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Prof. William T Ziemba introduces The Kelly Criterion (Video)


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As you may probably know, Prof. William Ziemba recently wrote the most comprehensive book ever published about the Kelly criterion, with over 884 pages of documentation and its history. He wrote the book in collaboration with Edward O. Thorp and Leonard C. MacLean. The book contains well-researched articles about John Kelly, Ed Thorp, Claude Shannon, Warren Buffett, Mohnish Pabrai, Bill Gross, Jim Simons, Elwyn Berlekamp, John von Neumann, Oskar Morgenstern and many others. Ziemba teaches as an Alumni Professor of Financial Modeling and Stochastic Optimization, Emeritus in the Sauder School of Business, University of British Columbia in Vancouver.

 

The publisher uploaded some videos to YouTube:

 

Kelly Capital.flv

Professor William T Ziemba introduces The Kelly Capital Growth Investment Criterion

Video (3:38min)

http://t0.gstatic.com/images?q=tbn:ANd9GcSIHM2oTzYBW0U0XCN8vOA5zGnS-p_txKQLHgSqs8xh5TPq8ALYqg

He talks about the book, risks, Kelly Criterion, Ed Thorp, and the MIT Blackjack team

 

RMS Research : Interview of William Ziemba, part 1 of 2

Video (11:31min)

http://t1.gstatic.com/images?q=tbn:ANd9GcQEe3h5f6yqKuHqa4cBWq9bJlFnmV3579CS7Wdy964gKjr5oEQS

 

RMS Research : Interview of William Ziemba, part 2 of 2

Video (13:36min)

http://t1.gstatic.com/images?q=tbn:ANd9GcQEe3h5f6yqKuHqa4cBWq9bJlFnmV3579CS7Wdy964gKjr5oEQS

 

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If you don't know about what book I'm talking, here's the publisher link again:

 

The Kelly Capital Growth Investment Criterion: Theory and Practice

(World Scientific Handbook in Financial Economic Series)

 

http://www.worldscibooks.com/covers/7598.jpg

http://www.worldscibooks.com/economics/7598.html

 

also the book @ Amazon.com:

http://www.amazon.com/Kelly-Capital-Growth-Investment-Criterion/dp/9814293490

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Dr William T. Ziemba - personal homepage

http://www.williamtziemba.com/

 

http://www.mfe.ntu.edu.sg/faculty/PublishingImages/img_WZiemba.jpg

 

Dr William T. Ziemba @ UBC.edu

The University of British Columbia - Vancouver, B.C., Canada

http://www.sauder.ubc.ca/Faculty/People/Faculty_Members/Ziemba_William

 

Dr William T. Ziemba @ mac.com - homepage

http://homepage.mac.com/wtzimi/home.htm

 

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Here's a Wikipedia article collection about the history of the Kelly Criterion and related subjects,

like Thorp's book "Beat the Dealer", the MIT Blackjack Team, Ben Mezrich book "Bringing Down the House:

The Inside Story of Six MIT Students Who Took Vegas for Millions  and the recent screen adaption in the movie "21".

 

Kelly Criterion @ Wikipedia

It was described by J. L. Kelly, Jr, in a 1956 issue of the Bell System Technical Journal

http://en.wikipedia.org/wiki/Kelly_criterion

 

John L. Kelly @ Wikipedia

He was also an associate of Claude Shannon at Bell Labs

http://en.wikipedia.org/wiki/John_Larry_Kelly,_Jr

 

Claude Shannon @ Wikipedia

Shannon was Kelly's boss at Bell Labs. Furthermore Shannon had the occasional encounter with John von Neumann,

Albert Einstein and Kurt Gödel at Princeton's Institute for Advanced Study.

http://en.wikipedia.org/wiki/Claude_Shannon

 

Elwyn Berlekamp @ Wikipedia

Berlekamp was John Kelly's research assistant.

http://en.wikipedia.org/wiki/Elwyn_Berlekamp

 

Elwyn Berlekamp article about the Kelly-Berlekamp-Simons connection.

