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# Kelly formula

Discussion in 'Risk Management' started by trading1, Aug 4, 2007.

Regarding the âKelly formulaâ which indicates the amount to stake, given the win/loss ratio and win probability, is there anyone familiar with or using this?

It seems it has a major flaw, because for trading stocks, it may not be known ahead of time the amount which is at stake, a win or a loss may result in anything from a tiny loss or win to a full stoploss trade.

Has anyone approached this problem? For the moment I am grouping trades together, so as to get a more predictable outcome and hence use Kelly.

2. ### joesan

I also have a question about kellys formula. Regarding the optimal fraction in kelly's formula, is this the percentage of the total account to be risked , or is this the percentage of the total amount that can be used to trade ?

For example, suppose you have a USD100,000 acount for trading stocks, kelly ratio is 20%, current price for ABC is 100 PER share,stop loss for stock ABC is USD10 away from the current price,. so how many shares you will buy for ABC, as follows

a)
USD100,000*20%/100=200 shares

b)
USD100,000*20%=USD20,000 as the total amount to be risked
USD20,000/10=2,000 shares

min(100000/100,2000)Â£Â½1000 shares

According to kelly's formula , a) or b) is correct ?

3. ### kut2k2

You've pinpointed a key issue with Kelly sizing. You need to establish a trade distribution baseline. Once you have the baseline, you can test the Kelly sizing with the remainder of the trades in your backtest. There's no hard and fast rule on how long the baseline should be, but anything less than 20 trades is probably asking for trouble.

4. ### oTzt

"a" is correct. K% is the percentage of your equity to use for a given trade, not the percentage to expose at risk.
Hence, your position size will be :
\$100,000*0.2= \$20000 available / \$100 per share = 200 shares.

Olivier.

5. ### maxpi

Kelly's math is for the fastest accumulation over time and it does not take into account risk of ruin. Most advice seems to center on risking 2% of capital per trade as a rule of thumb.

I was looking into calculation of risk of ruin and came across a formula that applied to a 1:1 reward/risk per average trade situation and the note that "if reward/risk is not 1:1 then the calculation of risk of ruin becomes much more complicated". I searched for calculators of risk of ruin and came across no free ones that were aimed at trading. I found some that were gambling oriented. Does anybody know of a calculator or formulas for ROR calculations? I'm not doubting that the 2% rule is not a good thing, I'm curious as to how ROR deviates as system parameters vary.

6. ### ronblack

This is the correct way to apply the formula.

If your stop is \$10 and the trade is a loser, the loss will be \$2,000 or 2% of your equity. The number of shares turns out to be equal to that obtained using the fixed risk percent strategy. This just happened of course because of the way you have chosen the numbers.

But if the stop is changed to \$20 instead, the loss becomes equal to 4% of the equity when using Kelly formula. For someone who risks only 1% - 2% this is way to high.

This means that risk is not controllable with the Kelly formula. What it attempts to do is a geometric maximization of returns assuming that you have a good system to trade.

Bottom line: you cannot do a geometric maximization of returns and control risk at the same time. You choose.

Ron

7. ### maxpi

You can relate Kelly to risk however. I found an assertion [unproven by the author or myself at this point] that at one kelly size you have a 1/3 chance of going to half your account before doubling, at half Kelly you have 1/9, etc. Maybe the comfort zone is at about 1/4 Kelly, 1/27 chance of going to half before doubling, seems ok to me.

My dilemma is I'm trading the YM which is by it's nature hugely leveraged. With my account size Kelly math is out of the question, I'm protected more by stop market orders [I'm not really sure where they reside at this point, IB is my broker], not holding overnight or during the thinly traded hours, and the fact that volatility on the underlying is not likely to take me out of the game with a large sudden move or a trading halt... still there is the black swan that has to happen at some point no matter what you do....

8. ### kut2k2

This is a common misconception with the Kelly fraction. Is there total risk control? No, total risk control would be to not trade at all. But if the Kelly fraction did not mitigate a lot of risk, there would be no maximization of returns. That's just a basic outcome of the mathematics. Despite ignorant claims by some, there is zero risk of ruin with the Kelly formula, and the remaining risk that is reduced by, say, half-Kelly sizing comes at a cost of taking twice as long to reach your same goal if you were full-Kelly sizing. A quarter-Kelly sizing would take four times as long.

TANSTAAFL

9. ### maxpi

I have always felt that lots of traders are way too risk averse. I see threads touting how the "big smart guys" are looking at their Sharpe ratio, etc. and other threads about the "Great Hedge Fund Meltdown" and how it is going to take out the economies of the world. You would think that the hedge fund guys would be the smart money, and Bear Stearns should be able to attract the talent..

I'm looking for the comfort zone for an autotraded system. Big drawdowns bring uncertainty and that is not comfortable. I've found that with 1.5:1 average reward to risk I want 65% winners, with 2:1, 50% minimum, with 3:1, 35% or so, and so on.

I like the Kelly bet sizing a lot, it guides my systems into the area I like to be in without applying it as a bet sizing formula per se.

I've been reading up on Tai Chi Chuan and looking at youtube videos on it and related arts. The Tai Chi practitioner is supposed to attain a relaxed and happy inner "landscape", that is when the body and the mind are both efficient. I don't think you can force that to happen, you have to really work at external things until they make sense.... if you are critical of your wife you have to get over it, if your trading systems are not well thought out and implemented, you have to work on it until they are.. I don't want trading to mess that up for me. There are lots of things in this world that are trying to mess that up for me, little by little over the years I have put them far away, I don't want trading to be the replacement for all of them!!

10. ### TSGannGalt

Max. Med. Min.

#10     Aug 5, 2007
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