Kelly formula is just for gamblers
- Thread starter ronblack
- Start date
This shows a profound misunderstanding of the Kelly fraction, or for that matter, any fractional betting strategy. The main advantage of fractional betting is that you are never risking all of your betting account, and therefore you never have a risk of ruin (100% loss).
The formula for risk from Kelly betting comes from one of the blackjack sites by Don Schlesinger:
Prob[A reaches yA before xA] = [x - 1]/[(x/y) - 1]
where A is the starting bankroll ;
x is any positive multiple ;
y is any other positive multiple.
So the probability that you double your betting account before seeing it cut in half when Kelly betting is [½ - 1]/[½/2 - 1] = 2/3 = 67%.
More to the issue of ruin, the probability of doubling, tripling, etc. your account before seeing it reduced to zero is [0 - 1]/[0/y - 1] = 1= 100%.
IOW, there is zero risk of ruin with Kelly.
True, but that's from a purely mathematical sense and not very practical. Like you were mentioning, the odds of you cutting your bank in half before doubling it is 1/3. The probability of that occurring 4 times in a row is (1/3)^4 = over 1%. So 1% of the time, you are left with 6.25% of your original bankroll. In the trading/blackjack world, that is basically considered "ruined". Or 12.5% of bank, 3.7% of the time. Or 25% of bank, 11% of the time. Risk like that is way too high and for all practical purposes bringing your account down to 1/10 it's size is basically "ruin".
To take an extreme example, risk 99% of your account on each trade. Obviously, if tick sizes were, infinitesimally small, you'd never be ruined, but that's not really the argument here...
If you continue to research the blackjack boards you will see that they suggest half or quarter kelly.
I'm with ya there. If I'm not making mistakes, I think something is wrong!
Note to young folks: Don't get old...
don't know why I happened to dredge up this old thread. But I was thinking a bit about the posts.
I used to think kelly meant a fraction of your captial to bet on each event. But it is not (in the case of trade position sizing). If k=10% and you have 100k capital, it does not imply betting 10,000, meaning you can only lose 10,000 max.
You have to go back and calculate your max risk/bet (ideal loss/stop) as = to k, and calculate the number of shares to buy meaning it can be much greater than 10% of your bankroll being bet (maybe even more than entire bankroll). Which is pretty ridiculous, because you are assuming your risk will be limited by a stop. What if your risk (stop/kelly fraction) is 4% and the equity/instrument gaps down 30-35% (FNM/WM/LEH anyone?).
Viewed in this context, the kelly formula as applied in most trading books is absurd. Why do they even promote that?
Any counter arguments?
I used to think kelly meant a fraction of your captial to bet on each event. But it is not (in the case of trade position sizing). If k=10% and you have 100k capital, it does not imply betting 10,000, meaning you can only lose 10,000 max.
You have to go back and calculate your max risk/bet (ideal loss/stop) as = to k, and calculate the number of shares to buy meaning it can be much greater than 10% of your bankroll being bet (maybe even more than entire bankroll). Which is pretty ridiculous, because you are assuming your risk will be limited by a stop. What if your risk (stop/kelly fraction) is 4% and the equity/instrument gaps down 30-35% (FNM/WM/LEH anyone?).
Viewed in this context, the kelly formula as applied in most trading books is absurd. Why do they even promote that?
Any counter arguments?
Either I am misunderstanding, you are misunderstanding, or the majority of textbook writers are misunderstanding. Thomas stridsman ( a respectable writer), shows an example whereby with 100k capital and a few win loss assumptions, you calculate kelly to be 6.7%; rather than risk 6.7% of the 100k capital ,however, he
1) calculates a stock at 50 with a 4 dollar stop (46 support), then proceeds to divide the risk amount 6,700 by the 4 pt. stop. Implying you can buy 1,675 shares. Then goes on to say 1,675*50 =83,759, which is the "amount of your capital that needs to go to this trade."
83,759 is NOT 6.7% of your bankroll, it is more like 83.7% of your bankroll, under the assumption that you will only lose the 4pt. stops worth of risk.
Again, if the stock gaps down 50% you are hosed. Applying the kelly formula as many of these authors have done, is implying that you will somehow not risk more than the x point stop/trade.
Which when taking slippage and massive gaps into account, renders the whole idea useless or worse.
Here is another example of a promoter, pushing the same concept (michael harris). It includes a perfect case of what you said "would never be an instance where Kelly would tell you to use more than your existing bankroll ."
Either your statement is wrong, or the far majority of trading promoters covering kelly are.
http://www.trading-lab.com/forums/kelly_bet_sizing_2-t308.html
Please explain to me my misunderstanding.
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P.S. The original author, kelly, intended for the variable to be k% of your bankroll period, under the assumption that the payout win or loss would ALWAYS be a fixed amount (i.e. 1dollar loss, 2 dollar win), so that in no case, would you ever lose more than k% or your bankroll per bet. Interpreting it as these authors have done, does not retain that property.
Kelly is being bastardized by the writer.
The writer is calculating the % to invest based on a stop which is not reality. As you correctly point out, a gap down is not accounted for the way the % was figured.
Kelly is simply your edge divided by your risk (odds). Adding other assumed factors to the equation IMO no longer makes it Kelly such as assuming your risk is only 10 when it could actually be a lot larger.
I use Kelly in my sports betting. It is much easier to apply to sports because in wagering you have a finite loss and if you know your statistical edge, Kelly applies very easily.
Joe.
The writer is calculating the % to invest based on a stop which is not reality. As you correctly point out, a gap down is not accounted for the way the % was figured.
Kelly is simply your edge divided by your risk (odds). Adding other assumed factors to the equation IMO no longer makes it Kelly such as assuming your risk is only 10 when it could actually be a lot larger.
I use Kelly in my sports betting. It is much easier to apply to sports because in wagering you have a finite loss and if you know your statistical edge, Kelly applies very easily.
Joe.
Interesting, glad to see I'm not going nuts here. I agree, the key is knowing you have a "Finite" loss, which is contrary to the trading author interpretations.
The crazy thing is I can point out a dozen trading books that regurgitate this as money management, yet do not point out the possibility of a gap or slippage.