A Failure to Understand Rebalancing

Recently, the Stingy Investor pointed to an article whose title caught my eye: The Academic Failure to Understand Rebalancing, written by mathematician and economist Michael Edesess.  He claims that academics get portfolio rebalancing all wrong, and that there’s more money to be made by not rebalancing.  Fortunately, his arguments are clear enough that it’s easy to see where his reasoning goes wrong.

Edesess’ argument

Edesess makes his case against portfolio rebalancing based on a simple hypothetical investment: either your money doubles or gets cut in half based on a coin flip.  If you let a dollar ride through 20 iterations of this investment, it could get cut in half as many as 20 times, or it could double as many as 20 times.  If you get exactly 10 heads and 10 tails, the doublings and halvings cancel and you’ll be left with just your original dollar.

The optimum way to use this investment based on the mathematics behind rebalancing and the Kelly criterion is to wager 50 cents and hold back the other 50 cents.  So, after a single coin flip, you’ll either gain 50 cents or lose 25 cents.  After 20 flips of wagering half your money each time, if you get 10 heads and 10 tails, you’ll be left with $3.25.  This is a big improvement over just getting back your original dollar when you bet the whole amount on each flip in this 10 heads and 10 tails scenario.  This is the advantage rebalancing gives you.

However, Edesess digs further.  If you wager everything each flip and get 11 good flips and 9 bad flips, you’ll have $4, and with the reverse outcome you’ll have 25 cents.  Either you gain $3 or lose only 75 cents.  At 12 good flips vs. 12 bad flips, the difference grows further to gaining $15 or losing 94 cents.  We see that the upside is substantially larger than the downside.

Let’s refer to one set of 20 flips starting with one dollar as a “game.”  We could think of playing this game multiple times, each time starting by wagering a single dollar.  Edesess calculates that “if you were to play the game 1,001 times, you would end up with $87,000 with the 100% buy-and-hold strategy,”  “but only $11,000 with the rebalancing strategy.”

The problem with this reasoning

Edesess’ calculations are correct.  If you play this game thousands of times, you’re virtually certain to come out far ahead by letting your money ride instead of risking only half on each flip.  However, this is only true if you start each game with a fresh dollar.

In the real world, we’re not gambling single dollars; we’re investing an entire portfolio.  If one iteration of the game goes badly, there is no reset button that allows you to restore your whole portfolio so you can try again in a second iteration of the game.

Edesess fundamentally misunderstands the nature of rebalancing and the Kelly criterion.  They don’t apply to how you handle single dollars or even a subset of your portfolio; they apply to how you handle your entire portfolio.  If you have a bad outcome and lose most of your portfolio, the damage is permanent; you don’t get to try again.  Unless you’re a sociopath who invests other people's money in insanely risky ways hoping to collect your slice from a big win, you don’t get to find more investment suckers to try again if the first game goes badly.

Warren Buffett has said “to succeed you must first survive.”  This applies here.  The main purpose of rebalancing is to control risk.  It may be true that several coin flips could turn your $100,000 portfolio into tens of millions, but it could also turn it into less than $1000.  The rebalancing path is much smarter; it will give you more predictable growth and make a complete blowup much less likely.  It turns out that the academics understand rebalancing just fine; it’s Edesess who is having trouble.