The Kelly Criterion is the brilliant summation of a betting strategy first discovered by Information Theorist John Kelly. Kelly came up with a betting system which optimizes bankroll growth based upon known odds and a definite payout. If you can find an exploitable, repeatable *edge*, Kelly’s system tells the maximum you should bet based upon that criteria.

## Using the Kelly Criterion with Your Portfolio

Extending Kelly a bit further (like Ed Thorp, author of two math bibles for the investor/bettor *Beat the Dealer* and *Beat the Market*, has done) we can do a bit of hand-waving and make it work for the stock market.

Some derivations of *“Stock Market Kelly”* involve using back-looking numbers such beta to approximate the continuous returns of securities. We’re going to do it in a discrete way, and use discrete numbers for **wins** and **losses**.

### The Kelly Criterion For Asset Allocation

Let’s say that you’re investing with a 10 year time-frame – you want to buy a house or retire, for example. You have an extra **$100,000** and are trying to determine the best allocating between stocks and treasury bonds.

Let’s try to calculate is your ‘*edge*‘ and your ‘*odds*‘.

It’s true: *garbage in, garbage out*. All we can do is take an educated guess and hope that it is close enough to reality to guide our choices. (See: past performance is no guarantee of future results.)

As they say, history doesn’t repeat itself *but it often rhymes*.

**Odds:** The S&P 500 beats 10 Year Treasuries roughly 85% of the time over rolling 10 year periods. We’ll then enter **.85** for our odds of stock out-performance.

**Edge:** Edge is tough, but for arguments sake, let’s use **5%**. Historically this is a decent choice; sometimes authors will take average earnings yield and subtract Treasury yield. Change it as you desire.

#### Using Odds and Edge to Optimize Asset Allocation

‘Normal’ or ‘Full’ Kelly is

(probability*(1+odds offered)-1)/(odds offered)

We need to modify the Kelly Criterion a bit to take into effect the fact that generally a security won’t ‘go to zero’. Even a losing ‘bet’ has some value.

We simplify the equation to

(Expected Value)/(odds offered)

Here’s the math:

Expected value = .85*.05 (5%) – .15*.02 (-2%) = 0.0395

Divide by the odds offered (winning bet: .05) = 79%.

So, in this theoretical portfolio with your historic estimate of odds and edge, aim for 79% stocks and 21% bonds. The standard disclaimer applies**: these numbers are guesses, so adjust your expectations accordingly.**

## Kelly Criterion Optimal Asset Allocation Calculator

Ready to try it out? Here’s a calculator which applies the concepts above to come up with an allocation: