# Long calendar spread with puts

- The Options Institute at CBOE®

### Potential goals

- To profit from neutral stock price action near the strike price of the calendar spread with limited risk in either direction.
- To profit from a directional stock price move to the strike price of the calendar spread with limited risk if the market goes in the other direction.

### Explanation

#### Example of long calendar spread with puts

Sell 1 28-day XYZ 100 put | 3.25 |

Buy 1 56-day XYZ 100 put | (4.60) |

Net cost = | (1.35) |

A long calendar spread with puts is created by buying one “longer-term” put and selling one “shorter-term” put with the same strike price. In the example a two-month (56 days to expiration) 100 Put is purchased and a one-month (28 days to expiration) 100 Put is sold. This strategy is established for a net debit (net cost), 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 puts on the expiration date of the short put, and the maximum risk is realized if the stock price moves sharply away from the strike price.

### Maximum profit

The maximum profit is realized if the stock price equals the strike price of the puts on the expiration date of the short put. This is the point of maximum profit, because the long put has maximum time value when the stock price equals the strike price. Also, since the short put expires worthless when the stock price equals the strike price at expiration, the difference in price between the two puts is at its greatest.

It is impossible to know for sure what the maximum profit will be, because the maximum profit depends of the price of long put which can vary based on the level of volatility.

### Maximum risk

The maximum risk of a long calendar spread with puts is equal to the cost of the spread including commissions. If the stock price moves sharply away from the strike price, then the difference between the two puts approaches zero and the full amount paid for the spread is lost. For example, if the stock price rises sharply, then the price of both puts approach zero for a net difference of zero. If the stock price falls sharply so that both puts are deep in the money, then the prices of both puts approach parity for a net difference of zero.

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

Conceptually, there are two breakeven points, one above the strike price of the calendar spread and one below. Also, conceptually, the breakeven points are the stock prices on the expiration date of the short put at which the time value of the long put equals the original price of the calendar spread. However, since the time value of the long put depends on the level of volatility, it is impossible to know for sure what the breakeven stock prices will be.

### Profit/Loss diagram and table: Long calendar spread with puts

Sell 1 28-day XYZ 100 put | 3.25 |

Buy 1 56-day XYZ 100 put | (4.60) |

Net cost = | (1.35) |

Stock Price at Expiration of the 28-day Put | Short 1 28-day 100 Put Profit/(Loss) at Expiration | Long 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 | (4.45) | (1.20) |

110 | +3.25 | (4.05) | (0.80) |

105 | +3.25 | (3.15) | +0.10 |

100 | +3.25 | (1.35) | +0.90 |

95 | (1.75) | +1.65 | (0.10) |

90 | (6.75) | +5.70 | (1.05) |

85 | (11.75) | +10.40 | (1.35) |

*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 calendar spread with puts realizes its maximum profit if the stock price equals the strike price on the expiration date of the short put. The forecast, therefore, can either be “neutral,” “modestly bullish,” or “modestly bearish,” depending on the relationship of the stock price to the strike price when the position is established.

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

If the stock price is below the strike price when the position is established, then the forecast must be for the stock price to rise to the strike price at expiration (modestly bullish).

### Strategy discussion

A long calendar spread with puts is the strategy of choice when the forecast is for stock price action near the strike price of the spread, because the strategy profits from time decay. While the “low” net cost to establish the strategy and the potentially “high” percentage profits are viewed as attractive features by some traders, calendar spreads require the stock price to be “near” the strike price as expiration approaches in order to realize a profit. Consequently, one cannot overlook the possibility of “high” percentage losses if the stock price moves away from the strike price. Long calendar spreads with puts, therefore, are suitable only for experienced traders who have the necessary patience and trading discipline. 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 as expiration approaches. Trading discipline is required, because “small” changes in stock price can have a high percentage impact on the price of a calendar 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. The net delta of a long calendar spread with puts is usually close to zero, but, as expiration approaches, it varies from −0.50 to +0.50 depending on the relationship of the stock price to the strike price of the spread.

With approximately 20 days to expiration of the short put, the net delta varies from approximately +0.10 with the stock price 5% below the strike price to −0.10 with the stock price 5% above the strike price.