He can probably be considered a Super Quant, because his  Axcom Trading Advisors,

eventually became the Medallion Fund/=RenTec run by James Simons.

http://www.castrader.com/2006/11/elwyn_berlekamp.html

 

Elwyn Berlekamp (homepage) @ Berkeley.edu

http://math.berkeley.edu/~berlek/index.html

http://www.eecs.berkeley.edu/Faculty/Homepages/berlekamp.html

http://math.berkeley.edu/index.php?module=mathfacultyman&MATHFACULTY_MAN_op=sView&MATHFACULTY_id=111

 

James H. Simons @ Wikipedia

He appears to have adopted at least part of Berlekamp's & Kelly's strategy at RenTec

http://en.wikipedia.org/wiki/James_Harris_Simons

 

Renaissance Technologies @ Wikipedia

http://en.wikipedia.org/wiki/Renaissance_Technologies

http://www.rentec.com

 

William Poundstone @ Wikipedia

He wrote the book "Fortune's Formula", a detailed history of the Kelly Criterion. 

http://en.wikipedia.org/wiki/William_Poundstone

 

Edward O. Thorp @ Wikipedia

http://en.wikipedia.org/wiki/Edward_O._Thorp

http://www.fortunesformula.com/about.html

http://blackjackidols.com/img/edward-o-thorp.jpg

http://www.edwardothorp.com/

 

Beat the Dealer @ Amazon

http://www.amazon.com/Beat-Dealer-Winning-Strategy-Twenty-One/dp/0394703103

 

MIT Blackjack Team @ Wikipedia

http://en.wikipedia.org/wiki/MIT_Blackjack_Team

 

Bringing Down the House (book) @ Wikipedia

http://en.wikipedia.org/wiki/Bringing_Down_the_House_(book)

 

21 - the movie (2008) @ Wikipedia

http://en.wikipedia.org/wiki/21_(2008_film)

 

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While we speak about Kelly, there's also an interesting video about "Claude Shannon",

Kelly's boss at Bell labs.

Codes and Clowns: Claude Shannon the juggling scientist

(4:35min)

http://www.inkwire.de/uploads/images/Events/Nixdorf/Claude-Shannon.jpg

http://www.youtube.com/watch?v=1zEsao7Da4s

 

Claude Shannon, biography at Wikipedia:

http://en.wikipedia.org/wiki/Claude_Shannon

 

For disclosure:  I edited the paragraph: "The Las Vegas connection: information theory and its applications to game theory" of that wikipedia page months ago. Wrote most parts of the paragraph and also about Elwyn Berlekamp connections. ::)

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Well,... and finally a mind-boggling video lecture with Kevin Spacey from the movie "21, the movie"

about "Variable Change" and the mathematical "Monty Hall Problem"

 

Monty Hall Problem From The Movie 21

about  Variable Change

(2:21min)

http://cache02.casttv.com/104x/1/peuh1v1/21-explains-the-monty-hall-problem.jpg

http://www.youtube.com/watch?v=Zr_xWfThjJ0

 

The Monty Hall Problem a cartoon videoclip

(5:49min)

The Monty Hall Problem is a famous (or rather infamous) probability puzzle.

Ron Clarke takes you through the puzzle and explains the counter-intuitive answer.

 

Monty Hall Problem @ Wikipedia

http://en.wikipedia.org/wiki/Monty_Hall_problem

 

 

hope i posted enough to keep your minds occupied over the weekend  :D

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It's a great book.  As mentioned on another thread, don't let the math scare you.  Go to Thorp's essays and read around any of the proofs you don't understand.  Thorp's  comments are written in plain language and are well worth the price of the book.  :)

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It's a great book.  As mentioned on another thread, don't let the math scare you.  Go to Thorp's essays and read around any of the proofs you don't understand.  Thorp's  comments are written in plain language and are well worth the price of the book.  :)

 

True words, and the folks that don't understand the mathematical stuff, just fly over to the interesting pages you can understand.

 

here's also a free 60 page earlier excerpt from the book:

http://stevanovichcenter.uchicago.edu/seminars/Handbook.pdf

 

and a PDF file from Ed Throp:

Medium Term Simulations of The Full Kelly and Fractional -- Kelly Investment Strategies

http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellySimulationsNew.pdf

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Anyone want to explain how it relates to investing? Just curious

 

it is used by some to figure out how much of your portfolio to invest/allocate to a given risk/security.

