "Truer words were never spoke."

The larger your trade size and the higher the account value, the more likely you are to sabotage your system.

 

 

The problem with using the Kelly formula, or any other formula that considers closed trades is that there is no consideration of what happens DURING the trade - in other words, the drawdown that can and does occur while waiting for the system to close out of the position.

 

Not only is there the drawdown that happens during one trade, but there is the accumulated drawdown from a series of trades. Even if your system produced 100% profitable trades on a closed trade basis, if the intra-trade drawdown is large, it is going to cause you much grief and it is likely you will bail on your trade and system well before your system pulls you out.

 

I use TradeStation to backtest my systems, and always look at the Strategy Performance Report. Then I look at the Max Drawdown Intra-day Peak to Valley calculation.

 

I then allocate 10x this number to trade 1 futures contract. This way, when this drawdown occurs again (and it WILL) I will only be down 10% in my account equity - a number I have found I can handle without getting extremely upset. If your account is small, you might be able to handle up to 30% drawdown before you panic, but as your account size increases, it becomes increasingly more difficult to take drawdown of this magnitude.

 

If you get extremely upset, and everyone has a different point where this occurs - but it does and will occur, you will 1) exit your trade at the wrong time, 2) be unable to sleep, 3) stop trading your system, or 4) some other irrational behavior. Have you ever just said, "I can't take this anymore", and just sold everything?

 

If you are overleveraged and trading futures, you may just run out of equity and get a margin call - and that's the end of your trading either permanently or temporarily.

 

The trouble with a system that shows a 2:1 profit factor, that is, winning trades make double the losing trades, but you have fewer than 50% winning trades, is that you have a lot of losing trades - tough to handle emotionally. Also, the winning trades come from a subset of the whole universe of closed trades, and this might mean that the winners were based on some unusual price behavior not llikely to occur in the future.

 

The ideal system has maximum gains and minimum drawdown, and ideally, seldom has a losing day.

 

The simplest example of a system that is almost impossible to trade, yet looks great on paper (compute the Kelly formula) , is a buy and hold. It may have 1 profitable trade,and no losing trades. However, the intra-day drawdown peak to valley might be HUGE. That's what will bury you as a trader.

[silentdud 10]

Edit: sunnyjharris just said exactly what i was going to lol

Edited June 2, 2011 by silentdud

[gianno 10]

You play with Kelly or Optimal-f, you play with fire.