if you think like a gambler you are going to end up like a gambler. this kelly is bullshit. not what you should be focusing on.
Does your 'gummy stuff' formula take into account transaction costs or price gaps...ummm....nope! Nice try on trying to obfuscate the argument though, you're a funny guy, have you considered a career in comedy?
Yes of course transaction costs and price gaps are a part of the trade returns used in the gummy formula. Why wouldn't they be? You're clutching at straws, hoping to justify Thorp's overly theoretical and unrealistic Kelly presentation. He came to Kelly from the gambling world and apparently he's still stuck there.
Gamblers can't use Kelly because they make zero- and negative-expectation bets. Gamers with skills like card counters, poker professionals and some horse and sports bettors can use Kelly because they have positive expectation. So what should we be focusing on?
OK so while we're waiting for the anti-Kelly crowd to get their act together and amuse us further with their anti-Kelly spiels, let's move on to more important topics. For example, let's look at Black Swans. Here is a simple example of a Black Swan : There is a 80% chance that you win your bet. There is a 19% chance that you lose your bet. There is a 1% chance that you lose four times your bet. Even before we do any calculations, common sense tells us that the Kelly fraction must be less than 25% or our trading account will be wiped out (aka "blown up") eventually. As demonstrated in the "Kelly for traders" thread, the Kelly fraction k satisfies the following equation : 0 = .80/(1+k) - .19/(1-k) - .04/(1-4k) Fortunately this simple 3-return example reduces to a quadratic equation: 0 = +57 - 343k + 400k^2 The solution is k = 0.22546 , which is pretty close to the doom ratio (0.25). Unfortunately this proximity makes estimating k challenging, and estimation is what we want to do because N (the number of trade returns) is going to be much larger IRL than this simple 3-return example. Using the LessBad Kelly calculation : k = .8/((.19+.04)/.2) - .2/1 = 0.495652 YIKES! :eek: Using the linear approximation from the "Kelly for traders" thread : k ~ (.8(+1) + .19(-1) + .01(-4))/(.8(+1) + .19(+1) + .01(+16)) = 0.495652 YIKES! :eek: Using a cubic approximation from expanding the Kelly equation: 0 ~ 3.55k^3 + .03k^2 + 1.15k - .57 k = .35466 Yikes! :eek: We can go to higher polynomial approximations but why bother. Clearly trying to estimate the Kelly fraction is a bust due to the presence of a Black Swan. So here,s the new rule for Kelly : If the Kelly approximation is greater than the reciprocal of the absolute value of the worst trade return in your backtest, then use 80% of said reciprocal as your trading fraction. .80/|-4| = .20 , which is fairly close to the true Kelly value and of course has a lower max drawdown.
Your understanding of the Kelly formulae shows that you seem to be somewhat good at math. There is multiple aspects of math. You have begun by assuming you have beaten the odds presented. Great, you proceed to calculate based on your calculation of what your black swan will do (1% chance of loosing 4 times your bet) Great, I pose 2 questions. 1. If you know what your black swan will do, why not stop trading before it arrives, or better yet flip your signals so they sell instead of buy. Your answer will most likely be that you do not know when, or how, but you only know the hardest part which is the end result. Great, What if you have 2 (or more) consecutive black swans. form wikipedia The black swan theory or theory of black swan events is a metaphor that describes an event that is a surprise (to the observer), has a major effect, and after the fact is often inappropriately rationalized with the benefit of hindsight. http://en.wikipedia.org/wiki/Black_swan_theory Since you have expected your worst case scenario, possibly from rationalizing previous black swans it will be doubly hard to surprise you. By concluding the out come of your black swan you have just made your next black swan worse. It is for this reason I assume my next black swan will be one that quadruples my money. If you are seeing any kind of consistency in your black swans that pop up , maybe they are not black swans, maybe they are simply due to the fact that you actually do not have a 1% advantage and every once in a while things the 40 60 reverts to the 50 50. If you feel preparing for a black swan is beneficial, then take a more realistic approach. Some MF global clients were making alot of money with great systems that had a huge edge, One day the law of the land came in and did its deed. In hindsight these traders will now account for it and avoid such a situation. They will re run their algos and the poor black swan will have to work overtime to surprise them. Through all of this with not even a zero balance but no balance at all, they will know that they are good traders that just need a boost to get back on track. Maybe they use Kelly to bring them on track. That being said, Im not really sure what the good or bad formulae is but I know some simply tweak it by dividing the out put (how much to invest) by a number they are more comfortable with. usually 2 to 10 %
kut2k2, i see your logic. To echo some of what traitor786 said, it is very difficult to assess downside exposure during worst case scenarios as their nature assures infrequent occurrences thus insufficient to be meaningful indicator of what's to come. This is an interesting and prudent way to think about position sizing. thank you, Yana
I guess a good thing to look at when back testing is points where max draw down increased. At what rate do they increase? how often do they increase? and does it occur enough times to draw any conclusions? Or, has your max draw down been hit consistently and always reversed at the same level of loss ? In other words, are your White swans mascaraing as black ones?
kut2k2, In your "Kelly for Traders" thread, you have: k ~ sum[Ri]_n / sum[Ri²]_n This is sometimes expressed by blackjack card counters as "expected return over expected squared return". Six little easy-to-remember words. The best things about this approximation are (1) it can be instantly updated with each new completed trade (or each new count after a blackjack hand) and (2) it will always underestimate the actual optimal betting/trading fraction, thus reducing the dreaded "Kelly risk". You have provided a counterexample to part (2) of the above statement. Thanks, Jim Murphy
True. If an outsized trading loss is not offset by a similar outsized trading gain, then the linear approximation can overestimate the Kelly fraction. Always check the reciprocal of the absolute value of your worst trading return for a complete risk assessment.