# Short diagonal spread with puts

- The Options Institute at CBOE®

### Potential goals

To profit from bullish stock price action with limited risk if the stock price falls.

### Explanation

#### Example of short diagonal spread with puts

Buy 1 28-day XYZ 100 put | (3.25) |

Sell 1 56-day XYZ 105 put | 7.60 |

Net credit = | 4.35 |

A short diagonal spread with puts is created by selling one “longer-term” put with a higher strike price and buying one “shorter-term” put with a lower strike price. In the example a two-month (56 days to expiration) 105 Put is sold and a one-month (28 days to expiration) 100 Put is purchased. This strategy is established for a net credit, and both the profit potential and risk are limited. The maximum profit is realized if the stock price rises sharply above the strike price of the short put, and the maximum risk is realized if the stock price is at the strike price of the long put on the expiration date of the long put.

### Maximum profit

The maximum profit potential of a short diagonal spread with puts is equal to the net credit received less commissions. If the stock price rises sharply above the strike price of the short put, then the value of the spread approaches zero; and the full credit received is kept as income.

### Maximum risk

The maximum risk is realized if the stock price is equal to the strike price of the long put on the expiration date of the long put. With the stock price at the strike price of the long put at expiration of the long put, the loss equals the price of the short put minus the net credit received when the position was established less commissions. This is the point of maximum loss because the short put has its maximum difference in price with the expiring long put. It is impossible to know for sure what the maximum loss potential is, because it depends of the price of short put, and that price is subject to the level of volatility which can change.

**Important!**
**If the short option is held beyond the long option expiration the new short only position will be considered uncovered and will have substantial downside risk.**

### Breakeven stock price at expiration of the long put

There is one breakeven point, which is above the strike price of the short put. Conceptually, the breakeven point at expiration of the long put is the stock price at which the price of the short put equals the net credit received for the spread. It is impossible to know for sure what the breakeven stock price will be, however, because it depends of the price of the short put which depends on the level of volatility.

### Profit/Loss diagram and table: short diagonal spread with puts

Buy 1 28-day XYZ 100 put | (3.25) |

Sell 1 56-day XYZ 105 put | 7.60 |

Net credit = | 4.35 |

Stock Price at Expiration of the 28-day Put | Long 1 28-day 100 Put Profit/(Loss) at Expiration | Short 1 56-day 100 Put Profit/(Loss) at Expiration of the 28-day Put* | Net Profit/(Loss) at Expiration of the 28-day Put |
---|---|---|---|

115 | (3.25) | +6.70 | +3.45 |

110 | (3.25) | +5.60 | +2.35 |

105 | (3.25) | +3.70 | +0.45 |

100 | (3.25) | +0.80 | (2.45) |

95 | +1.75 | (3.00) | (1.25) |

90 | +6.75 | (7.60) | (0.85) |

85 | +11.75 | (12.35) | (0.60) |

*Profit or loss of the short put is based on its estimated value on the expiration date of the long put. This value was calculated using a standard Black-Scholes options pricing formula with the following assumptions: 28 days to expiration, volatility of 30%, interest rate of 1% and no dividend.

### Appropriate market forecast

A short diagonal spread with puts realizes its maximum profit if the stock price is sharply above the strike price of the short put on the expiration date of the long put. The forecast, therefore, must be “bullish.”

### Strategy discussion

A short diagonal spread with puts is a logical strategy choice when the stock price is below the strike price of the short put and the forecast is for bullish stock price action.

Short diagonal spreads with puts are frequently compared to simple bull spreads with puts in which both puts have the same expiration date. The differences between the two strategies are the profit potential, the risk, and the alternative courses of action at expiration of the long put. Short diagonal spreads are established for a greater net credit than comparable bull put spreads, because the price of the longer-dated short put is higher than the price of the same-strike, shorter-dated put in a comparable bull put spread. Also, the maximum risk is less if the stock price falls sharply.

The tradeoff is that a short diagonal spread incurs a loss if the stock price is at the strike price of the short put on the expiration date of the long put, while a bull put spread would realize a profit. In this scenario, the longer-dated short put in a short diagonal spread experiences less time decay than the shorter-dated, same-strike put in a comparable bull put spread.

A potential benefit of a short diagonal spread with puts is that, after the long put expires, the short put remains open and can be “managed” in a number of ways. First, the short put can be left open in the hopes that it will expire worthless. Although this strategy has unlimited risk and is not suitable for many investors, it offers the possibility of earning the maximum profit potential of the strategy. Second, the short put can be converted to a bull put spread by buying a put with a lower strike price and the same expiration date as the open short put. This limits risk and leaves intact the potential for additional profits. Third, the short put can be converted to a bear put spread by buying a put with a higher strike price and the same expiration date as the open short put. While this managing alternative increases risk if the stock price rises, it offers potential profits if the stock price forecast has changed to bearish.

