Occasionally one comes across a book that is educational, historical, about economics and that could be made into a movie. Fortune’s Formula by William Poundstone is just such a book.
What a lot of investors and fund managers don’t realize is
that they are gambling blindly. I won’t go into my issues with mean-variance asset
allocation, but suffice it to say, I consider mean variance approaches and VaR as belief systems that are far too popular
for our own systemic good.
Fortune's Formula includes great bios of Claude
Shannon and Ed Thorpe and an introduction to something known as the Kelly
Formula. Ed Thorpe is a mathematician,
hedge fund practitioner and in the eyes of some, including Nasim Taleb the
rightful co-creater of what is now known as the Black Scholes formula or the
(Thorpe-Bachelier) theorem. See Wilmott
Those of you familiar with LTCM are now thinking, “…an
academic mathematician hedge fund manager, this is going to have a nasty punch
line at the end of it.” The punch line
in this case is thankfully flat and deeply impressive, Billions of dollars
managed in one of the lowest variance profiles for decades. Thorpe has delivered the best financials met
by a very small handful of managers.
Kelly is described as:
“…working at the esteemed Bell Labs, a chain smoker, liberal drinker, a lot of fun, the life of the party. He was gregarious loud, and funny, quick to loosen his tie and kick off his shoes.”
He was also brilliant.
He came up with the optimal “bet” asset allocation strategy assuming one
knows the odds of playing the game and the payoff. His approach to asset allocation provides the
maximum return over a given set of time.
Please re-read the last sentence if it didn’t impact you enough.
The basic formula is: Edge/odds=portfolio allocation (bet size) …what the heck does that mean and how does one use it? If you are a gambler it clicks immediately, if you are trader or mathematician, have patience. For those familiar with Markowitz asset allocation there is a nice section on Kelly vs. Markowitz. I personally consider Markowitz a version of trend following and dangerously suspect in regards to the instability of correlation drift.
The basic premise of Kelly allocation is that in order to maximize the geometric return of a series of bets over time, one should go about allocating capital based on the average edge one has in “winning” versus the odds of winning that are paid out.
greater your perceived information edge, the more you should concentrate your
bet. There are many Kelly sites and
tools, some of dubious merit and intent.
For those of you in the money management business, you may
want to “tone down” the geometric return and perform a variance analysis
relative to the risk profile of investors you have holding your fund.
Simple rules of thumb may be good sanity
checks. Having grown up in
Investing is a marathon event. Long tortoise, short hare. Investment clients may say they want the highest return possible, most wouldn’t stick around after the drawdown associated with a higher volatility approach even if they wanted to be “part of the plan” in the early days. The pros, Fund of Funds etc. usually say they are comfortable with a certain volatility profile, but will bolt at certain drawdown levels.
True fact: most investors under perform their investment vehicles. I have studied this using both hedge and mutual fund flow data. Investors, invest high and exit low. In gamblers parlance, they make horrible jockeys and can be their own worst enemies.
A simple tool is provided for playing with the concept at the bottom of the post, I just lifted it off the web so make no endorsements for it or anything related to it. This approach might make sense for a portfolio of investment, drug candidates, product launches etc., just beware of your own biases inherent in the estimates. Like all models it recycles all too efficiently: put garbage in and you will get garbage out.
The nice thing about investing buy and hold in equities, is that unlike a casino, the odds are actually in your favor over time, assuming your horizon is great enough to overcome transaction costs.
As a money manager I find this ties in nicely with Buffet’s approach of a few eggs in a basket watched closely. The greater your information edge (remember to be humble) the greater your holding concentration should be.
To learn more I would highly recommend buying the book, the story is a heck of a read. If there is a movie it will probably be horrible.
Even Warren Buffet makes an entrance into the book with his passing interest in nontransitive dice. Warren is all Midwestern style, he speaks plainly, seems to listen a lot and gets results without a lot of fuss, still waters running deeply.