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ipfmanager (98.28)

The Kelly Criterion, Diversification , and Penny Stocks

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June 10, 2009 – Comments (6) | RELATED TICKERS: BCON , SIRI , RFMD

THE KELLY CRITERION

YOUR NEW BEST FRIEND

This is an article I wrote for a poker magazine in 2005.  Not a bad theory to apply it to stock picking, especially penny stocks.  Lover to hear comments on this.  The Kelly Criterion is a very powerful system to find the best possible investment for your bankroll and could really help for diversifing properly when taking huge risks (namely penny-stocks).

The original application of Kelly Criterion is Information Theory which was discovered by Claude Shannon at Bell Labs circa 1948.  Information Theory calculates the minimum amount of information necessary to communicate a message through binary code on noisy channels via cell phones, telegraphs, and walkie-talkies.  This formula changed the digital world into how we know it--enabling communication to compress itself through any bandwidth, saving tremendous amounts of memory space and speeding up communication lines to new levels.

People argue that Shannon’s Information Theory is more important than the Theory of Relativity because of it’s relevance to the actual world.  This may be true. I’ve never calculated my mass when nearing the speed of light in a rocket ship, but I play cards online almost every day.

Just a few years later John Kelly realized this formula was also the best way to bet on horse races and wrote about it in his legendary article A New Interpretation of Information Rate (Bell System Technical Journal, 35, 917-926).  This article started the idea that the Kelly Criterion is the optimal wagering system.  More recently, the Kelly Criterion has come into practical use for investing, hedge fund management, and Capital Asset Pricing Models (CAP-M).  Although it is quasi-irrelevant where this theory comes from, I find the serendipitous manner it was created to be charming and it deserves to be commented on.

By its own claim the Kelly criterion is the mathematical formula for the best possible bankroll management.  John Kelly devised it at bell labs in the 1950s as a systematic way to gain capital in horse racing.  Kelly states that as long as you never spend more than your edge on a single investment you will never go broke.  This means a) you will never go broke since your bets are in proportion to your bank roll. And, b) you will know the best bet to grow your bankroll faster than any other type of method.  This is an uber-powerful statement for a poker player.  The first time I heard the formula I started to salivate thinking about what it meant to me.  This criterion, if you have not heard this before, should be your new Maxim. Any speculation you make at the tables, investing, or anything in life should heed to this criterion. 


So, what’s the formula?

Fair question.  Here you go...

f* = (bp - q) / b  

where:


   f* = percentage of current bankroll to wager;    b = odds received on the wager;    p = probability of winning;    q = probability of losing = 1 - p.The previous may have caused you to get a bit dizzy at first, but it is a simple formula.  It’s basically this: double your edge. For an even-money bet (bet a dollar, win a dollar) if you have a 55% chance of winning, you should risk 10% of your working capital. Your edge is 5%, so the Kelly bet (double your edge of 5%) would be 10%.  If you have a 90% edge, you should be risking 80% of your capital (double your 40% edge).

Well, that’s all for now.  The next installment of these articles will include some practical table applications with this formula, some major pitfalls of this formula, and my reconciliation of these problems.  In the meantime, check out the above link and try to plug some leaks in your game if you did not already know about John Kelly and his great, and accidental, contribution to poker.

For TMF discussion:

For stocks we'd basically take the the frequency of an expected positive return, the average implied return, and solve for diversifacation %'s.  Anyone know how volitility would help with calcualting these implied #'s?  Would love some comments...

6 Comments – Post Your Own

#1) On June 10, 2009 at 12:59 PM, iamamartin (97.08) wrote:

Interesting. Of course all Investing has an implied edge. All other things being equal (ie the company can afford to pay), the Expected rate of return (say the dividend or bond coupon yield) would be representative of your overall advantage (like the small advantage Blackjack player have at playing cards).

So....Using the Kelly Criterion for a 5% yield from a US Treasury (assumed (!) 100% return of principle)

f* = (bp - q) / b  

f*  = 0.05 * 1.0 - 0 / 0.05 = 1  => Bet all your bankroll on a sure thing.

However, the Kelly Criterion ignores the time value of your bankroll. Most bets are "instantaneous". Ideally you would like  a bet you can make often and quickly that is as sure as a US Treasury (Fed printing / Dollar Crisis not withstanding). The problem is the US Treasury only returns 5% pa. On the other hand perhaps a dividend harvesting strategy could use this idea to great effect - each dividend payout event being equivalent to a "bet".

 

  

 

 

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#2) On June 10, 2009 at 1:31 PM, ipfmanager (98.28) wrote:

I like that angle of it.  Might be useful to generate some better returns from junk bonds.  However when you have a probability of 100% (like in AAA gov't bond) return of principal, Kelly would say bet it all.   I'm looking for how implied volatility could dictate what the expected return could be versus the risk of it not happening.  

Think call options, where a strike will return X and the risk of it not getting to strike price is Y.  You could get a Kelly wager by plugging in volatility or maybe doing something with Black Scholles.  The B/S model actually is based off of information theory, so if I were smart maybe I wouldn't be asking so many questions.

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#3) On June 10, 2009 at 2:31 PM, appertjt (75.13) wrote:

There is a book on Options by an author named Rheel that covers what you are talking about.  The math is slightly more complicated because when trading options it is not always a win/lose trade with an all or nothing pay-out. Also, while the f* value given is probably close enough it is good to keep in mind that the model is based on a log-normal distribution of stock price movement which does not accurately represent price movements in real life (the tails will be fatter and the peak of the curve narrower.)

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#4) On June 10, 2009 at 9:26 PM, ChrisGraley (99.70) wrote:

The value of money over time needs to be factored in. Also inflation would need to be factored in. A swing Trader or Day Trader could probably do pretty good with this though.

I'm gonna investigate it more for my options trades since time is figured into price in that scenario and inflation would really only have an effect on LEAPS.

I'malso going to check out that book appertjt mentioned.

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#5) On June 10, 2009 at 10:14 PM, walt373 (31.36) wrote:

Nice job. This is a great explanation. To me, the Kelly Formula is like the holy grail of investing, something that's a bit magical. Almost everything else investing-related is inexact and sometimes even superstitious or totally unscientific, but the Kelly Formula proves that it's the best way to manage money for optimum growth. It's a free lunch. By the way, if you guys want to read more about this, I recommend the book Fortune's Formula by William Poundstone.

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#6) On June 10, 2009 at 11:44 PM, ipfmanager (98.28) wrote:

About time factors; that is why I want to know about an options probably can be stuck based on volatility, leaving time decay to be factored in on top of that.  I think to calculate it is profit from strike divides into volatility and or risk.  

Check out this site which has a pretty easy calculator. You can input stuff to showe what your bet should be.  My problem is how do you calculate the probability field in that table?

  http://www.albionresearch.com/kelly/  

 I guess what I really need to know is what is the best way to calculate the probability of an option striking and/or a penny stock actually doing what everyone is betting it will.  Maybe you could calculate this through black-scholes or some kind of volatility figure that I don't understand.  

So basically I'm taking time value out is because I'm looking to do short term stuff or options...I'd get those numbers first and then factor in time decay. It's already confusing enough.

Any ideas?  

Also, I have read Fortunes Fotunes formula, haven't read that options book and thanks for the comments!

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