 

based on probability of winning + how much you gain or lose  i.e if probably is high, potential loss is low,and potential gain is high then allocate a high amount or go all in vs (at the other extreme)  don t allocate any amount if there is any chance that particular investment could go to zero

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Anyone want to explain how it relates to investing? Just curious

 

The most important idea is to size the positions in your portfolio by risk/reward rather than by arbitrary proportions or other means.  It's important to realize that you can lose a lot of money by using a full Kelly.  With a full Kelly you have a 50% chance of a 50% drawdown below the initial value, but only a 25% chance of a 50% drawdown using half Kelly position sizing.  Interestingly, with a full Kelly, you have a 1% probability of a 99% drawdown.  Even half Kelly sizing is too volatile for most risk adverse people, especially in view of the fact that low risk/high reward situations are rare, and it's not likely to be able to keep rolling the dice until your number comes up.

 

 

The most important aspect of risk/reward when using The Kelly Criterion is the risk part.  In other words, when sizing positions, the probability of a successful outcome should be the main focus, not the expected value of the peceived percentage gain on what you have at risk.  :)

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How have you been able to quantify the upside/downside probability?  I have tried to use this but have had a hard time handicaping highly leveraged (inlcuding LEAPs) investments.

 

Packer

 

Leverage multiplies risk.  Not a good thing for lowering risk, unless it means replacing owned shares with leaps and putting the cash difference into something secure.  :)  Owning leaps on a great company is far less risky than the situation where the leverage is internal, within the company  That situation is analogous to owning stocks in an account that is heavily margined.  Lots of things can go wrong. 

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I will give you a current example.  Take Lodgenet.  It is trading at $2.00 or 1.4x FCF.  The leverage is 3.2x EBITDA (leveraged but not crazy) for a hotel cable-type system.  Lets say a normal EBITDA multiple is about 6.0x (below the current multiples of cable operators but at a premium to telcos).  In that case, the upside would be 290% and the downside lets say is 100% loss.  How do you determine the upside downside %s.  I have been using 50/50 but was wondering if you had other ways of quantifying this.  Thx.

 

 

Packer

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I will give you a current example.  Take Lodgenet.  It is trading at $2.00 or 1.4x FCF.  The leverage is 3.2x EBITDA (leveraged but not crazy) for a hotel cable-type system.  Lets say a normal EBITDA multiple is about 6.0x (below the current multiples of cable operators but at a premium to telcos).  In that case, the upside would be 290% and the downside lets say is 100% loss.  How do you determine the upside downside %s.  I have been using 50/50 but was wondering if you had other ways of quantifying this.  Thx.

 

 

Packer

 

The probability of a highly leveraged company working out well is far less than with a company with little or no leverage for many reasons.  The main reason is that hitting a speed bump can be fatal to a highly leveraged company.  Experiencing any difficulty can cause the screws to be tightened, sending the leveraged company into survival mode.  The only time having lots of leverage might  make sense is when a business has a great moat or is firing on all cylinders with the wind beneath their wings.  Otherwise, lots of leverage merely multiplies the problems.

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How have you been able to quantify the upside/downside probability?  I have tried to use this but have had a hard time handicaping highly leveraged (inlcuding LEAPs) investments.

 

Packer

 

Leverage multiplies risk.  Not a good thing for lowering risk, unless it means replacing owned shares with leaps and putting the cash difference into something secure.  :)  Owning leaps on a great company is far less risky than the situation where the leverage is internal, within the company  That situation is analogous to owning stocks in an account that is heavily margined.  Lots of things can go wrong.  

 

Quantifying probabilities is imperfect, but necessary.  The key determinant is the upside/downside probability.  Look at all factors that might bear on that estimation.

 

For example, after considering all known key factors, I estimate conservatively .90 probability that the Transatlantic Holdings risk arbitrage described on another thread will work out favorably.  Next, I estimate the payout odds as 1:1, meaning that a favorable outcome would have about the same gain as would be the loss for an unfavorable outcome.  This estimation is also conservative because there are three bidders for TRH, and this means that there are multiple layers of downside protection.  The low P/B of the target and the fact that it is a good business that holds liquid assets and isn't highly leveraged offers additional downside protection.

 

Finally, I go to albionresearch.com and use their Kelly calculator and discover that 80% of my capital is the optimal full Kelly bet.  Of course, I'm not going to use a full Kelly, but I'm comfortable using a one fourth to a one half Kelly because I think my estimates are conservative, and I think my realistic downside volatility limit is about 20% to 30% of the funds I put at risk because IPC never sold off that much despite the market turmoil when they were a target a few years ago.   :)

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I think Mark Sellers used a full Kelly criteria allocation in his hedge fund which prompted him to invest like 95% of his assets into MCF.  MCF subsequently fell 50% as natural gas went from $13/mcf to $2/mcf.  This was the end of his hedge fund career.  I think this highlights the dangers of a full Kelly criteria application. 

