yoneda


Total Posts: 17 
Joined: Jun 2019 


Hi all, I recently came across the book The Kelly Capital Growth Investment Criterion and it seems very interesting. Are people here familiar with the performance of this class of strategies in practice (with fees)? Is RenTec's return consistent with Kelly too?
My current understanding about this strategy is that it is very sensitive to error in estimating the future mean return so unless I discover some real (and consistent) alpha I cannot really use Kelly sizing at all. Kind of chicken and egg problem. There is the universal portfolio of Cover which claims to bypass estimating future return. Cover also use this strategy for his hedge fund but I am not sure how it performs.
I hope you guys can give me some pointers. And please be kind ;) 




doomanx


Total Posts: 115 
Joined: Jul 2018 


Kelly is just optimal way to size positions to maximise multi period geometric growth of wealth. It is equivalent to maximising log utility, but this is to make the multiplicative growth of the repeated bets additive so that we get a law of large numbers effect rather than these economics interpretations of whether it’s risk averse or whatever.
To apply it to a fairly good approximation you just need to estimate expected return and standard deviation of returns (which you should be doing for a decent strategy anyway otherwise you are just guessing). It is not a strategy in itself, just bet sizing method. It is only optimal on frequency of your returns but you could go bust say intraday if you compute on daily returns, and it has some unattractive properties about how long it takes to dominate other betting systems (see filthys book chapter 8 for excellent discussion. Most people using Kelly use fractional kelly in practice (scale down Kelly sizing) to lower the reliance on path dependence in early stages of growth as well as account for modelling errors. 
did you use VWAP or triplereinforced GAN execution?



hftpm


Total Posts: 9 
Joined: Oct 2013 


Medallion returns have nothing to do with Kelly. It's just leveraged short term LS US equity portfolio. The rest of Rentec funds are hyped up standard HF portfolios.
Cover is dead and so is his ideas 




ahd


Total Posts: 32 
Joined: May 2017 


With all due modesty, have a look at https://arxiv.org/abs/0908.1444 I thought about the problem you're asking about back in the day and wrote up how I thought about it. Kelly corresponds to log utility, as @doomanx said. In the paper, it corresponds to x=0 for the exponent in the power utility. The whole thing's about parameter uncertainty, but the second footnote makes the connection with fractional Kelly strategies explicit. Enjoy. 



yoneda


Total Posts: 17 
Joined: Jun 2019 


@ahd, thanks for sharing your research. I had a quick look but will study in more details.
@doomanx, i had a look again at chapter 8 of filthy's book and understand kelly a bit better (definitely gain an opposing perspective as compared to reading Ziemba only). 




TSWP


Total Posts: 454 
Joined: May 2012 


Well estimating size of bet based on probabilities it's not a very smart approach unless you know the real probabilities and here a very long debate could start and so I will stop....
Kelly is just theory... 



doomanx


Total Posts: 115 
Joined: Jul 2018 


https://twitter.com/financequant/status/1008769775693189120?lang=en  Here's Rob Frey confirming Rentech have been using Kelly's ideas since the 80's. Think it's fair to say it's not 'just theory'. 
did you use VWAP or triplereinforced GAN execution?




jslade


Total Posts: 1246 
Joined: Feb 2007 


It's pretty well documented that Kelly betting is one of the things Berlekamp brought to Rentech/Axcom back in the 80s. I assume the new book on them mentions it.
Thorp used it too! He actually wrote about it in a fair amount of detail in his books.
FWIIW Cover Portfolios are a sort of generalization of the idea, but in addition to being kind of weird in its assumptions, they're extremely path dependent on small data sets. In fact, looking at the data sets in the literature, they seem kinda like classic overfitting (I spent an afternoon fooling with it; hardly an expert opinion, but I did notice). 
"Learning, n. The kind of ignorance distinguishing the studious." 


Maggette


Total Posts: 1326 
Joined: Jun 2007 


Well. You need some kind of loss or utility function. The Kelly is just a log utility function...which has some desirable and some less desireable properties. It is actually an quite aggressive way of risk management and will hurt you if you are wrong about your assumptions.
I learned a lot about it playing with simulated data. IMHO half Kelly is quite a solid heuristic.
I guess there are members on this board who are more sophisticated. 
Ich kam hierher und sah dich und deine Leute lächeln,
und sagte mir: Maggette, scheiss auf den small talk,
lass lieber deine Fäuste sprechen...




doomanx


Total Posts: 115 
Joined: Jul 2018 


@Mag True, and yes it corresponds to maximisation of logwealth but it's not because log shows some kind of favourable properties, it's for the reason I stated above. It's all about multiperiod growth and it's the optimal way to achieve infinite period growth ceteris paribus.
I quote from Kelly's original 1956 paper: "The gambler introduced here follows an essentially different criterion from the classical gambler. At every bet he maximizes the expected value of the logarithm of his capital. The reason has nothing to do with the value function which he attached to his money, but merely with the fact that it is the logarithm which is additive in repeated bets and to which the law of large numbers applies.
Suppose the situation were different; for example, suppose the gambler’s wife allowed him to bet one dollar each week but not to reinvest his winnings. He should then maximize his expectation (expected value of capital) on each bet. He would bet all his available capital (one dollar) on the event yielding the highest expectation. With probability one he would get ahead of anyone dividing his money differently. "
Another interesting quote (quite likely the generalisations Frey is talking about alongside multiasset scenarios): "It should be noted that we have only shown that our gambler’s capital will surpass, with probability one, that of any gambler apportioning his money differently from ours but still in a fixed way for each received symbol, independent of time or past events. Theorems remain to be proved showing in what sense, if any, our strategy is superior to others involving a(s/r) which are not constant."
Sorry to hijack this thread, but have any NPers ever had a read of the guy Frey is replying to in that thread, Ole Peters? Seems to be the leading man in this so called 'ergodicity economics' movement, trying to rewrite economic theory without the assumption of ergodicity. Some of it seems interesting but I get a crankish vibe from it. 
did you use VWAP or triplereinforced GAN execution?



