Selling naked strangles can be a risky options strategy no matter what strikes you choose. But there may be ways to choose your short strikes without chasing probabilities.

By thinkMoney Authors
March 30, 2020

Photo by Dan Saelinger

- Learn how you might choose strikes for your short strangles
- Understand how to pick short strikes that don’t involve chasing probabilities
- Know how to combine probabilities and theta when integrating short strangles into your trading plan

You probably know that time can suck the life out of options premiums. That’s typically bad if you own options, but great if you’re short options. This “positive” time decay comes from short options. If you want to get more time decay (theta), you might consider one of the time-decay-iest and riskiest strategies around: the short strangle, which is a short call plus a short put. And that means a big move—higher or lower—in the stock or index could cause big losses. Short strangles also require a large amount of trading capital. So why would anyone trade this type of strategy?

When you sell a strangle, the typical set up is a short out-of-the-money (OTM) call and a short OTM put. You’re speculating that the price of a stock or index will stay in between the strike prices of the options—above the strike price of the short OTM put and below the strike price of the OTM call. As time passes, and if the stock or index behaves the way you want it to, you can in theory collect a lot of positive theta.

Here’s how the sausage is made. When you sell a strangle, you collect a credit—its max potential profit. That’s achieved if the price of the underlying is above the strike price of the short put and below the strike price of the short call at expiration.

The break-even points on a short strangle are the put strike price minus the credit of the strangle, and the call strike price plus the strangle credit. The max potential loss is unlimited to the upside if the stock breaks through the upper break-even point and keeps going. The loss to the downside is limited only to the put strike price, minus the credit of the strangle, if the stock goes to $0.

All things being equal, here’s the rationale for trading a short strangle: A stock is more likely to have smaller price changes than bigger price changes. For example, a very volatile stock might be moving up and down 5% each day. Sometimes it might change 10% or 15%. But on most days, it changes 5%. That’s not to say it won’t move 10%, 15%, 20%, or more. It’s just that those bigger price changes happen less frequently. How can you tell? Just look at how further OTM options get cheaper and cheaper. The market is suggesting that the likelihood of the stock reaching those further OTM strikes—either higher or lower—is lower than the likelihood of reaching closer OTM strikes. And a short strangle is a speculation that the stock price will go through more of those small price changes versus the rarer, bigger ones before expiration.

Say you’ve found a stock or index you think might not have a big move and might trade in a range. And you’re willing to take the risk of a short strangle to capture positive theta. But which strikes do you choose for the short call and put? As you scan the options prices, you see that if you choose to sell strikes close to the current stock price—not too far OTM—you collect more premium and generate more positive theta. But the probability of the stock moving below the short put strike or above the short call strike is higher.

On the other hand, if you choose to sell strikes further away from the current stock price, i.e., further OTM, you collect less premium for the strangle. But the probability of the stock moving below the short put strike, or above the short call strike, is lower.

All of this illustrates the first trade-off with short strangles. If you want a higher credit (more positive theta and higher potential profit), you’ll have to accept that the short strangle has a greater probability of losing money. If you sell a further OTM call and put, the likelihood of the stock dropping below the short put strike, or rising above the short call strike, is lower, but you’ll collect less premium and generate less positive theta. In general, you may want to avoid chasing probabilities. If, for example, a short strangle has a 70% probability of making money at expiration, then another short strangle with a 75% probability is better, right? And a short strangle with a 95% probability is better still? Not necessarily.

The further OTM options don’t generate as much positive time decay as quickly as the closer OTM options. So you may have to hold those further OTM strangles longer to achieve a profit target. And if you sell a really far OTM strangle with a high probability of profit, you may be generating a small credit. Yet, the potential return is just too small, considering the risk you’re taking to sell any strangle, including the far OTM ones. Selling a closer OTM strangle could mean you don’t need to hold the trade as long to achieve the same profit target.

Let’s look at a hypothetical example using S&P 500 (SPX) options. Please note that for the sake of simplicity, the examples that follow do not include transaction costs.*

If you sell the 2885/3025 strangle, you get a credit of $76.45 and 1.23 theoretical daily theta.

SPX = 2960 | Theoretical Probability of Expiring OTM |

2885 put with 49 days til expiration (DTE) | 65% |

3025 call with 49 DTE | 65% |

If you sell the 2715/3095 strangle, you get a credit of $28.65 and 0.85 theoretical daily theta.

