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By Grahamified
September 25, 2006

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This year marks the 50th anniversary of John Kelly's contribution to Money-Management-Using-the-Gambler's-Edge-vis-�-vis-A-New-Interpretation-Of-The-Information-Rate. Today, even the Church of Advanced Investment Thought�Michael Mauboussin, for example�has some very nice and maybe hyper-dilatory things to say about the Kelly Betting Model. The only problem plaguing investors is how to make any practical use of it.

Unfortunately, illustrious advocates of Kelly Portfolio Optimization are a bit vague about how to invest with it in the securities markets. The unadulterated formula is, of course, deceptively straightforward (% to bet = edge/odds), but investors determined to plug their stock selection strategies into the Kelly Betting Model will probably experience a lot of head-scratching.

It does not necessarily follow that the Kelly formula should be placed in the same department as Accumulation Swing Indexes, Decennial Cycles, K Hooks, Kagi Charts, Advance/Decline Divergence Oscillators, DiNapoli Levels, Futures Rollover Algorithms, Keltner Channels with Exponential Moving Average Filters, Bollinger Bands, Japanese Candlesticks, Commodity Channel Indexes, Chande Channel Indexes, Fibonacci Bands, Herrick Channel Indexes, McClellan Summation Indexes, Exponential Moving Average Crossovers, or Klinger Oscillators. Lest we forget, even Charlie Munger seems to advocate the Kelly formula �or at least he seems to advocate studying two books, The Warren Buffett Portfolio and Fortune's Formula, that goad investors about its potential power.

In real-time, however, the Kelly formula displays certain emissions problems similar to those in other heavily merchandised modern finance concepts such as Economic Value Added and its brethren Cost of Equity Capital. Actually, some of the Kelly Portfolio Optimization's illustrious advocates either are, or were, disciples of these other nouveau metrics. A mere coincidence, perhaps. In any case, the emissions of all these metrics reek of "seductive precision" (Warren Buffett's phrase); although the Kelly's form of precision probably leads many investors to a more expeditious and spectacular sense of futility.

When the former trendy concepts meandered into the modern finance lexicon, common sense provoked some investors to question the vague, lamely circular logic of cost of capital (i.e., a business' economic value is always based on the volatility of its stock price relative to the market, which is, if Benjamin Graham was correct, sometimes based on its business economics). Now that the Kelly Betting Model is gathering momentum in modern finance literature, perhaps it's time for common sense to determine whether Kelly Portfolio Optimization really serves as a useful investment management tool. Here we will resort to a flip anecdote rather than a welter of Monte Carlo simulations, because the latter deigns exactly nothing about how investors will be compelled to tweak, if not overtly disregard, whatever is instructed by a Kelly dictate.

Well, monthly portfolio statements are gathered. The internal rate of return for all investments over the past 10 years in the securities markets is meticulously calculated to constitute an "edge", along with the historical "odds" of "wins" and "losses". Next, a spreadsheet is fired up, the figures entered, and...

What?! The computed Kelly allocation is 72.5%. Yes, the Kelly Allocation Spreadsheet says that 72.5% of investment capital should be bet on a single cigar-butt stock that trades in the pink sheets. Okay? We can relax, though, because everyone knows that a Half-Kelly bet is both statistically prudent and nearly as profitable as the Full-Kelly variety. What a relief �we are left with a Half-Kelly capital allocation of 36.25%. It's a lot less stressful that a mere 36.25% of investment capital will be allocated to a single bet on an illiquid stock in the securities markets.

When the lights are dimmed, deep-value die-hards are going to swallow hard and prepare to execute...maybe a One-Thirtieth Kelly. Wait �this smaller bet will surely mutilate the magnificent exponential growth curve as illustrated in books such as Fortune's Formula. Maybe 72.5% of investment capital should be allocated to a bunch of cigar-butts all purchased at the same time. Or maybe 36.25% should be allocated to a bunch of cigar-butts. So what if the Kelly formula was never intended for this purpose!!!

Wait �what if buying a bunch of cigar-butts all at once captures some mischievous correlation that isn't even recognized by the Kelly formula? This tactic just can't be congruous with the painstakingly rendered internal rate of return calculation gathered for the past 10 year's piecemeal investments. Can it?. Maybe we should just artificially lower our historical return expectations until a comfortable allocation number comes up on the spreadsheet, and...

Ed Thorp, who famously used the Kelly formula for blackjack, and who later gained both notoriety and great wealth through the successful exploitation of market inefficiencies such as market-neutral convertible hedging, apparently did not have to deal with the reality of large investment allocations dictated by the Kelly betting scheme. There was simply never enough product to sufficiently cover the much larger recommended portfolio allocations. By necessity, Thorp's fund was widely diversified with many smaller simultaneous positions. Thus, despite all the paeans and hoopla concerning the real-time power of the Kelly Betting Model in books such as Fortune's Formula, Kelly Portfolio Optimization did not exactly receive a large-scale work-out at Thorp's firm. Market inefficiencies and plain-vanilla, Ben Graham-style diversification, rather than Kelly Portfolio Optimization, were the catalysts of Thorp's success in the securities markets.

Nothing about real-world Kelly Portfolio Optimization sounds "seductively precise". So where is all the seductive precision? It's stuffed into the historical rate of return calculations and the associated probabilities of "wins" and "losses" that are meticulously extrapolated prima facia into the future. Past performance guarantees future results.

Let's see. Here is a Kelly allocation for a 30% internal rate of return with 80% wins: 64%. Here is a Kelly allocation for a 20% internal rate of return with 70% wins: 45%. Here is one for a 20% internal rate of return with 60% wins: 26.6%. Here is one for a 15% internal rate of return with 75% wins: 53%. And another for a 15% internal rate of return with 60% wins: 25%. And here, finally, are two questions that pertain to on-going simultaneous investment in the securities markets: Given even great success, do you know any equities investors with portfolios that performed as predicted by past results? And what to do with investments that take 3 years, rather than 6 months, to show a profit? It is, after all, the precision of prediction that truly drives the Kelly Betting Model.

Now, 50 years after its introduction, it is tantalizing to read storied accounts about the wizardry of John Kelly's side-handed contribution to modern finance. That's because optimum position sizing remains one of the more elusive and vexing problems even for the most successful value investor. In this discipline, though, Kelly Portfolio Optimization will probably continue to work especially well until it is actually used.

 


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