 

I think the Kelly criteria is good to think about in the abstract than in actual practice.  Position sizing should not be an exact science as it is impossible to calculate the upside/downside exactly.  Kelly should be used as a guide to being vaguely right in your position size than thinking some position needs to be 25.4324% of your portfolio. 

 

Example with DIMEQ (see DIMEQ thread for more info)

 

I know that the downside is zero.

I know that the upside is 3.5-4 to 1 odds at the current price of 65 cents.

I believe the odds of achieving that upside is around 80%

 

Using the Kelly formula on http://www.albionresearch.com site it says to put 74.81% of my capital into DIMEQ.  Now if I were running a hedge fund I would only put 3% of my capital in DIMEQ, which using the Kelly formula means I am only betting that there is a 22-23% chance of winning. 

 

By allocating 3% into DIMEQ being pretty sure of a win (80%), means if they do win, that would be a gain of 9% for my fund, or equivalent to an average years worth of gain in the S&P 500. If I lose and am still sure my probabilities were correct, I could live with the 3% loss of capital.  Thats the art of position sizing versus the science of the Kelly criteria. 

 

If I used the Kelly criteria and lost, meaning a 75% capital loss in my fund, I would quit and start opening up bars across the country. 

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I think Mark Sellers used a full Kelly criteria allocation in his hedge fund which prompted him to invest like 95% of his assets into MCF.  MCF subsequently fell 50% as natural gas went from $13/mcf to $2/mcf.  This was the end of his hedge fund career.  I think this highlights the dangers of a full Kelly criteria application.  

 

I think the Kelly criteria is good to think about in the abstract than in actual practice.  Position sizing should not be an exact science as it is impossible to calculate the upside/downside exactly.  Kelly should be used as a guide to being vaguely right in your position size than thinking some position needs to be 25.4324% of your portfolio.  

 

Example with DIMEQ (see DIMEQ thread for more info)

 

I know that the downside is zero.

I know that the upside is 3.5-4 to 1 odds at the current price of 65 cents.

I believe the odds of achieving that upside is around 80%

 

Using the Kelly formula on http://www.albionresearch.com site it says to put 74.81% of my capital into DIMEQ.  Now if I were running a hedge fund I would only put 3% of my capital in DIMEQ, which using the Kelly formula means I am only betting that there is a 22-23% chance of winning.  

 

By allocating 3% into DIMEQ being pretty sure of a win (80%), means if they do win, that would be a gain of 9% for my fund, or equivalent to an average years worth of gain in the S&P 500. If I lose and am still sure my probabilities were correct, I could live with the 3% loss of capital.  Thats the art of position sizing versus the science of the Kelly criteria.  

 

If I used the Kelly criteria and lost, meaning a 75% capital loss in my fund, I would quit and start opening up bars across the country.  

 

Excellent points.  I remember listening to Sellers tell about how he was using Kelly to have these huge allocations to Contango, and I remember thinking how blind he is to risk as his main allocation was to a cyclical stock at the peak of the market.  But the truth is that we all have our blind spots.  That's why it's good to see if others can poke holes in our enthusiasms.

 

I shared your view about DIMEQ's probability of working out favorably until I asked our securities lawyer to take a look at it.  He told me that it was a crap shoot because the Judge didn't understand the arguments.  He said that an appeals court probably would understand the merits of the LTW holders' argument, but they would probably uphold the Bankruptcy judge's decision.  Since then, he thinks the judge is starting to understand the argument better, but he still realizes that there are so many variables that it's hard to make a prediction.  As a result of his feedback, we cut our probability estimate down from .80 to .60.  Since then, our estimate has been creeping back up because it is becoming more and more apparent to the WAMU BOD that they have major liability for shafting the LTW holders.  

 

This is how we use Kelly.  We continually recalculate the probabilities as new information surfaces.

 

Our allocation to TRH is almost all of our cash, but only about 40% of our total portfolio value.  As such, it's about a half Kelly as calculated with estimated probabilities and odds.  This would be way too high if I were running a fund because investors could get spooked and redeem their funds.  One reason I'm OK with this amount is that the downside volatility seems to have a practical limit of about 20% to 30%.  This would be only a 12% drawdown in total capital.  That's less than half what we're up this year to date.  I'm OK with this risk, and friends and family are too as we've had highly positive absolute returns over several years.

