The Shannon Method

Welcome, readers from Trading Psychology and the Motley Fool, and thanks to Dr. Steenbarger and "bladow," a poster on the Mechanical Investing board at the Fool for recommending this blog.  I was in Montana at the time most of you arrived, but I extend a belated welcome to all of you.  Also, thanks to Rod at Perfectly Reasonable Deviations for the words of encouragement on this blog.

Claude Shannon is widely recognized as the father of the information age and is featured prominently in the book Fortune's Formula, which I previously reviewed.  In a previous post, I discussed briefly a relatively unknown, but simple and elegant portfolio management method attributable to Claude Shannon.  Oaktree Research sums up the method nicely (as does Fortune's Formula in the section called "Shannon's Demon"):

In the 1960s, Shannon gave a lecture in a hall packed with students and teachers alike in MIT, on the topic of maximizing the growth rate of wealth. He detailed a method on how you can grow your portfolio by rebalancing your fund between a stock and cash, while this stock stays in a random ranging market. (He used a geometric Wiener example). Essentially, you buy more when stock price is low, using the cash at hand, or sell more when stock price is high, with allocation of 50-50% value at each interval.

Considering how simplistic it is, it's unusual in that it's a guaranteed market timing model.  If you follow it, you are guaranteed to be selling some of your position at or near market tops and buying at or near market bottoms, depending on how often you adjust the 50-50 split.  It's also somewhat unusual in that volatility is your friend, not your enemy.  According to Fortune's Formula, when asked if he used the method to manage money, Shannon replied that "the transaction costs would kill you."  Transaction costs now of course are much less than in Shannon's day.

Shannon's method is nothing more than a simplified case of the more widely known method of rebalancing, which to my knowledge traceable back to Harry Markowitz's Efficient Frontier, developed in the early 1950s.  Shannon's method could even be considered a special case of the Kelly Criterion, where a fixed percentage of your bankroll is "bet" at any given time.  Yet Kelly's work in the 1950s was influenced by Shannon's earlier work in the 1940's.

In any event, the Shannon method of 50-50 allocation can be shown to be optimal, and it is much simpler in application than either the Efficient Frontier or even the Kelly Criterion.  Although a casual reading of Poundstone's book would give an impression that it works better than it does, it is well worth investigating.  Well before Poundstone's book, and before even hearing that Shannon investigated the same thing, I investigated the method independently.  The question of how well it works is best illustrated in pictures.  At left is what would have happened if you had applied the method for 10 years to JDSU stock starting December 1993.  Note that there are no transaction costs assumed, but there is also no interest paid on the 50% cash stake either.

At left is the method applied to JPM for 10 years beginning 1984.  So does the Shannon method work?  The answer probably depends on how you measure performance, as well as what stocks you choose to apply the method to, and even what other investment alternatives you have.   Almost invariably, after running the Shannon method on a stock for some time, you will discover some point in that stock's history where the Shannon portfolio briefly matches or surpasses buy and hold due to a selloff in the stock.  For example, this happened with JPM in February 1988 and again in November of 1990.  Oddly, this point often uncannily marks a major bottom in the stock.

You will also discover that there will be long periods where Shannon will underperform on a total return basis.  This is true even if transaction costs are free and some moderate interest rate is paid on the 50% cash position.  What these graphs don't tell you, however, is that the Internal Rate of Return (IRR) of the Shannon method nearly always beats buy and hold, often by substantial amounts.  This is because the Shannon method harvests volatility, typically investing cash in a stock when it drops and then quickly selling it for a small profit when it rises.  For some small and volatile stocks, the Shannon method generates as much as a 35% IRR vs. 10% for buy and hold.  Interestingly, my research indicated that although the Shannon method could be applied at very small price changes, it works nearly as well at say 3-4% price changes in the stock, even if there are no transaction costs.  Thus you can minimize transaction costs and still get most of the benefit of the Shannon method.

A high IRR doesn't do you much good though unless you can reinvest the proceeds in something equally good.  I mentioned in the previous post that I use a method similar to Shannon's method to manage my investments now.  What I do is select several diverse (and hopefully uncorrelated stocks) and apply the Shannon method.  The trick is that they all share the same virtual pool of cash.  So I pretend each stock investment has an equal amount of cash reserve, even though my total portfolio has only say 20% cash.  The theory of this is that I am putting some of that IRR of one stock to work in another stock when one goes up and the other goes down. 

To the extent stock bounce around randomly (and uncorrelated), I profit from volatility.  If all the stocks drop substantial amounts, the shared cash pool would dry up and I either stop the Shannon method or go on margin if I think it's justified.  Based on my experience and my stock selections, this method returns 3-4% over and above buying and holding the stocks individually (after transaction costs).  With a 401K account, the method can be tax efficient too.

Assuming the new CASTrader works, it will handle portfolio management rather than my twist on the Shannon method.  The Shannon method will live on in CASTrader, however, as a sort of market maker on the dark market I am building in.  The Shannon Trader, as I will call it, will always have a bid/ask just below/above the current price on the frictionless CASTrader dark market.  The more volatile the dark market is, the more the Shannon Trader will profit, and the more partial diversity, price stability and dark liquidity it will provide the other traders.

Update: Additional info on Shannon's Demon at Nuclear Phynance.

Comments

[JOE]

Shannon's method (also Kelly's) ONLY works when you have information EDGE !!

If it is NO ANY EDGE, Kelly told you NOT to bet !!

In your JDSU case, you simply guess.

[Warren D' Struction]

Sorry but holding an edge precludes the possibility of a random walk scenario. You talking about physics in economic class.

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The Whittaker–Shannon interpolation formula is a method to reconstruct a continuous-time bandlimited signal from a set of equally spaced samples.

The interpolation formula, as it is commonly called, dates back to works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935 in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949. It is also commonly called Shannon's interpolation formula and Whittaker's interpolation formula. E. T. Whittaker, who published it in 1915, called it the Cardinal series.