Successful options trading is based on understanding the statistical probabilities and using those probabilities to create an “edge”. The Kelly Criterion is one method that traders use to determine the appropriate position sizing for a given trade. The underlying principle is that you should not put all of your money into a single trade, but rather put in an amount that is appropriate given the probable outcome of the trade and the impact that it may have on the overall account. However, position sizing is not the only use for the Kelly Criterion in trading options.

The Kelly Criterion (or Kelly formula) emerged from statistical work done by John Kelly at Bell Laboratories in the 1950’s to help figure out better ways to deal with signal-noise issues in long-distance telephone communications. Soon after it was published, the formula became very popular with gamblers who found that it could be used as a consistent money management system.

Calculating the Kelly Criterion relies on two basic components: a trading strategy’s percentage of winning trades (or probability of profit) and its win/loss ratio. The win/loss ratio is equal to the average profit from winning trades divided by the average loss from losing trades. With these two components, it is easy to calculate what percentage of a trading account should be risked on any given trade.

The formula for the Kelly Criterion is:

Kelly % = W – [(1 – W) /R]

where

W = Win percentage (probability of profit)

R = Win/ loss ratio

For example, let’s assume that a hypothetical trade has a 60% probability of profit and will generate a maximum of a $600 profit or a $400 loss. The calculation for the Kelly percentage is as follows:

W = 0.60 (or 60% probability of profit)

R = 1.5 (or Max Profit of $600 divided by Max Loss of $400)

Kelly % = 0.60 – [(1 – 0.60) /1.5]

Kelly % = 0.33 or 33%

Based on the formula, up to 33% of the account equity can be risked on this trade. Unfortunately, in trading it is rare to find trades with this good of a risk/reward ratio.

Let’s look at another example which will utilize the formula in a real world options trade. With IWM trading at 117 and 38 days to expiration, we will sell a vertical credit spread for 1/3 the width of the strikes.

Sell 1 IWM Dec 121/122 Call Vertical @ $0.33

The probability of profit on this trade is 67%. Let’s plug this information into the Kelly formula.

W = 0.67 (or 67% probability of profit)

R = 0.493 (or Max Profit of $0.33 divided by Max Loss of $0.67)

Kelly % = 0.67 – [(1 – 0.67) /0.493]

Kelly % = 0

The Kelly formula is telling us that 0% of our capital should be allocated to this trade! Why? Because statistically, over time, this trade as no “edge” and therefore zero expectancy for success. Many options traders do not hold trades through expiration, but choose to take profits earlier (i.e. 50% of max profit). Does this improve the situation? Quite the contrary. If losing trades are allowed to run to maximum loss, then winning trades must also be allowed to run to maximum profit in order to just break even. If winners are taken off earlier (while still allowing losers to run to max loss), it results in a negative expectancy (or negative Kelly %). This is a key takeaway that runs counter to what many experts recommend with regards to defined-risk trades. If we are going to manage winners, we must also manage losers

This is where I feel the Kelly Criterion is a game changer. Rather than solving for the Kelly %, we can use the formula to solve for the point at which to close a losing trade. Having an exit strategy is a critical part of trading. I have had no problems exiting winning trades. I typically exit credit spreads and strangles when I have received 50% of the maximum profit. However, at least for me, determining the exit point on a losing trade has been a bit more ambiguous. By using the Kelly Criterion we can calculate the point to exit a losing trade that will provide the trader with an “edge.” First, we will re-arrange the formula to determine where to take losses in order to break even (Kelly % = 0).

R = (1 /W) -1

In the prior example we sold the IWM 121/122 call credit spread. Let’s now assume that we plan to take profits at 50% of maximum profit. The spread that we sold for $0.33 will be closed for $0.17 ($0.33 * .50 = $0.165). W equals the probability of profit (in this case, 67%).

R = (1 / .67) -1

R = 0.493

R is the profit divided by the loss and, in this case, is equal to 0.493. By dividing the 50% max profit by the value of R (0.493) we can determine that the max loss should equal 1.01 times (or 101%) the total credit received. We would exit the trade when the loss was $0.33 per contract (1.01 * 0.33).

Let’s look at another real-world example from a trade I placed this week.

On Monday, I sold the /ES Mar 16 2250/2300/1725/1675 iron condor for $6.75 ($337.50 credit received). At the time the trade was placed, it had a probability of profit (POP) of 84.37%. I plan to close the trade at 50% of max profit (Pmax).

R = (1 / POP) -1

R = (1 / .8437) -1

R = 0.185

Average Loss = Pmax / R

Average Loss = 0.50 / 0.185

Average Loss = 2.70 (or 270%)

This establishes the average loss at $18.23 (or 270% of the credit received). By adding the initial premium ($6.75) to the max loss ($18.23) we are able to determine the price at which to close the trade ($24.97) to break even over time.

However, we don’t want to just break even. By closing losing trades *prior* to the breakeven point provides the trader with the “edge” necessary for long-term profitability. In this particular trade, we would want to take our loss *before* it reached 270% of max profit.

How much edge you wish to give yourself is a personal preference. In “How to Price and Trade Options” by Al Sherbin, it is suggested that an edge of 10-15% is appropriate in most cases. For this next example, we will use a 15% edge. We subtract the edge from the probability of profit when solving for R. For example,

R = [1 / (POP – Edge)] -1

R = [1 / (.8437-.15)] -1

R = 0.442

Average Loss = 0.50 / 0.442

Average Loss = 1.13 (or 113%)

For the same /ES iron condor with a 15% edge on probabilities, we will now exit the trade if the loss exceeds 113% of the credit received ($6.75 * 1.13 = $7.63). Adding the original trade price (credit received) of $6.75 to the max loss of $7.63 sets a price of $14.38 at which we will exit the trade.

The math may seem a bit daunting at first, but a simple spreadsheet makes calculating profit at and loss levels a breeze. I have included the formulas below that I utilize in my spreadsheet.

Pmax = % of max profit to close profitable trade

Lmax = % of credit received to close a losing trade (average loss)

POP = % probability of profit

E = % edge on probilities

C = credit received per contract

Lmax = Pmax / ((1 / (POP – E)) -1)

Take profits at = C * (1 – Pmax)

Take losses at = C * (1 + Lmax)

Being able to place a trade with known exit points that provide a statistical edge to the trader is going to be a real game changer for my own trading. When placing trades, I have always entered a GTC order to close the trade at the target profit level. In addition, I am now also setting an alert in the trading platform which notifies me via text message when a loss approaches the point determined by the Kelly formula.

If you wish to read further on the subject, I would highly recommend Al Sherbin’s book, **How to Price and Trade Options**.

I have included an interactive calculator in the **Members** section which can be utilized to experiment with the formula. Special thanks to Henrik Santander of **The Lazy Trader** for writing this script for me.

Pingback: Weekend Portfolio Analysis (November 14, 2015) • Trade with Aram()

Pingback: Managing Energy Trades • Trade with Aram()