# Long diagonal spread with puts

- The Options Institute at CBOE®

### Potential goals

- To profit from neutral stock price action near the strike price of the short put with limited risk on the downside and limited profit potential on the upside.
- To profit from a bearish stock price move to the strike price of the short put with lower risk than a simple long put but also with limited profit potential if the stock price falls above the strike price of the short put.

### Explanation

#### Example of long diagonal spread with puts

Sell 1 28-day XYZ 100 put | 3.25 |

Buy 1 56-day XYZ 105 put | (7.60) |

Net cost = | (4.35) |

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

### Maximum profit

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

### Maximum risk

The maximum risk of a long diagonal spread with puts is equal to the net cost of the spread including commissions. If the stock price rises sharply above the strike price of the long put, then the value of the spread approaches zero; and the full amount paid for the spread is lost.

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

There is one breakeven point, which is above the strike price of the short put. Conceptually, the breakeven point at expiration of the short put is the stock price at which the price of the long put equals the net cost of 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 long put which depends on the level of volatility.

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

Sell 1 28-day XYZ 100 put | 3.25 |

Buy 1 56-day XYZ 105 put | (7.60) |

Net cost = | (4.35) |

Stock Price at Expiration of the 28-day Put | Short 1 28-day 100 Put Profit/(Loss) at Expiration | Long 1 56-day 105 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 | (5.70) | (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 long put is based on its estimated value on the expiration date of the short 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 long diagonal spread with puts realizes its maximum profit if the stock price equals the strike price of the short put on the expiration date of the short put. The forecast, therefore, can either be “neutral” or “modestly bearish,” depending on the relationship of the stock price to the strike price of the short put when the position is established.

If the stock price is at or near the strike price of the short put when the position is established, then the forecast must be for unchanged, or neutral, price action.

If the stock price is above the strike price of the short put when the position is established, then the forecast must be for the stock price to fall to the strike price at expiration (modestly bearish).

While one can imagine a scenario in which the stock price is below the strike price of the short put and a diagonal spread with puts would profit from bullish stock price action, it is most likely that another strategy would be a more profitable choice for a bullish forecast.

### Strategy discussion

A long diagonal spread with puts is the strategy of choice when the forecast is for stock price action near the strike price of the short put, because the strategy profits from time decay of the short put. However, unlike a long calendar spread with puts, a long diagonal spread can still earn a profit if the stock falls sharply below the strike price of the short put. The tradeoff is that a long diagonal spread costs more than a long calendar spread, so the risk is greater if the stock price rises.

Long diagonal spreads with puts are frequently compared to simple vertical spreads in which both puts have the same expiration date. The differences between the two strategies are the initial investment, the risk, the profit potential and the available courses of action at expiration. Long diagonal spreads cost more to establish, because the longer-dated long put has a higher price than the same-strike, shorter-dated put in a comparable vertical spread. As a result, the risk is greater. Also, the profit potential of a long diagonal spread is less if one considers only the expiration date of the short put. The potential benefit of a long diagonal spread, however, is that, after the short put expires, the long put remains open and has substantial profit potential. One should not forget, however, that the risk of a long diagonal spread is still 100% of the cost of the position. Therefore, even if the short put in a diagonal spread expires worthless, the remaining open long put can still incur a loss if the stock price does not fall.

Patience and trading discipline are required when trading long diagonal spreads. Patience is required because this strategy profits from time decay, and stock price action can be unsettling as it rises and falls around the strike price of the short put as expiration approaches. Trading discipline is required, because “small” changes in stock price can have a high percentage impact on the price of a diagonal spread. Traders must, therefore, be disciplined in taking partial profits if possible and also in taking “small” losses before the losses become “big.”

### 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 long diagonal spread with puts is negative. With changes in stock price and passing time, however, the net delta varies from slightly positive 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 short put.

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

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

The position delta approaches zero if the stock price rises sharply above the strike price of the long 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 long diagonal spread with puts generally has a net positive vega when the position is first established. Consequently, rising volatility generally helps the position and falling volatility generally hurts. The vega is highest when the stock price is equal to the strike price of the long put, and it is lowest when the stock price is equal to the strike price of the short put.

The net vega approaches zero if the stock price rises sharply above the strike price of the long put or falls sharply below the strike price of the short 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.

Long diagonal spreads with puts generally have a net negative theta when first established, because the negative theta of the long put more than offsets the positive theta of the short put. However, the theta can vary from negative to positive 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 short put.

The theta is most negative when the stock price is close to the strike price of the long put, and it is the least negative or possibly positive when the stock price is close to the strike price of the short 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 long diagonal spread with puts has no risk of early assignment, the short put does have such risk. 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 puts whose time value is less than the dividend have a high likelihood of being assigned.

If the short put is assigned, 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. Remember, however, that exercising a long put will forfeit the time value of that put. Therefore, it is generally preferable to sell shares to close the long stock position and then sell the long put. This two-part action recovers the time value of the long put. One caveat is commissions. 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.

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 short put

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

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

### 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.