Kelly Criterion & Risk Of Ruin As Risk Management Tool

[rvince99]

No, I don't. Sorry. It would be a great idea though for some sort of intern, I'll look into it. It an also get pretty computationally intense & lengthy (its a genuine distributed processing problem as the number of components starts to increase).

It gets even more intense when we look to solve for criteria other than just being "expected growth-optimal (all else be damned)." For example, most of us want growth withing some sort of constraint. One common measure might be, say, expected growth with respect to amount risked as far better criterion than just what many colloquially refer to as "Kelly," but I refer to (for the sake of accuracy) "Expected growth-optimal."

Such a thing is solvable by the same equation, optimized for a different target, but it gets a little mind-bending for most: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2364092
and the slides to a talk one of my coauthors did on it (perhaps a little simpler):
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624329
That's all theoretical though, and since I manage two hedge funds, like most traders, I have the day-to-day real world slog of bridging the theoretical with the real world. So much of my time in recent years has been spent on robust approximations which can be implemented i the markets themselves, realizing there is a big difference between the academic world and the trading world (and I come from the latter). So my efforts have been along the lines of:
-How can you define the shape of this "manifold" without going into heavy math, doing it simply, with fair approximations?
-How do you travel through this manifold, i.e. what quantity should i have on at present to satisfy my criteria in the markets with respect to current risks, capital available, etc. and do so in a manner tht doesn't require supercomputers solving very complex equations running parallel! I am i the day-to-day foxhole of the markets and I need robust tools that will work for me there.

 

[MrScalper]

No, I don't. Sorry. It would be a great idea though for some sort of intern, I'll look into it. It an also get pretty computationally intense & lengthy (its a genuine distributed processing problem as the number of components starts to increase).

It gets even more intense when we look to solve for criteria other than just being "expected growth-optimal (all else be damned)." For example, most of us want growth withing some sort of constraint. One common measure might be, say, expected growth with respect to amount risked as far better criterion than just what many colloquially refer to as "Kelly," but I refer to (for the sake of accuracy) "Expected growth-optimal."

Such a thing is solvable by the same equation, optimized for a different target, but it gets a little mind-bending for most: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2364092
and the slides to a talk one of my coauthors did on it (perhaps a little simpler):
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2624329
That's all theoretical though, and since I manage two hedge funds, like most traders, I have the day-to-day real world slog of bridging the theoretical with the real world. So much of my time in recent years has been spent on robust approximations which can be implemented i the markets themselves, realizing there is a big difference between the academic world and the trading world (and I come from the latter). So my efforts have been along the lines of:
-How can you define the shape of this "manifold" without going into heavy math, doing it simply, with fair approximations?
-How do you travel through this manifold, i.e. what quantity should i have on at present to satisfy my criteria in the markets with respect to current risks, capital available, etc. and do so in a manner tht doesn't require supercomputers solving very complex equations running parallel! I am i the day-to-day foxhole of the markets and I need robust tools that will work for me there.

i often wonder what emphasis those in charge of large hedge funds place on identifying the best people to trade relevant markets..one is led to believe that those with high IQ and best head for maths land the best paying jobs..but..if these people were to trade their own money..would they take the same risks..just wondering!!

one chap that can teach anyone an awaful lot about trading or investing is Harry Markopolos!!

 

[ironchef]

The Kelly Criterion is just a postulate. Kelly (and Graham as well as Shannon, both of who signed off on the paper) solved for this supposed asymptotic growth-optimal fraction in the 1956 Bell Labs paper, despite the fact that they thought they did solve for it. Actually, they solved for something else. They deluded themselves as they were solving for a subset of problems, the answer to which equaled the asymptotic growth optimal fraction in the narrow cases they were concerned with! Yet people accepted it as fact and still mistakenly do.

The first one to solve for the asymptotic growth optimal fraction was Thorp with his "Kelly Formulas," closed-end formulas for solving for the asymptotic growth-optimal fraction for binomially-distributed outcomes.

The Optimal f formula I put forth in the late 1980s does solve for the asymptotic growth-optimal fraction, for one or more simultaneous propositions (portfolio components/systems/markets). But it too is asymptotic, that is, it is a fraction approached (albeit very quickly) as the number of trials/trades/holding periods increases.

Consider however a game with a positive expectation where you wat to determine the expected growth optimal fraction, but you are quitting after only one play? In such cases, the expected growth optimal fraction, the Optimal f value is 1, or risk 100% to maximize your expected growth after one play.