With approximately 10 days to expiration of the short put, the net delta varies from approximately +0.20 with the stock price 5% below the strike price to −0.20 with the stock price 5% above the strike price.

When the stock price is slightly above the strike price as expiration approaches, the position delta approaches −0.50, because the delta of the long put is approximately −0.50 and the delta of the short put approaches 0.00.

When the stock price is slightly below the strike price as expiration approaches, the position delta approaches +0.50, because the delta of the long put is approximately −0.50 and the delta of the short put approaches +1.00.

The position delta approaches 0.00 if the puts are deep in the money (stock price below strike price) or far out of the money (stock price above strike price). If the puts are deep in the money, then the delta of the long put approaches −1.00 and the delta of the short put approaches +1.00 for a net spread delta of 0.00. If the puts are out of the money, then the deltas of both puts approach 0.00.

### 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 a long calendar spread with puts has one short put with less time to expiration and one long put with the same strike price and more time, the impact of changing volatility is slightly positive, but very close to zero. The net vega is slightly positive, because the vega of the long put is slightly greater than the vega of the short put. As expiration approaches, the net vega of the spread approaches the vega of the long put, because the vega of the short put approaches 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.

Since a long calendar spread with puts has one short put with less time to expiration and one long put with the same strike price and more time, the impact of time erosion is positive if the stock price is near the strike price of the puts. In the language of options, this is a “net positive theta.” Furthermore, the positive impact of time erosion increases as expiration approaches, because the value of the short-term short at-the-money put decays at an increasing rate.

If the stock price rises above or falls below the strike price of the calendar spread, however, the impact of time erosion becomes negative. In either of these cases, the time value of the shorter-term short put approaches zero, but the time value of the longer-term long put remains positive and decreases with passing time.

### 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 long calendar 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 assignment is deemed likely and if a long stock position is not wanted, then appropriate action must be taken. Before assignment occurs, the risk of assignment can be eliminated in two ways. First, the entire spread can be closed by selling the long put to close and buying the short put to close. Alternatively, the short put can be purchased to close and the long put can be kept open.

If early assignment of the short put does occur, stock is purchased, and a long stock position is created. If a long stock position is not wanted, there are two choices. First, the long stock can be closed by exercising the long put. Second, the shares can be sold in the marketplace and the long put can be left open. Generally, if there is time value in the long put, then it is preferable to sell shares rather than to exercise the long put. It is preferable to sell shares in this case, because the time value will be lost if the put is exercised.

Note, also, that whichever method is used to close the long stock position, 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

If the short put is assigned, then stock is purchased and a long stock position is created. In a long calendar spread with puts, the result is a two-part position consisting of long stock and long put. This position has limited risk on the downside and substantial profit potential on the upside. If a trader has a bullish forecast, then this position can be maintained in hopes that the forecast will be realized and a profit earned. If the long stock position is not wanted, then the position must be closed either by exercising the put or by sell stock and selling the put (see Risk of Early Assignment above).

### Other considerations

Long calendar spreads with puts are frequently compared to short straddles and short strangles, because all three strategies profit from “low volatility” in the underlying stock. The differences between the three strategies are the initial investment (or margin requirement), the risk and the profit potential. In dollar terms, short straddles and short strangles require much more capital to establish, have unlimited risk and have a larger, albeit limited, profit potential. Long calendar spreads, in contrast, require less capital, have limited risk and have a smaller limited profit potential. Traders who are not suited to the unlimited risk of short straddles or strangles might consider long calendar spreads as a limited-risk alternative to profit from a neutral forecast. One should not forget, however, that the risk of a long calendar spread is still 100% of the capital committed. The decision to trade any strategy involves choosing an amount of capital that will be placed at risk and potentially lost if the market forecast is not realized. In this regard, choosing a long calendar spread is similar to choosing any strategy.

The long calendar spread with puts is also known by two other names, a “long time spread” and a “long horizontal spread.” “Long” in the strategy name implies that the strategy is established for a net debit, or net cost. The terms “time” and “horizontal” describe the relationship between the expiration dates. “Time” implies that the options expire at different times, or on different dates. The term “horizontal” originated when options prices were listed in newspapers in a tabular format. Strike prices were listed vertically, and expirations were listed horizontally. Therefore a “horizontal spread” involved options in the same row of the table; they had the same strike price but they had different expiration dates.