Kelly Criterion

The Kelly Criterion is a popular staking method which suggests that your stake should be proportional to the perceived edge. Kelly Criterion Staking Method Explained What is the Kelly Criterion formula? The basic Kelly Criterion formula is: (bp-q)/b B = the Decimal odds -1 P = the probability of success Q = the probability of failure. The Kelly Criterion helps you calculate the optimal amount you should wager when there is a difference between the true odds and the given odds. A mathematician called John Kelly Jr.

Bettors should always look for a mathematical edge rather than rely on their impulses. Learning how to use the Kelly Criterion, for example, is a great way for bettors to determine how much they should stake. Read on to find out.

Prior to placing a bet bettors should consider six important questions: who, what, when, where, why and how? But for this article, it is the how, as in how much to bet, we are interested in.

Popular staking method which suggests that stake should be proportional to the perceived edge.

Consider placing a bet on the English Premier League. We can adapt these questions accordingly:

• Who to bet on? Manchester United
• What to bet on? Top 4 finish
• When to bet on? Now
• Where to bet on? Pinnacle tend to offer the best odds
• Why to bet on? They seem to be under-priced
• How much? How much to bet on this outcome?

Most articles focus on the first five questions, typically using mathematical or statistical justifications on answering ‘why’ - such as the article on how to use Monte Carlo methods.

In making financial decisions, the key issue is not only finding the adequate financial products to invest in but also deciding how to subdivide one’s portfolio. Similarly, an important question for a bettor, is how much to wager?

Many papers recommend using the Kelly Criterion or a derivative of it - such as my 2013 paper appearing in the The Journal of Gambling Business and Economics. In essence, the Kelly Criterion calculates the proportion of your own funds to bet on an outcome whose odds are higher than expected, so that your own funds grow exponentially.

B = the Decimal odds -1
P = the probability of success
Q = the probability of failure (i.e. 1-p)

Kelly Criterion Sports Betting

Using a coin as an example of Kelly Criterion staking

For example, consider you are betting on a coin to land on heads at 2.00. However, the coin is biased and has a 52% chance of ending up on heads.

In this case:

P= 0.52
Q = 1-0.52 = 0.48
B = 2-1 = 1.

This works out at: (0.52x1 – 0.48) / 1 = 0.04

Therefore the Kelly Criterion would recommend you bet 4%. A positive percentage implies an edge in favour of your bankroll, so your funds grow exponentially. You can also test the criterion for different values in this online sheet by using the code below.

Ultimately the Kelly Criterion offers a distinct advantage over other staking methods such as Fibonacci and Arbitrage methods as there is a lower risk. However, it does require precise calculation of the likelihood of an event outcome, and discipline of this method will not provide explosive growth of your bankroll.

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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.

Kelly Criterion Optimal Asset Allocation Calculator

Here's a calculator which applies the concepts in this post to come up with an allocation:

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.)

Kelly Criterion Simulation

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%.

Kelly Criterion Calculator Excel

Historically 5% 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

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' almost always has some value in the stock market).

We simplify the equation to

Here's the math using the assumptions in the previous section:

Kelly Criterion Proof

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.

For traditional Kelly applications, also try the Kelly Calculator for bet sizing.