One poker player bluffs his way to a jackpot with a pair of deuces, while another folds because he doesn’t have at least a straight. Their strategies diverge because the first player’s acting on instinct and the second’s playing the odds – but neither can escape the probabilities.

It’s the same in the world of options trading. Some investors spend time analyzing an entry point and then execute a trade that reflects their assumption. Others trade off of instinct or hunches. What’s interesting is that two investors can feel bullish about a stock like Netflix (Netflix) but have completely different trades and probabilities of success. That breadth of possibility seduces some into a life of trading.

So once they’re hooked, how can traders use probabilities to make intelligent trading decisions?

First, they should understand that the probability of profit (POP) for a trade or strategy means the probability of making at least \$0.01 on that trade by a specific date in the future, such as an option’s expiration. Profit and loss can and will fluctuate daily, but the POP of a given trade at expiration can be estimated based on current implied volatility levels, how many days remain until expiration and how much extrinsic value is associated with that trade. But before diving into that idea, consider how POP is calculated.

#### The math behind POP

In the simplest terms, probability of profit is an extension of the probability of an option expiring in-the-money (ITM) or out-of-the-money (OTM).

For short-option trades, POP will be greater than the probability of that option expiring OTM. For long-option trades, POP will be less than the probability of that option expiring ITM.

The reason is the option’s extrinsic value.

Extrinsic value is the portion of an option’s value that’s tied to time and volatility. It’s separate from intrinsic value, which is based on where the stock price is relative to the option’s strike price. The value of an out-of-the-money option is 100% extrinsic. Extrinsic value will be \$0.00 at expiration, and the profit or loss of an option trade will be determined by whether or not it has intrinsic value at expiration. Short-option sellers want their options to have zero intrinsic value at expiration, and long-option buyers want as much intrinsic value as possible at expiration. Keeping that in mind, the discussion can turn to how probabilities start to unfold through the lens of extrinsic value.

#### Short-option sellers

Short sellers of option contracts benefit if the option expires OTM (which is completely opposite of long buyers of option contracts).The short seller keeps the credit received up front for taking on the risk — after all, the short seller has more theoretical adverse risk than the option buyer.

If traders feel bullish on Netflix and decide to sell a put at the 320 strike, they would collect a \$6.10 credit for taking the risk of the stock falling below their strike of \$320, where they would be obligated to purchase 100 shares at expiration. This credit is 100% extrinsic value at this point because Netflix is trading at around \$357 per share and the strike is at \$320 — it’s OTM. The probability of that option expiring OTM is 76% in this expiration cycle, but the probability of profit is actually higher than that at around 81%. (See “Extrinsic value,” below).

Why? The answer has to do with extrinsic value. The green profit zone on the tastyworks curve view doesn’t turn into a red loss zone until the \$313.90 mark. That’s because the trader would have already collected \$6.10 to open the trade, and that credit can be used to offset intrinsic value losses at expiration if Netflix is below \$320. If Netflix were at \$313.90 at the option’s expiration,the trader would be at break even on the trade (no loss or profit) because the option’s intrinsic value (\$6.10) equals the credit received (\$6.10).

Going back to the definition of POP, which is the probability of making at least \$0.01 on the trade, it becomes clear why POP is a higher number than the probability of the strike expiring OTM. Because the trader collected an extrinsic value credit to open the trade, that value can be used to offset losses past the strike price to a point. The break even point of the trade (\$313.90) is further away from the option’s strike price (\$320). It’s less likely for Netflix to drop below \$313.90 than it is for the stock to drop below \$320.

Because of that, POP is higher than the strike expiring OTM for short option sellers, as that \$0.01 profit point is below the strike in this example, at \$313.9. In other words, short OTM option sellers can see profit at expiration even if the strike is ITM. This extrinsic value credit can do wonders for probabilities of success and can be thought of as a defensive mechanism just as much as an offensive mechanism.

After that crash course on why POP is higher than the probability of a short-option expiring OTM, the class can turn their attention to long options. Can extrinsic value help traders in the same way at expiration? Unfortunately, when buying options in most cases, the answer is a resounding “No!”

When buying an option to open for a debit, traders benefit most if the option expires ITM by more than they paid for the option initially. If that happens, the trader can sell the option for a larger credit than the debit they paid for it, and realize a profit.