It's actually a little more complicated than this. Assume a p=.1 to win 10 units and q=.9 to lose 1 unit. Though there is a positive expectation, it is a game you should not play if you are going to quit after one play. Similarly, if we have a negative expectation game with p=.9 to win 1 unit and q=.9 to lose 10 units, and you wish to maximize your expected growth, quitting after one play, your Optimal f = 1, or risk it all on the one play. The Kelly Criterion, even Thorp's Kelly formulas for these binomial outcomes give you entirely different (and incorrect) results.

I refer you to my paper on this at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2577782

This will give you what the expected growth optimal fraction(s) are for one or more simultaneous propositions, for 1 to infinitely many trials.Further, there are other considerations, such as the fact the there is a cost of funds involved (trades don't transpire instantaneously in most cases), etc.

Anyone who has used "Kelly" with success has been using something that is mathematically incorrect, and the success may in many cases be attributable to luck (you cannot determine an expected growth optimal fraction for most capital market situations with any of what has been referred to as "Kelly," nor can you even apply it, correctly mathematically to the game of blackjack, and favorable results garnered from such were done so with grossly inaccurate calculations).

Finally, all of this assumes your criterion in trading is to be expected growth-optimal, all else (including drawdown or other risk measures) be damned. This is ok provided that really is your criterion.

Since the actual Optimal f value (or value sets) exit between the bookends of 0 and 1, there are other points of geometrical interest within that manifold. Further, everyone in every assumed proposition or set of propositions exists within that manifold,unwittingly in most cases, and are covering paths through it, unwittingly again in most cases.They are paying the consequence and reaping the benefits in terms of performance characteristics that these various points of geometric consequence (aside form the peak, the Optimal f points) imbue. In fact, various points and paths in this manifold can be constructed to satisfy ant trading criteria. It really is not very complicated -- I'm not trying to sell anything, razzle-dazzle anyone, but rather to edify this area that is always misunderstood.

Thank you Mr. Vince for your thoughtful post. It will take me a while to digest your post and especially your paper on Growth Optimal Fraction. My layperson's understand of what you meant by growth optimal fraction is what we call the Kelly?

I am math challenged and will never be able to understand let alone derive the optimal fraction. However, most of us traders instinctively determined that it is much "safer" for us to trade with a fraction much less than Kelly (e.g., 1/4 Kelly) in order to avoid the risk of ruin.

The most provocative thought for me is this:

It's actually a little more complicated than this. Assume a p=.1 to win 10 units and q=.9 to lose 1 unit. Though there is a positive expectation, it is a game you should not play if you are going to quit after one play. Similarly, if we have a negative expectation game with p=.9 to win 1 unit and q=.9 to lose 10 units, and you wish to maximize your expected growth, quitting after one play, your Optimal f = 1, or risk it all on the one play. The Kelly Criterion, even Thorp's Kelly formulas for these binomial outcomes give you entirely different (and incorrect) results.

As a purchaser and writer of options this is actually very helpful. Thank you.

PS: I hope you can provide me with answers if I have questions after digesting your paper.

Regards,

 

[rvince99]

PS: I hope you can provide me with answers if I have questions after digesting your paper.
Regards,

I'll do what I can to answer things (I'm just learning myself, though that's been going on for decades on this obsession of mine).

Thank you Mr. Vince for your thoughtful post. It will take me a while to digest your post and especially your paper on Growth Optimal Fraction. My layperson's understand of what you meant by growth optimal fraction is what we call the Kelly?

I am math challenged ...

Yes.

(And FWIW I am "Math challenged" too).

...most of us traders instinctively determined that it is much "safer" for us to trade with a fraction much less than Kelly (e.g., 1/4 Kelly) in order to avoid the risk of ruin.

Yes, very true -- most people's criteria in trading does not encompass seeking "expected growth-optimality, all else be damned." Most people have a risk concern/constraint, and this therefore implies trading some sort of quantity calculation more towards zero and away from the peak (what people refer to as "Kelly"). And every discussion about these diluted allocations are ad-hoc, capricious and absent any rigor because the dynamics of that region haven;t been examined, and I've tried to do that and my point is there are values in that diluted region that are more "optimal" to us, as traders, with our risk considerations, than just mere growth-optimality.
.
Interestingly, to the "right" of the peak, that is, the insane region between the peak and 1.0, is an area with significant geometric consequences to situations where one would seek growth diminishment. We don't often consider that since, as traders, we are concerned with growth. Yet there are many functions in human experience where the curtailment of growth is desirable (e.g. federal debt, pathology, etc.) which the material is germane to.

 

[ironchef]

I'll do what I can to answer things (I'm just learning myself, though that's been going on for decades on this obsession of mine).



Yes.

(And FWIW I am "Math challenged" too).



