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:

jephiter Samson says

I like this allocation so much. I use it in allocating my property. thanks

PK says

Jephiter,

Pretty awesome that you’re able to use Kelly for Real Estate! Have you found any disadvantages to the system? Any surprises you didn’t account for?

TM @ Young and Thrifty says

That’s a pretty cool method of calculating your risk and return. I’ve never seen it broken down in formula form like that. Always cool to see some original posts!

PK says

Thanks!

Calculating expected returns is kind of hand wavey, but if you can somehow get a good guess, Kelly is perfect for your asset allocation. I’ll try to get a more advanced Kelly calculator at some point!

Irish57 says

As of 7-29-15, the Kelly Criterion Calculator seems to be frozen. I enjoy using this from time to time, and thank you for making it available. Will you please trouble-shoot and let me know if there is a problem or if it is “user error.”

Thanks in advance!

PK says

My apologies! It was the worst type of error, operator error.

I realize now I never made my ‘hardcore’ calculator… if you’re still using this one, is there anything you’d like to see in a sequel? I’ve built up all sorts of tools in the meantime which might make useful inputs to a Kelly Calculator: https://dqydj.com/calculators-and-visualizations/

Irish57 says

Hi PK:

Since you asked…

I have read DQYDJ’s posts on Valuation-based investing based on the Shiller P/E levels. Wade Pfau recently had a couple of articles on this formula method earlier in July in Forbes. (links) I believe it is under-appreciated, and I am using it in my investing program.

Part 1 of Pfau series: http://www.forbes.com/sites/wadepfau/2015/07/08/is-a-high-cape-cause-for-alarm-part-1-capes-relationship-to-stock-returns/

Part 2 of Pfau series: http://www.forbes.com/sites/wadepfau/2015/07/09/is-a-high-cape-cause-for-alarm-part-2-valuation-based-asset-allocation/

A few years ago, there was an article at Business Insider (BI) which I reference from time to time (link). It had a table that showed Credit Suisse’s analysis of historical dispersions of subsequent 3-year stock returns at various Shiller P/E levels.

http://www.businessinsider.com/chart-shiller-pe-returns-2013-6

Pfau’s article (Forbes) recommended break points at 2/3 and 4/3 of the Shiller long term mean for allocation decisions (based on Graham and Dodd suggestions). But that basically only boils down to three stock allocations buckets: 25% stocks, 50% stocks, and 75% stocks.

As of July 2015, with Shiller P/E of 26, a valuation- based investor following the Pfau methodology would already be hunkered down with only 25% stocks. In this era of sub-atomic interest rates on cash and bonds, I think most of us would like to keep our stock allocations as high as possible–within reason–always with eye on valuation and probable outcomes.

I have been trying to determine the probabilities of outcomes shown in the BI table and have been inputitng them into with the Kelly calculator to determine stock allocations at the various Shiller P/E levels. At Shiller P/E of 26 (where we are today) , the article said this is the level when problems start to crop up, i.e. possible negative subsequent 3- year returns.

For example, the table in the article implies there were nine (9) historical market experiences starting at the Shiller P/E 26 and higher. Three (3) of those 9 were negative returns in the subsequent 3- year periods. That seems to suggests that the success rate of a positive return is 66% at Shiller P/E of 26. (6 out of 9). At those odds of success, the Kelly calculator suggests a 50% bet. At Shiller P/E of 27, the success rate of a positive outcome drops to about 62%. At those odds, the Kelly output is 47% stocks. And so on. Both are considerably higher than 25% as recommended at this Shiller level in the Pfau article. Pretty big differences.

Is it a reasonable request that a DQYDJ team member build a calculator in which an investor could plug in the various Shiller P/E levels, and based on the historical outcomes from the Credit Suisse findings and the Kelly calculator criterion running in the back ground, it would output stock allocations ?

If that is too much to ask, I do have a question now that you understand how I am using the existing calculator. Since the BI article shows the dispersion of outcomes and subsequent 3 year returns (not 10 years as hinted in your original explanation for input) at the various Shiller levels, what are the best inputs I should be using given 3- year returns in the BI table at the current Shiller P/E of 26? (i.e. 66% success rate for a positive return)

Thanks for your time and consideration.

Sincerely,

Irish57

PK says

I think that is a reasonable request, yes – but I can’t guarantee it’ll come quickly (or before any future stock market falls, heh). Let me think on some of the options – it seems that any sort of a Kelly Calculator Reprise should do some sort of automatic odds calculations – perhaps with Shiller PE, or perhaps with something else (or even a blend). Have you seen our recent Shiller PE/CAPE calculator?

My issue would be with considering something like 3 years ‘long term’. I don’t know what the exact definition of long term should be, but common rules of thumb are usually something like “if you need it in the next 5 years, be safe” or something like that – and we usually average around a decade for a full market cycle. So, I don’t think I can comment on how to adjust it for 3 years – but I’d suggest using a conservative Kelly value, perhaps half or quarter Kelly?