### Impact of stock price change

“Delta” estimates how much a position will change in price as the stock price changes. Long puts have negative deltas, and short puts have positive deltas. When the position is first established, the net delta of a short diagonal spread with puts is positive. With changes in stock price and passing time, however, the net delta varies from slightly negative to approximately +0.90, depending on the relationship of the stock price to the strike prices of the puts and on the time to expiration of the long put.

If the stock price equals the strike price of the long put at expiration of the long put, the position delta approaches +0.90. In this case, the delta of the in-the-money short put approaches +0.90 (depending on volatility and on the time to expiration), and the delta of the expiring long put goes to zero.

When the stock price is below the strike price of the long put at expiration of the long put, the position delta is slightly negative, because the delta of the short put approaches +0.90 and the delta of the in-the-money expiring long put approaches −1.00.

The position delta approaches zero if the stock price rises sharply above the strike price of the short put, because the deltas of both puts approach zero.

### Impact of change in volatility

Volatility is a measure of how much a stock price fluctuates in percentage terms, and volatility is a factor in option prices. As volatility rises, option prices tend to rise if other factors such as stock price and time to expiration remain constant. Long options, therefore, rise in price and make money when volatility rises, and short options rise in price and lose money when volatility rises. When volatility falls, the opposite happens; long options lose money and short options make money. “Vega” is a measure of how much changing volatility affects the net price of a position.

Since vegas decrease as expiration approaches, a short diagonal spread with puts generally has a net negative vega when the position is first established. Consequently, rising volatility generally hurts the position and falling volatility generally helps. The vega is most negative when the stock price is equal to the strike price of the short put, and it is least negative when the stock price is equal to the strike price of the long put.

The net vega approaches zero if the stock price rises sharply above the strike price of the short put or falls sharply below the strike price of the long put. In both cases, with the options both far out of the money or both deep in the money, both vegas approach zero.

### Impact of time

The time value portion of an option’s total price decreases as expiration approaches. This is known as time erosion. “Theta” is a measure of how much time erosion affects the net price of a position. Long option positions have negative theta, which means they lose money from time erosion, if other factors remain constant; and short options have positive theta, which means they make money from time erosion.

Short diagonal spreads with puts generally have a net positive theta when first established, because the positive theta of the short put more than offsets the negative theta of the long put. However, the theta can vary from positive to negative depending on the relationship of the stock price to the strike prices of the puts and on the time to expiration of the shorter-dated long put.

The theta is most positive when the stock price is close to the strike price of the short put, and it is the least positive or possibly negative when the stock price is close to the strike price of the long put.

### Risk of early assignment

Stock options in the United States can be exercised on any business day, and holders of short stock option positions have no control over when they will be required to fulfill the obligation. Therefore, the risk of early assignment is a real risk that must be considered when entering into positions involving short options.

While the long put in a short diagonal spread with puts has no risk of early assignment, the short put does have such risk, even though there is considerable time to its expiration. While one might think that a short option with 28 days or more to expiration has a near-zero chance of being assigned, this thinking is incorrect. Early assignment of stock options is generally related to dividends, and short puts that are assigned early are generally assigned on the ex-dividend date. In-the-money short puts whose time value is less than the dividend have a high likelihood of being assigned. Even long-term options are assigned early when the conditions are right.

If the short put is assigned prior to the expiration of the long put, then 100 shares of stock are purchased and the long put remains open. If a long stock position is not wanted, it can be closed in one of two ways. First, 100 shares can be sold in the marketplace. Second, the long 100-share position can be closed by exercising the long put. Although exercising a long put will forfeit the time value of that put, in the case of a short diagonal spread with puts, this is rarely a concern for the following reason. If the longer-term short put in a short diagonal spread is assigned, then there is probably no time value in the long put as it is much closer to its expiration. Therefore, in a short diagonal spread with puts, it is generally preferable to exercise the long put to close the long stock position. Selling shares to close the long stock position and then selling the long put is only advantageous if the commissions are less than the time value of the long put, which, as noted above, is unlikely if the time value of the longer-dated short put is less than the dividend.

Note, however, that whichever method is used, selling stock or exercising the long put, the date of the stock sale will be one day later than the date of the purchase. This difference will result in additional fees, including interest charges and commissions. Assignment of a short put might also trigger a margin call if there is not sufficient account equity to support the long stock position.

### Potential position created at expiration of the long put

The position at expiration of the long put depends on the relationship of the stock price to the strike price of the long put. If the stock price is at or above the strike price of the long put, then the long put expires worthless and the short put remains open.

If the stock price is below the strike price of the long put, then the long put is exercised. The result is a two-part position consisting of a short put and short 100 shares of stock. If the stock price is below the strike price of the long put immediately prior to its expiration, and if a position of short 100 shares is not wanted, then the long put must be closed (sold).

### Other considerations

The term “diagonal” in the strategy name originated when options prices were listed in newspapers in a tabular format. Strike prices were listed vertically in rows, and expirations were listed horizontally in columns. Therefore a “diagonal spread” involved options in different rows and different columns of the table; i.e., they had different strike prices and different expiration dates.