SPX = 2960 | Theoretical Probability of Expiring OTM |

2715 put with 49 DTE | 85% |

3095 call with 49 DTE | 85% |

Explore the probability of options expiring OTM on the** Trade** tab of the thinkorswim® platform from TD Ameritrade.

- Select an option
- Select Option Theoreticals and Greeks
- Select Probability OTM

You’ll see a theoretical probability that the underlying will be above a put strike or below a call strike at expiration. But because these probabilities are purely theoretical, they can change over the life of a trade.

The 2885/3025 strangle has 2.66x greater credit and 1.44x greater theoretical daily theta than the 2715/3095 strangle. Yet, taking that greater credit and theta, the short strikes of the 2885/3025 strangle are much closer to the SPX price of 2960 than the short strikes of the 2715/3095 strangle. The 2885 put is about 2% OTM, while the 2715 put is about 8.4% OTM. The 3025 call is about 2.7% OTM, while the 3095 call is about 4.4% OTM. The 2715/3095 strangle gives the SPX more room to move up and down. In other words, a 3% increase or decrease in the SPX would move it past 2885 and 3025. This would create a loss for the short 2885/3025 strangle, while the short 2715/3095 strangle might still be profitable.

Let’s see what happens to the theoretical values of the two short strangles over time (see sidebar, “What Happens to Options Over Time?”), assuming SPX is still at 2960 and volatility (vol) hasn’t changed. It’s a big assumption, but illustrates the point. The magnitude of losses can be much larger in practice.

Keep in mind that with more time, there’s often more potential for SPX, or any stock or index, to have a large price change. Of course, big changes can happen anytime. But with more time comes more uncertainty. And holding a trade longer assumes the risk of that uncertainty. As an engaged, self-directed trader, you may not want to hold an options position through to its expiration. Taking a short strangle off before expiration and capturing something less than the max potential profit might be a smart approach if either: (1) your opinion of the stock or index has changed, and you think it might make a big move up or down; and/or (2) you’re content with the amount of profit the short strangle has already generated, and you don’t want to continue taking the risk of the short strangle.

In general, traders know what “just right” feels like. And as an example, you may want to start your search for the short call and short put at strikes that have about a 70% probability of expiring worthless. Beyond those OTM strikes, for any given volatility, time to expiration, and stock price, theoretical theta starts to drop off more rapidly. Closer OTM than those strikes, and the probabilities of the stock moving past the short strikes can rise rapidly. That’s not to say selling options with a 70% probability of expiring worthless is the best or even a smart trade. You may see this behavior of theta and probability at different strikes. It’s just that starting your analysis there could save time.

If you integrate short strangles into your trading plan, understanding how to combine probabilities and theta is a powerful step in your trading education.

• Theoretical value of the 2885/3025 strangle is 72.68.

• Theoretical value of the 2715/3095 strangle is 25.63.

Compare the theoretical values to the original prices of the strangles, and the 2885/3025 would have a theoretical profit of $3.77, and the 2715/3095 strangle would have a theoretical profit of $3.02. Not a huge difference in profits.

• Theoretical value of the 2885/3025 strangle is 67.50.

• Theoretical value of the 2715/3095 strangle is 20.80.

Compare the theoretical values to the original prices of the strangles, and the 2885/3025 would have a theoretical profit of $8.95, and the 2715/3095 strangle would have a theoretical profit of $7.85. The difference in profits is getting wider.

• Theoretical value of the 2885/3025 strangle is 41.68.

• Theoretical value of the 2715/3095 strangle is 10.11.

Compare the theoretical values to the original prices of the strangles, and the 2885/3025 would have a theoretical profit of $34.77, and the 2715/3095 strangle would have a theoretical profit of $18.54. Even if you were to hold the 2715/3095 strangle for another 28 days until expiration, its max profit of $28.65 is still less than the theoretical profit on the 2885/3025 strangle after 21 days.

• The 2885/3025 strangle would have a theoretical value of 219.28, creating a loss of at least $142.83.

• The 2715/3095 strangle would have a theoretical value of 92.96, creating a loss of $64.31.

• The 2885/3025 strangle would have a theoretical value of 238.16, creating a loss of at least $161.71.

• The 2715/3095 strangle would have a theoretical value of 168.80, creating a theoretical loss of $140.15.

- Learn how you might choose strikes for your short strangles
- Understand how to pick short strikes that don’t involve chasing probabilities
- Know how to combine probabilities and theta when integrating short strangles into your trading plan

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