The chart in “Bullish on Netflix,” above, shows that if traders are bullish on Netflix and decide to buy a call at the 360 strike, they would pay an \$18.90 debit for the right to buy shares at \$360 at the option’s expiration. That debit is 100% extrinsic value at that point because Netflix is trading just under \$360 per share and the strike is at \$360. That’s not good for the trader at expiration because, as the image indicates, the green profit zone doesn’t begin until the \$378.91 mark. If traders pay \$18.90 for the contract, Netflix must be above the \$360 strike by at least \$18.91 at expiration for the trader to realize a profit. So, \$378.90 is, as many readers will have guessed, the breakeven price of that long call.

The probability of that option expiring ITM is 47%, but the probability of profit is much lower than that at around 32%. Because the option must be significantly ITM for the trade to be at least \$0.01 profitable, the trader wants the stock price of Netflix to move much higher. It’s harder for Netflix to rise above \$378.90 than it is for it to rise above \$360. Typically, when a big movement is needed in a specific direction in a short time, probabilities start to decline.

So what can a trader do, if anything, to mitigate the low probability of success at expiration associated with buying at-the-money (ATM) options? The answer has to do with extrinsic value, yet again.

#### Dealing with extrinsic value

Based on what’s been covered so far, it’s clear that paying for extrinsic value in a long option isn’t ideal if traders are holding the option to expiration. On the other hand, collecting extrinsic value in a short option can make the difference between profit and loss if the trader’s holding the option to expiration. If traders tie this together with POP, they should make the most of extrinsic value when selling options, and pay as little as possible when buying options. In a high implied volatility (IV) environment,extrinsic value could be higher than normal, and in a low IV environment, extrinsic value could be low. At the end of the day, implied volatility is directly related to extrinsic value because IV is derived from current option prices.

For short-option sellers, the tactic is easy to see — the more premium traders can collect up front for selling the option, the better off they will be in terms of breakeven price and POP. That might mean sticking it out and waiting patiently for high IV.

What this means for long-option buyers is paying more attention to the setup of the trade, rather than the environment. Even in a low IV environment, when extrinsic value is lower, there’s still a staggering difference in POP between a long ATM option and a long ITM option— take a look at the Netflix example in “Low IV,” below, to see why.

In that image, the trader is buying the \$300 strike call instead of the \$360 strike call. Yes, the option will be more expensive overall because it’s now ITM, but does that make it a higher-probability trade compared with the \$360 strike call? The answer is yes, based on extrinsic value. When buying the 360 strike call, the trader would have paid around \$18.90 in extrinsic value to own the option. Netflix would have to climb to \$378.90 by expiration just for the trader to break even.

Buying the \$300 strike call, the trader is paying \$62.50 for the option, which has only \$3.65 of extrinsic value. That’s because the option has \$58.85 of intrinsic value with Netflix at \$358.85. Because traders can maintain all of that intrinsic value if the stock stays at the same price, they no longer need for the stock to move up as much to be profitable on the trade at expiration.

Long-option buyers only need to make up for the extrinsic value they pay for the option to be profitable at expiration, and in this case it’s about 80% less extrinsic value than the \$360 strike call. That’s clearly reflected in the difference in POP, which increases to 45%. Netflix only has to rise to \$362.51 at expiration for this trade to be profitable compared to \$378.91 in the earlier example.

And it’s easier for Netflix to rise above \$362.50 than for it to rise above \$378.90. The probability of Netflix landing at or above \$362.50 at expiration is around 45%, and the probability of Netflix expiring at or above \$378.90 is around 32%. Extrapolate that over a large number of occurrences, and the difference in potential success becomes huge.

Remember that options traders take risks with the objective of turning a profit. Regardless of how they arrive at a directional or neutral assumption, they should approach it in a methodical and intelligent way. For long-option buyers, that could mean minimizing extrinsic value as much as possible. For short-option sellers, that could mean maximizing it. After all, it could make the difference between profit and loss at expiration.

Mike Bulter, a self-taught trader, serves as host of Mike and his White Board and co-host of Market Mindset on the tastytrade network. @tastytraderMike

## Probability of Profit (P.O.P.)

In a strategy game such as poker, some players make decisions off of instinct, while others use probabilities and numbers to make decisions.

In the world of options trading, the same behavior can be observed. As a trader, it’s best to put feelings to the side so that strategies are mechanical and based on probabilities rather than emotions.

You may be thinking to yourself, ok, that’s great and all, but how can I use probabilities (specifically P.O.P.) to help make me a smarter trader?

Well, in this post we will seek to answer that question.

First, one important facet you should understand is that when we say P.O.P., what we mean specifically is – the probability of making at least \$0.01 on a trade.

