I’m about 60% through William Poundstone’s Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street.
It’s a gripping narrative full of 20th century trivia that ties together the birth of information theory, some of the greatest scientific minds of the 1900s, the rise of quantitative finance, and the role of organized crime. These topics come alive in a fresh, memorable way when discovered through the lens of its colorful characters.
It chronicles the history of the efficient market hypothesis (MIT, U Chicago, Paul Samuelson). You can organize its conclusion around this excerpt:
There is much truth in the efficient market hypothesis. The controversy has always been over just how far the claim can be pressed. Asking whether markets are efficient is like asking whether the world is round. The best way to answer depends on the expectations and sophistication of the questioner. If someone is asking whether the world is round or flat, as fifteenth-century Europeans might have asked, then “round” is a better answer. If someone knows that and is asking whether the earth is a geometrically perfect sphere, the answer is no.
A few ideas that struck me:
An industry uses academic research to protect itself from…academic research
In 1959, Harry Markowitz published his famous book on Portfolio Selection. Everyone in finance read that, or said they did. Financial advisers responded to Markowitz’s model. They were growing aware of this new and threatening current in academic thought: the efficient market hypothesis. Markowitz demonstrated that all portfolios are not alike when you factor in risk.
Investopedia aside:
The efficient frontier is the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.
Poundstone continues:
Therefore, even in an efficient market, there is reason for investors to pay handsomely for financial advice. Mean-variance analysis quickly swept through the financial profession and academia alike, establishing itself as orthodoxy.
The Problem With Markowitz
1) Indecision
The Hamlet-like indecision of mean-variance analysis
When portfolios are equal on the efficient frontier, the investor’s risk appetite to decide. Unsatisfying.
2) Only useful for single period analysis
Most people do not invest this way. They buy stocks and bonds and hang on to them until they have a strong reason to sell. Market bets ride, by default. This makes a difference because there are gambles that look favorable as a one-shot, yet are ruinous when repeated over and over. Any type of extreme “overbetting” would fit that description.
(emphasis mine)
Standard mean-variance analysis does not treat the compounding of investments. It is, you might say, a theory for Kelly’s dollar-a-week gambler. But as the wealth to be amassed by compounding is so fantastically greater than can be achieved otherwise, a practical theory of investment must largely be a theory of reinvestment.
A solution to both problems
Indecision
I made up this example inspired by a demonstration in the book.
Consider 2 investments that each have 10 possible discrete returns. The balanced one and the skewed one.
Simple mean-variance metrics will mislead you into thinking the skewed asset is superior. It has a
- higher return
- lower volatility
- cheaper straddle price
- higher Sharpe ratio
But the so-called “third moment” of the distribution (the skew) cannot hide from the geometric return which leaves no ambiguity about which investment is superior for a long-term hold.
Aside for masochists
The closer an asset’s return distribution looks to a bell-curve, the closer the straddle price will approximate 80% of the volatility. But when the straddle value is less than .80 of the volatility, you know there is skew or outliers lurking. If you are inspecting an asset’s returns for the first time, a quick trick is to compute the ratio of MAD to Volatility to see if it’s less than .8
A place where this is very handy is in looking at the price changes in inter-month future spreads. If you trade options on them this has important ramifications for pricing. But the lessons extrapolate.
If you need a refresher on MAD and straddles see:
Multi-period
In my contrived example, you are bound to get a “whammy” if you keep pressing.
Poundstone writes:
When you try to apply Markowitz theory to compounding, the results can be absurd. One of Ed Thorp’s theoretical contributions to the Kelly criterion literature is a 1969 paper in which he demonstrated the partial incompatibility of mean-variance analysis and the policy of maximizing the geometric mean. Thorp closes his article by declaring that “the Kelly criterion should replace the Markowitz criterion as the guide to portfolio selection.”
Perhaps no economist of the time would have dared such a heresy. It seems unlikely a major economic journal would have published such talk. Thorp’s article appeared in the Review of the International Statistical Institute. Probably few economists saw it. In any event, few economists had heard of John Kelly. That was about to change.
Oft-forgotten history
Defense of Markowitz
Markowitz devoted a chapter of Portfolio Selection to the geometric mean criterion (possibly the most ignored chapter in the book) and cited Latane’s work in the bibliography. Markowitz was virtually the only big-name economist to see much merit in the geometric mean criterion. He recognized that mean-variance analysis is a static, single-period theory. In effect, it assumes that you plan to buy some stocks now and sell them at the end of a given time frame. Markowitz theory tries to balance risk and return for that single period.
The insights derived from the Kelly Criterion have a complex history
Because of this complex lineage, the Kelly criterion has gone by a multitude of names. Not surprisingly, Henry Latané never used “Kelly criterion.” He favored “geometric mean principle.” He occasionally abbreviated that to the catchier “G policy” or even, simply, to “G.”
Breiman used “capital growth criterion,” and the innocuous-sounding “capital growth theory” is also heard. Markowitz used MEL, for “maximize expected logarithm” of wealth. In one article, Thorp called it the “Kelly[-Breiman-Bernoulli-Latané or capital growth] criterion.” This is not counting the yet-more-numerous discussions of logarithmic utility.
This confusion of names has made it relatively difficult for the uninitiated to follow the idea in the economic literature. The person most shortchanged by this nomenclature is probably Daniel Bernoulli. He had 218 years’ priority on Kelly. The unique and unprecedented part of Kelly’s article is the connection between inside information and capital growth. This is a connection that could not have been made before Shannon rendered information measurable. Bernoulli considers a world where the cards are on the table, so to speak, and all the probabilities are public knowledge. There is no hidden information.
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