Yes, very true -- most people's criteria in trading does not encompass seeking "expected growth-optimality, all else be damned." Most people have a risk concern/constraint, and this therefore implies trading some sort of quantity calculation more towards zero and away from the peak (what people refer to as "Kelly"). And every discussion about these diluted allocations are ad-hoc, capricious and absent any rigor because the dynamics of that region haven;t been examined, and I've tried to do that and my point is there are values in that diluted region that are more "optimal" to us, as traders, with our risk considerations, than just mere growth-optimality.
.
Interestingly, to the "right" of the peak, that is, the insane region between the peak and 1.0, is an area with significant geometric consequences to situations where one would seek growth diminishment. We don't often consider that since, as traders, we are concerned with growth. Yet there are many functions in human experience where the curtailment of growth is desirable (e.g. federal debt, pathology, etc.) which the material is germane to.

You may find this interesting:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2259133

Regards,

 

[rvince99]

I'm familiar with it. Interestingly, the academic community is painfully behind what the gambling and trading community has been doing in this arena (and in large part, because we have not played by their rules, and they have made little attempt to do anything but build on past endeavors in academia, to their detriment).

This work was first performed (to the best of my knowledge) by a guy named Mike Pascual, in Vegas, who introduced it for multiple, simultaneous sports book gambling with an edge. It was circulated but unpublished. I have an original mimeograph of his hand-written book (and code) at a home I have in another state. I don;t know if Mike is still with us.

 

[murray t turtle]

when you get to the stage where it becomes boring.. you will then clearly see all the...... course sellers for what they really are......

i can not say that i was any different..in fact i was one of the biggest fools out there..but as you get older..you certainly get wiser..and there comes a time when you will look back and laugh at how silly you were..and how silly it all still is

making money is not that hard.. holding on to it is a different story!!

golden rule..always put money aside for the rainy day..as if you risk too much..for whatever reason..

keep it simple..know your market..never over trade..never get greedy..help those in need..and always be kind to animals..you do not have to be kind to humans who are not kind to you

%%
Good point Mr Scalper; overtrading for me, also includes.......NOT have too big of a comission to profit ratio.
Never bought in to strange idea trading/investing had to be boring; but that could mean the same as panic sellers/buyers never win.Planned sellers/buyers can win. Agree always be kind to animals, but i seldom put up with a biting or clawing animal

 

[MrScalper]

%%
Good point Mr Scalper; overtrading for me, also includes.......NOT have too big of a comission to profit ratio.
Never bought in to strange idea trading/investing had to be boring; but that could mean the same as panic sellers/buyers never win.Planned sellers/buyers can win. Agree always be kind to animals, but i seldom put up with a biting or clawing animal

sometimes i wonder how i was so silly in the past..i remember coming back from an occasion..we all headed to the local pub after for some drinks..after about 1 hour i left and went home..turned on my pc..and logged into woodie giving a chat about his magical method for short term trading the ES..the famous woodie's cci..all i will say is that i now laugh at how silly it all was..i wasted about an hour and went back to the pub

 

[ironchef]

It is time for me to summarize what I get out of this thread. Anyone disagree or have other ideas are welcome to comment:

1. It is beyond my ability to derive the equations of or comprehend Kelly or Growth Optimal Fraction but intuitively, I came to the realization that trading at fraction Kelly will lower my risk of ruin.

2. If there is no positive expectancy, risk of ruin is a certainty, Kelly or Growth Optimal Fraction be damned. So, I should definitely determine if my method has any positive expectancy before even trying to determine Kelly or Growth Optimal Fraction.

3. Kelly, or Growth Optimal Fraction do not deal with risk of ruin, only optimal growth? For one without infinite funds, and non asymptotic trades, one better trades with a fraction of Kelly or Optimal Fraction or else risk of ruin can easily wipe out one's account.

4. For low win rate methods, like long DOTM options, assuming positive expectancy, to get positive returns, one should execute a large number of trades to capture the occasional "lottery type" winning potentials. So, trade often and trade small.

5. For high win rate methods, like shorting DOTM options, again assuming positive expectancy, perhaps one should limit the number of trades and try to avoid the occasional "black swans". So, trade a few times with huge leverage then retires, riding into the sunset! Trade often and trade small is the wrong way to go, counter the coaching of websites like tastytrade?

 

[nonlinear5]

1. It is beyond my ability to derive the equations of or comprehend Kelly or Growth Optimal Fraction but intuitively, I came to the realization that trading at fraction Kelly will lower my risk of ruin.

It's not that complicated, really. It comes down to this: to figure out your optimal position size, find the leverage that maximizes the sum of log-returns of your past trades. Then trade with a fraction (such as 0.25) of that leverage.

Yes, it gets more involved when you have to deal with portfolio allocation where you may need to trade (and hold positions in) multiple instruments at the same time, and to allocate for the specific time horizons. This is where it gets computationally intense.