## How Is P.O.P. Calculated?

Now let’s discuss the calculation of probability of profit, which can get a little statistically heavy in some cases, but I’ll do my best to keep it light!

To make it a little easier, we will stick with rough calculations on a couple of more basic options strategies: credit/debit spreads (defined risk trades) and naked options (undefined risk trades). It’s not important to memorize these formulas, but it is useful to see them ‘on paper’ in order to help you to gain a full understanding of what P.O.P. is.

For credit spreads, the rough POP calculation is…

100 – [(the credit received / strike price width) x 100].

For example, if you have a \$1 wide spread and you receive \$0.40 (which is actually \$40 – remember that 1 option contract controls 100 shares of stock so you have to multiply \$.40 x 100 to get \$40), you can expect to have close to a 60% POP.

For debit spreads, it is a similar calculation, but you will take max profit into consideration. You can take…

100 – [(the max profit / strike price width) x 100].

For example, if you pay a \$0.10 debit (which is actually \$10 – remember that 1 option contract controls 100 shares of stock so you have to multiply \$.10 x 100 to get \$10) to potentially make \$0.90 on a \$1.00 wide spread; you would have a P.O.P. close to about 10%. Formula: 100 – [(.90 / 1) x 100]

### Naked Options

For naked options, we look at the probability out of the money (OTM). It is important to note that your P.O.P. will be greater than the probability OTM when selling naked options because the credit moves the break-even point in your favor.

For example, if you sell a put option at a strike price of \$95, for a \$1.00 credit (which is actually \$100 – remember that 1 option contract controls 100 shares of stock so you have to multiply \$1.00 x 100 to get \$100), your break-even point (the point where your gains are equal to losses) is really \$94. This gives you \$1 of wiggle room.

Below you’ll find the calculations for a few additional strategies as well as the ones that we have mentioned…

By now, you may be wondering: am I really expected to calculate my probability of profit every time I make a trade? How do I know what it is for other strategies?

These are both great questions! And the easy answer is – use the tastyworks trading application! If you choose not to use it, you may have to do it the ole’ fashioned way.

In tastyworks, P.O.P. is featured in a number of different places. The P.O.P. for individual positions is displayed on the Positions page and new trades on the Trade page. POP is a very important concept to understand, so let’s get into it!

## Why Is P.O.P. Important For Options Traders?

P.O.P. is important for a variety of reasons, but the most obvious is that it is the best indication of whether a trade has the opportunity to be a winner or not and is rooted in statistics. If a trade is placed that has a probability of profit that is 72% (like the below example), we can expect that around 7 out of 10 times, the trade will be a winner.

Statistically, P.O.P. can be utilized in conjunction with the statistics based strategy of having a high number of trading occurrences. Studies done by tastytrade have shown that an important aspect of success in trading is accumulating a number of occurrences while keeping trade sizes small relative to our portfolio. Specifically, we’re talking hundreds to even thousands of occurrences over the years, while only using a small percentage of our portfolio.

Why is having a high number of occurrences favorable for traders? Well, it is because when you have a large number of occurrences with high P.O.P., statistically, you can expect that as you increase your number of occurrences, the probability of those trades being winners moves closer and closer to the combined probability of profit for all of those trades. That may be a little confusing, so let us try another example.

Let’s break it down using the trusty coin flip example. If you flip a coin, there’s a 50/50 chance of head or tails, right? But if you flip it five times, it could potentially land on tails five times. This doesn’t mean that the coin is rigged or that the probabilities have changed, it just means there hasn’t been a high enough number of occurrences for the probabilities to play out. If you were to continue flipping it a few hundred times, the probabilities would move closer and closer to 50/50 as you continue flipping. For a more detailed explanation, check out this article.

At the end of the day, probabilities are probabilities. If we risk our entire account on one trade that has a P.O.P. of 80%, we may win; however, the statistics tell us that we will lose approximately 20% of those trades over time. If one of those times happens to be now, we would be wiped out with no cash left to put on more trades!

One final thing to note about P.O.P. is that it is directly related to the profit you can potentially make on a trade. Generally, the lower the P.O.P., the more profit you can make. The higher the P.O.P. the less profit you can make.

## I Think I’ve Got It, But Can You Summarize?!

• P.O.P. stands for Probability of Profit, and is calculated for you in the tastyworks trading application
• The higher the POP the lower potential profit for a trade, and vice versa.
• Over a large number of occurrences, we can expect P.O.P. to average out to our average P.O.P. on trade entry