By Michael J. Wiener
Special to the Financial Independence Hub
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. Continue Reading…