It is scientific. I'm not sure if it's publishable. The Kelly problem is to maximise some function given a set of expected outcomes and probabilities. The function is not up for grabs, its expected log utility. If you change that function you're doing something else - it isn't "Kelly". That might be publishable, although the economics literature seems to have tired of publishing papers with novel utility functions. As several posters have shown it's possible to get a "perfect" answer (or at least as many decimal places as you like) using numerical analysis for any discrete set of outcomes. (Technical note - this also means it's possible to get a "perfect" answer for any continous distribution since you can chop that up into 'small enough' discrete pieces and then do the same optimisation) The original Kelly fraction solved this function for simple cases with two outcomes. There is also the simple continous version which solves it for Gaussian returns. It's my understanding that @kut2k2 is using some mathematical tools to provide closer and more accurate approximations for more complex cases. From another post on the subject I would say those tools aren't novel; although I don't think it's fair to speculate on what they are. If @kut2k2 doesn't want to tell anyone his method that's entirely up to him. However if he has come up with a genuinely novel way to approximate solutions to this class of non linear functions then I'd urge him to publish it. The financial value of this technology is limited since as I've said the uncertainty of the estimates completely dominates the precision of the formula. That would be true even if it was applied in another field like option pricing. But having a published paper would be cool. GAT
I agree. There is no uncertainty in trade returns.... in the past. You know exactly what they are. You can calculate what the right Kelly should have been in the past precisely. This is no use in determing the right fraction in the future. I assume that's what we're trying to do once we've moved to the real world and away from the fascinating but financially unrenumerative world of problem solving. So how do we determine the right fraction in the future? We can assume that the future will be exactly like the past. But in another post you agreed that this was silly. These are financial markets. If the market falls by 5% every 500 days, that doesn't mean it will do the same thing again in the future. There is uncertainty in the future. Thus we need some kind of model of how to project the returns of the past into the future, accounting for uncertainty. Fiction eh? Well let me tell a story then. The model I use* is something like this: * and, you know, all of finance Treat the markets as a card game, in which each hand is a new return. We're being dealt from an infinitely large shoe of multiple decks. We can see all the cards that have been dealt so far (no need for card counting, just go to yahoo finance and get it for free). Suppose we see twice as many jacks as queens. Does that mean I should assume I'm exactly twice as likely to get a jack than a queen? Actually I can never say that with certainty. But what I can do is look at how many cards I have been dealt so far. I can look at how variable the jack:queen ratio is. I can chop the stacks of cards dealt up randomly and measure the ratio inside each stack (bootstrapping). If I do that it will tell me that on average there are twice as many jacks as queens. But it will also tell me that there is a 10% chance of being in a situation with twice as many queens as jacks. If I'm sensible I shouldn't play the game in such a way that I assume I will definitely get twice as many jacks as queens on every hand. This is semantics. A set of past returns always forms a distribution. It doesn't have to be parametric (i.e. with a cool name like Gaussian, and with a finite number of parameters). You can still do this kind of exercise with a non parametric distribution - just the stream of returns without summarising it by fitting it to a set of parameters. You don't need the distribution to work out your betting fraction. But you do need to understand that the fraction is based on some estimates, and those estimates are uncertain. You need to have some model of that uncertainty or you're kidding yourself that you can predict the future. This isn't a casino. And it doesn't matter if: a) you estimate the mean, standard decviation and other moments and use them in a closed form Kelly solution. b) You use the actual returns and use them in whatever you're doing, or in the numerical solution we've discussed. It happens to be easier to do (a) which is why I used it in the examples In both cases you're using some data, and you need to think about what the uncertainty is in that data. Look your formulas are clever. I like them. They're neat. But I don't want anyone reading this to think that it's possible to know your correct position size to 3 decimal places in a real trading enviroment. GAT
The best discussion and explanation on Kelly, with a practical example, I found here: https://www.quantstart.com/articles/Money-Management-via-the-Kelly-Criterion
By the way there is a way to calculate Kelly from a "stream" of trade returns, whilst taking uncertainty into account. You can use a Bayesian updating, which takes account of the uncertainty in the estimates you have so far. So for example if you saw one hundred +1%, and one -5%, you wouldn't use a Kelly that you'd use if you thought that was the 'true' set of outcomes and probabilities (== distribution) you'd get in the future. You'd use something much more conservative that reflected the fact you only had 101 observations. It would be much, much less than half Kelly. Then if you got another +1% you would very slightly increase your Kelly fraction to reflect the fact you have slightly more data. It's exactly the same as in my last post, but its just redefining the process in terms of a 'stream' from which you update your estimate of what you think the return distribution is AND the uncertainty of those estimates. However from the way you're discussing the subject I don't think thats what you're advocating. GAT
Depends what you mean by original Kelly. If it's this https://en.wikipedia.org/wiki/Kelly_criterion then I can't see a way of making f>1. Sometimes the results is quoted in leverage terms, or as an annual risk target. Clearly these can be more than 1.0 GAT
%% Less is more; Jack Schwager Top Traders books gives some %'s Really depends on the business; i can get a refund [30 days same as cash]on home improve materials, usually bid is same as ask, with proper reciept.
What's the difference between Bayesian updating and the updating the new Kelly formula is already designed to do? http://www.elitetrader.com/et/index.php?threads/a-new-kelly-formula.291307/ Sorry but Wikipedia was no help. I have no idea what "prior" to use.
A Bayesian updating would take care of the fact that both the expected distribution and the uncertainty in that distribution were changing. I think new Kelly only does the former. I have no idea what prior to use eithier, I was just trying to second guess what you might be doing privately.... thinking aloud. I guess a good prior would be "I am guaranteed to lose 100% of my money if I bet". Or another slightly less pessimsitic one might be a guassian distribution of returns, mean zero, massive standard deviation. Or a uniform distribution of returns from -100% to +100%, mean zero (if you want the possibility of total loss firmly in your mind). Then you'd do nothing until there was evidence there was probably a positive expectation. Defining 'probably' is tricky too. Someone has probably done this before (it's hardly rocket science) and if I have time I will have a google to see. There are lots of question marks about this method, which is why I prefer the simpler idea of going with the past distribution of returns, but then looking at the uncertainty in my estimates of that distribution, although they should come out with the same answer. (By the way another way of doing this is to bootstrap from the history of returns, work out the optimal kelly on each bootstrap, and then plot the distribution of those optimal Kelly fractions. Then you'd go for something conservative like maybe the lowest fraction or slightly above the lowest) GAT
As my account is little so I risk around 25$ to 40$ on a trade. I set different TP's with multiple entries but risking the same dollar amount.