Azx


Total Posts: 46 
Joined: Sep 2009 


HalfKelly is just maximizing isoelastic utility with a specific degree of riskaversion. A more relevant formulation for actual trading is maximizing utility with a drift that is only partially observed, which enables you to determine the correct riskaversion given the uncertainty.
@doomanx: is the term crank even applicable in the field of economics? It's not like he's trying to disprove relativity here. But yeah he does seem to have a hard time getting his ideas across. 




Maggette


Total Posts: 1326 
Joined: Jun 2007 


Thanks for pointing that out doomax.
Ole Peters: I have to admit the first time I ran into that name was when I had a short look at the new Taleb opus:).

Ich kam hierher und sah dich und deine Leute lächeln,
und sagte mir: Maggette, scheiss auf den small talk,
lass lieber deine Fäuste sprechen...




Kelly is a great framework to think about sizing a series of bets. However, in trading, you can rarely estimate your edge as precisely as in blackjack, roulette or other gambling situations (ludic fallacy, yadda yadda).
Even if you did perfectly know the odds, Kelly gives you the *maximum* you would want to bet. Bet more and you *decrease* your longterm expected growth rate. Bet 2x Kelly and your longterm growth rate becomes *zero*, even though you had the edge. That's IMHO the interesting insight: even if you find a profitable pattern, you can screw it up by overbetting.
Also, full Kelly is very high volatility, you've probably heard that. But let me put that in concrete terms: if your signal has a Sharpe Ratio of 1, full Kelly would have you leverage it to a 100% annual volatility. Can you, and your investors, stomach that?
For these reasons, traders usually use a fraction of full Kelly, with half Kelly still being considered pretty punchy. Some old school trend followers like Dunn trade around half Kelly, i.e. 30% vol for a 0.6 Sharpe. Would you want to be more aggressive than that? 
"Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016) 




Double post. 
"Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016) 



Triple post, damn 
"Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016) 



yoneda


Total Posts: 17 
Joined: Jun 2019 


@TSWP: well if you dont mind please start this discussion. I dont know how else to approach the market without statistical methods. Though there is certainly tricky issue in how you map the time series into events and probabilities. This is probably where the debate starts...
@doomaxx: yeah i know about this Ole Peters guy. by any chance you know the "breakingthemarket" guy?
@NeroTulip: for sure you dont want to go full Kelly as the main problem is with estimating probability and size of returns. I agree with you that the main point of Kelly is that you can fail even if you have real edge. That's quite scary!
By the way do you guys know of some papers or books on trend following and mean reversal strategies? I want to take a *universe of securities* and analyze for trend and reversal signals. Note my emphasis on universe of securities: i think consistent profit can be made by exploiting existing correlations in the market created by other players (as in some RenTec quote I forgot the exact statement but its along the line that someone has to create the correlations we observe in the market).




nikol


Total Posts: 1397 
Joined: Jun 2005 


Decided to continue this one. Problem formulation (simplified). I am given with:
Capital, C. N strategies. For each I have Sharpe and vol of PnL. Apparently, I can get Kelly, f_i. I see two steps: 1. Use Sharpe to optimally allocate Capital to each strategy, C_i, i=1...N, sum(C_i)=C. 2. Decide how much to bet within each allocation by using Kelly. So, every time I bet C_i * f_i.
Of course, optimal portfolio of all strategies should include diversification effect, hence vol_portfolio is less than sum of contributing vols, therefore, Kelly of portfolio should be higher. How to deal with that formally?
Also, by playing with numbers I see that under perfect diffusion (mean_pnl~t, vol_pnl ~ sqrt(t)) I have increasing Sharpe with increase of investment horizon (let's say from 1 day to 1 year). Kelly, f, remains constant, which my intuition has a difficulty to swallow.
Any thoughts/objections to my approach? 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 



ahd


Total Posts: 32 
Joined: May 2017 


turns out that i still get emails about this thread because i contributed to it years ago.
quick answer and comment before i change that setting...
Q: "Kelly of portfolio should be higher. How to deal with that formally?" A: Treat the portfolio as an asset with a volatility and apply Kelly!
"I see that under perfect diffusion ...I have increasing Sharpe with increase of investment horizon..." This is false. Sharpe is not pnl drift / pnl vol, it's return drift / return vol. So it doesn't grow as the capital to which you apply the returns is growing. 



nikol


Total Posts: 1397 
Joined: Jun 2005 


thanks. I disagree.
ROI = end_period_PnL / Total Assets, where Total Assets is at the beginning of the period and hence is constant. I used Investment to proxy that. So, TotAssets gets cancelled in the ratio and I can work with mean(PnL) ~ end_period_PnL and std(PnL) as risk measure.
I try to get intuition behind this. Exact formulas is for later.
PS. sorry, forgot to mention, I assumed all costs = 0. Realistically, with growing investment horizon it should go down. 
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) 



ahd


Total Posts: 32 
Joined: May 2017 


sharpe is annualized. here are 3 ways to compute something that people call the sharpe ratios (assume risk free rate = 0 to save typing)
1. mean(annual returns) / stdev(annual returns) 2. sqrt(12) * mean(monthly returns) / stdev(monthly returns) 3. sqrt(252) * mean(daily returns) / stdev(daily returns)
convention is that everything is trued up to a 1 year horizon as above. that's why sharpes differ from tstats by a factor of sqrt(num observations) and sharpes for short histories, aka small samples, are less meaningful than sharpes for long histories. 


