Kelly sizing...

[logic_man]

Quote from goodgoing:



If one has developed a new system the question is when does one start applying Kelly? You do not know whether the system will remain profitable or generate a large drawdown and lose money. If one applies Kelly to an unprofitable system, then that guarantees ruin. Some other method must be applied until one is sure about the system parameter values and especially the win rate p and the R:R ratio.

If you do a lot of backtesting with Kelly as your position-sizing (or optimal f, I would assume) you will probably see your system go through at least one drawdown of 90%+. If it recovers and makes a new equity high in the backtest, chances increase that your system has some value. Would it be able to do the same thing under live conditions? Who knows. Maybe the only time it would ever come back from a 90% drawdown was during the backtest period. Maybe not and it would go on to make new equity highs again and again and each 90% drawdown would still be higher than the trough of the prior 90% drawdown.

I would also think that during your backtesting, you would notice that your account equity spends a large amount of time down 50% or more from its highs (assuming you haven't calculated your position-sizing method to limit drawdown to any set amount less than 50%). You have to be prepared to always be thinking, "If I'd just stopped trading a little while ago, I'd have twice as much money as I have now". If you are going to be successful at trading this way (assuming your method is good enough, as you say), you have to always keep in mind that your best benchmark is your starting equity, not your high-water mark and that if your method remains viable, you'll eventually make another high.

 

[kut2k2]

Quote from goodgoing:

Hey guys, I also don't like R Vince's refusal to answer specific questions a couple of posters asked but I can understand his points and where he is coming from. He is basically saying amongst other things that Kelly can cause ruin. This is true because Kelly involves stochastic components. R. Vince essentially agrees with Michael Harris in that one. Harris also states in his paper that Kelly can only apply to systems with stationary values for p and R:R. Here is the link to that free paper link.

I'm very leery of any scholarly paper with a typo in its title (EXPECT GAIN rather than EXPECTED GAIN). And Harris doesn't disappoint: he makes the classic and colossal mistake of reducing a multi-outcome situation to a two-outcome situation. Trading is a multi-outcome situation. This means that "average win", "average loss" and "win probability" are all very misguided for calculating the optimal growth fraction. As I pointed out in my thread, even reducing a three-outcome situation to a two-outcome situation can result in overbetting/overtrading, and that is always undesirable.

Quote from goodgoing:

If one has developed a new system the question is when does one start applying Kelly? You do not know whether the system will remain profitable or generate a large drawdown and lose money. If one applies Kelly to an unprofitable system, then that guarantees ruin. Some other method must be applied until one is sure about the system parameter values and especially the win rate p and the R:R ratio.

You start applying Kelly when you know you have a winning trading system. You know you have a winning trading system when you have backtested it with a large number of trades and generated a gain rather than a loss. If your expected gain is negative or zero, then your Kelly fraction is negative or zero and this tells you "don't bet" or "don't trade".

Quote from goodgoing:

I therefore think that R Vince is correct to advice against Kelly because most are struggling with their systems. Maybe some here have systems with stationary values that are profitable but most do not.

One great thing about "expected return over expected squared return" is that it can be updated with each new completed trade. If you're in a losing streak, your Kelly fraction will automatically shrink. It will grow if you're in a winning streak. Nothing is fixed in concrete.

 

[Eight]

Quote from tim888:

So what? This doesn't mean that the guy with the best account made money by chance. He may have an edge. The simulation just says that given a large number of market players who bet optimally, their equity curves will be normally distributed according to their win rate and R:R. That is all. Nothing spectacular. You don't need a simulation to know that.

if one of them had an edge, it brought his results to the settings in the simulator, they all had exactly the same overall results either by chance or whatever but they all had exactly the same chance on average and one guy was killing it and another one was destroyed... no wonder these discussions go on so long...

I'll repeat it, they all have exactly random chance, and one guy is killing it, another is destroyed... and they all are a joke...

 

[Eight]

Quote from kut2k2:

I'm very leery of any scholarly paper with a typo in its title (EXPECT GAIN rather than EXPECTED GAIN). And Harris doesn't disappoint: he makes the classic and colossal mistake of reducing a multi-outcome situation to a two-outcome situation. Trading is a multi-outcome situation. This means that "average win", "average loss" and "win probability" are all very misguided for calculating the optimal growth fraction. As I pointed out in my thread, even reducing a three-outcome situation to a two-outcome situation can result in overbetting/overtrading, and that is always undesirable.

You start applying Kelly when you know you have a winning trading system. You know you have a winning trading system when you have backtested it with a large number of trades and generated a gain rather than a loss. If your expected gain is negative or zero, then your Kelly fraction is negative or zero and this tells you "don't bet" or "don't trade".

One great thing about "expected return over expected squared return" is that it can be updated with each new completed trade. If you're in a losing streak, your Kelly fraction will automatically shrink. It will grow if you're in a winning streak. Nothing is fixed in concrete.

How is trading having more outcomes than two if you exclude black swans? You get your entry, place your bracket and wait...