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TWACOWFCA,

 

40% seems very courageous especially if it is other peoples money, especially when those people are family + friends.

 

How high of an allocation would you ever go,or what is your highest % amount have you allocated to a single security.

 

Its good having courage + capital with these volatile times. Do you ever worry that a better buy comes along + you don t have the powder for instance Lancashire gets cut by 50% (I guess you would sell some TRH  to buy it).

 

I am working on using more than a thimble when opportunity comes around.

 

Then again I never have trouble sleeping at night.

 

Thanks for all your previous  comments + the albionresearch site

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TWACOWFCA,

 

40% seems very courageous especially if it is other peoples money, especially when those people are family + friends.

 

How high of an allocation would you ever go,or what is your highest % amount have you allocated to a single security.

 

Its good having courage + capital with these volatile times. Do you ever worry that a better buy comes along + you don t have the powder for instance Lancashire gets cut by 50% (I guess you would sell some TRH  to buy it).

 

I am working on using more than a thimble when opportunity comes around.

 

Then again I never have trouble sleeping at night.

 

Thanks for all your previous  comments + the albionresearch site

 

Very thoughtful questions.  I don't think our strategy is particularly courageous, but risk averse.  We had a lot of cash before the recent sell off by design as the psychological inflection point of the end of QE2 approached.  The TRH trade presented as the market was about to bounce.  The trade appeared to have a better risk/reward than playing the bounce.  If the trade goes against us, we probably won't be much worse off than if we had been fully invested going into summer.  If the trade works out well, we have a pegged price with protection against another step down in the market, and we could exit the trade with little or no transaction haircut before the terminal date and use funds to pick up any compelling bargains that may present.

 

My take on risk is very different than the conventional view.  At one time or another, we've had more than 40% of assets in FFH, BRK and LRE.  These are all run by ethical men who are about the best of class in what they do with very long term records to prove it.  They have most of their wealth tied up in the companies they run.  Two of these companies are acyclical or contracyclical and actually saw their market price go up during the 08 to 09 market meltdown.  This was a better outcome than most diversified portfolios experienced. 

 

With most of our assets invested in these owner operated companies, and the occasional special situation like TRH, we have done remarkably well in the value of all accounts from the market peak in 07.

 

Friends and family accounts are the most difficult, but there is much goodwill there after the excellent returns over the years.  My sister, especially doesn't like hairy situations, but doesn't mind having almost all her funds in LRE, FFH or BRK.  :)

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Thanks, twacowcfa

 

So do you aim for a large %(say 60%) in owner operated companies that are acyclical or counter cyclical and then the rest in cash or special situations (arbitrage, etc)?

 

If so, I like it.

 

There are other great owner operated companies, of course, but it's rare that we can buy them at a great price compared to IV.  Owner operated companies generally outperform the market by a very large amount. On average about 80 of the S&P500 firms  are owner operated.  These account for about half the real returns of that index over a long period of time.  When one can find a great one at a good price, the outperformance is awesome!  :)

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I would also highly recommend Fortune's Formula by William Poundstone.  It's a good introduction and history of edge/odds.

 

I'm reading it now, about 1/4th through and it is very interesting. Still not sure how I could apply any of it, but more practical investing stuff might come later in the book.

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I'm reading it now, about 1/4th through and it is very interesting. Still not sure how I could apply any of it, but more practical investing stuff might come later in the book.

 

Not that you asked me, but since I also recommended the book I thought I'd chime in.

 

Think about how High Frequency Trading is similar to what was originally done by the track bettors with the wire service.  Those that can get access to information faster than others, can get guaranteed success. 

 

Today it is happening amazingly faster compred to back then but it is exactly the same.

 

Someone like Munger might say this idea should be a mental model.  If one had this as a mental model, one would have immediately noticed that, for example, the spread of the internet would kill (or at least greatly diminish the competitive advantages) of a large group of middlemen who relied on have information sooner than others to make their living.  As well, one might also have realized that those selling specialized products but with little ability to pay for advertising would greatly benefit from the internet.  Etc., etc.

 

In any case, I recommended it because I thought it was such a well written and insightful book but there is also lots to take away from it to add to mental models, in my opinion.

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I'm now about 3/4th through, and I'm curious to know if the book had the same impact on others who have ready it: Did it make you want to punch Paul Samuelson in the face?

 

He comes across as so arrogant and borders on intellectual dishonesty...

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