 

[One]

Quote from rvince:

I won't elaborate further on that, but if you;re interested this is detailed in the forthcoming Journal of the International Federation of Technical Analysts, presented in Berlin next month, or in Tampa in November (see ralphvince.com for more on this) -Ralph Vince

RV,

Past and current issues of the IFTA Journal are available for free at their site, but I could not find your article in the 2010 issue. On your homepage it shows a date of 2010, but I suspect that was the date you wrote or submitted the article and that it will be published in the 2011 issue next year - is that right?

 

[kut2k2]

Quote from Eight:

How is trading having more outcomes than two if you exclude black swans? You get your entry, place your bracket and wait...

Each trade is a separate outcome. The odds of having two or more trades with identical returns (as if it was a gambling situation) are extremely small. So treat each trade as unique and calculate the Kelly fraction using the generalized formula I or gummy specified.

And why would you exclude black swans?

 

[The Big D]

I'm not going to bother going back and reading this entire thread, but it is correct that Kelly should reflect all possible outcomes, not be artificially reduced to two. In cases where you know there will "black swan" outliers not reflected in your test data set, you need to add them manually.

Really, Kelly should be stated as "Maximize the average of the log of your results" and left at that. Anyone who can't apply the calculus to solve that statement for their given situation is too poorly educated to be helped anyways.

That said while full Kelly maximizes the exponential growth of your bankroll, it's overbetting from a psychological perspective. 1/2 to 1/4 Kelly is much more palatable.

 

[logic_man]

Quote from kut2k2:

Each trade is a separate outcome. The odds of having two or more trades with identical returns (as if it was a gambling situation) are extremely small. So treat each trade as unique and calculate the Kelly fraction using the generalized formula I or gummy specified.

And why would you exclude black swans?

If I truly thought each trade situation was unique, why would I not develop a new methodology for each trade? Isn't it implicit in the fact that I am using a methodology which I've used in past circumstances I've identified as similar to current circumstances that I believe my outcome will be somewhat similar, even if not exactly similar? If I identify a situation which has an average (or, use medians, if you want to avoid the impact of fat tails) payout of 2 to 1 and my winning percentage in those situation implies a bet size of X, why would I not bet X? If I have an accurate taxonomy of situations, I know the historical payouts well enough to have an accurate estimate of what my odds are. I would be much better off with a number of different Kellys (one for long trades and short trades, at a minimum and probably one of each for "bull" markets and "bear" markets, since the market acts differently in both), rather than one number.

On "black swans", aren't there both positive and negative black swans? Anyone going long at the beginning of September was the beneficiary of a positive black swan, no? Best September in 70+ years. Or anyone who got long in March 2009, which had something like the best 2-week percentage run in 80 years. Unless you have bad luck as a trader, wouldn't the distribution of "black swans" you face be equally positive and negative, canceling out over time? You could also limit the negative impact of black swans by only buying options, so that you could never lose more than your premium.

 

[logic_man]

Quote from The Big D:



That said while full Kelly maximizes the exponential growth of your bankroll, it's overbetting from a psychological perspective. 1/2 to 1/4 Kelly is much more palatable.

The problem with this is that the relationship between the amount you decrement from full Kelly and the ending amount of your bankroll isn't linear, because of the decreased reinvestment at each trade. The amount you end up costing yourself in foregone gains (yes, they are hypothetical, but are you going to tell me you wouldn't go back to the tape for the days you would have made those trades and re-calculate what you could have made on them? "Risk aversion" in real-time often gives way to "what if?" when you have a moment to reflect back) is far in excess of the psychological relief that comes from not experiencing a 90% drawdown, but experiencing a 50% drawdown. Both drawdown levels will make you ill, but the Kelly fraction you are betting to give you the 90% drawdown will make you much, much richer than the fraction leading to the 50% drawdown. When I ran the numbers, I think it was the case that by betting half-Kelly, I ended up with 20% of what I would have had with full Kelly and my max drawdown was still about 60% of the size of the max drawdown with full Kelly.

The answer to the psychological difficulties is to segregate a specific amount of your account, even if it is 1% of your total capital, and then trade that using Kelly (or, as is the case in this thread, optimal f) and periodically (I would say, based on the trade frequency of your methods) rebalance between the two accounts. My guess is that, again, depending on the frequency of your trading and the amount of your initial capital, the "Kelly" part of your capital will contribute more to your overall ending bankroll than the non-Kelly part. And, you'll be able to sleep at night knowing that every month or 6 months or whatever, you'll sweep that Kelly account into your "small bet" account or a vacation fund or something, and if it's in a drawdown mode and there's nothing to sweep, it is still only a small proportion of your current capital.

For fans of optimal f, substitute that for Kelly.

 

[The Big D]

Quote from logic_man:
On "black swans", aren't there both positive and negative black swans? [/B]

Doesn't matter. Do this experiment: calculate the Kelly bet size for this bet:

0.6: +1
0.4: -1

and then do this one:

0.01: +100
0.59: +1
0.39: -1
0.01 -100

Your Kelly size will be radically smaller for bet 2 than for bet 1 even though they have the same expectation and the "black swan" events are symmetrical.

When you understand intuitively why that is, you'll be somewhere.