# Bullish split-strike synthetic (also known as Risk Reversal)

### Goal

Speculators: To profit from a price rise in the underlying stock.

Investors: To buy stock below the current price and to have “upside insurance” in case the stock price rises.

### Explanation

A bullish split-strike synthetic position consists of one long call with a higher strike price and one short put with a lower strike price. Both options have the same underlying stock and the same expiration date, but they have different strike prices. A bullish split-strike synthetic position can be established for either a net debit (net cost) or a net credit (net receipt), depending on the relationship of the stock price to the strike prices when the position is established. The strategy tends to profit as the underlying stock rises in price and especially as it rises above the strike price of the long call. Profit potential is unlimited, and potential loss is substantial.

## Example of bullish split-strike synthetic

 Buy 1 XYZ 105 call at (1.50) Sell 1 XYZ 95 put at 1.30 Net cost = (0.20)

### Maximum profit

The profit potential is unlimited and derives from the long call. The profit potential of a long call is unlimited, because the stock price can rise indefinitely.

### Maximum risk

The maximum risk of a short put is substantial, because the stock price can fall to zero.

### Breakeven stock price at expiration

If a split-strike synthetic is established for a net debit as in the example above, the breakeven stock price is the strike price of the call plus the net debit plus commissions. In the example above: 105.00 + 0.20 = 105.20

If a split-strike synthetic is established for a net credit, the breakeven stock price is the strike price of the put minus the net credit less commissions. Had the example been established for a net credit of 0.20: 95.00 – 0.20 = 94.80

### Profit/Loss diagram and table: bullish split-strike synthetic

 Long 1 105 call at (1.50) Short 1 95 put at 1.30 Net cost = (0.20)
Stock Price at Expiration Long 105 Call Profit/(Loss) at Expiration Short 95 Put Profit/(Loss) at Expiration Bullish Split-Strike Synthetic Profit / (Loss) at Expiration
110 +3.50 +1.30 +4.80
109 +2.50 +1.30 +3.80
108 +1.50 +1.30 +2.80
107 +0.50 +1.30 +1.80
106 (0.50) +1.30 +0.80
105 (1.50) +1.30 (0.20)
104 (1.50) +1.30 (0.20)
103 (1.50) +1.30 (0.20)
102 (1.50) +1.30 (0.20)
101 (1.50) +1.30 (0.20)
100 (1.50) +1.30 (0.20)
99 (1.50) +1.30 (0.20)
98 (1.50) +1.30 (0.20)
97 (1.50) +1.30 (0.20)
96 (1.50) +1.30 (0.20)
95 (1.50) +1.30 (0.20)
94 (1.50) +0.30 (1.20)
93 (1.50) (0.70) (2.20)
92 (1.50) (1.70) (3.20)
91 (1.50) (2.70) (4.20)
90 (1.50) (3.70) (5.20)

### Appropriate market forecast

Speculators, who typically seek a short-term profit and do not want to buy the underlying stock, use this strategy when the forecast is “very bullish.” Investors, however, who want to buy stock at the strike price of the put, use this strategy when the forecast is neutral. See the strategy discussion below.

### Strategy discussion

A bullish split-strike synthetic position profits most when the price of the underlying stock rises above the strike price of the long call. However, the short put contains an obligation to buy stock below the current price, and stock buyers want to buy at the lowest possible price. As a result, speculators and investors use this strategy differently.

Speculators typically seek short-term profits and do not want to buy the underlying stock. Speculators, therefore, use this strategy when the forecast is “very bullish.” The short put has a lower margin requirement than purchasing stock, so less capital is required. Also, the put premium is used to reduce the cost of the call, which has two advantages. First, it lowers risk if the stock trades sideways and, second, it lowers the breakeven point if the stock rises. The disadvantage is that the short put has substantial risk.

Investors, who want to buy the stock at the strike price of the put, would feel comfortable if the price declined slightly where the put could potentially be assigned. The call option is viewed as “upside insurance.” If the stock price rises, contrary to the neutral-to-bearish forecast, then at least stock can be purchased at the strike price of the call.

### Impact of stock price change

As the stock price rises, the long call rises in price and profits and the short put declines in price and profits. As a result, a bullish split-strike synthetic position profits as the stock price rises and loses as the stock price falls. This means that the position has a “positive delta.” Delta estimates how much an option price will change as the stock price changes, and the change in option price is generally less than dollar-for-dollar with the change in stock price. Also, because a bullish split-strike synthetic position consists of one short put, the net delta changes very little when the stock price is between the strike prices of the call and put. In the language of options, this is a “near-zero gamma.” Gamma estimates how much the delta of a position changes as the stock price changes. However, as the stock price rises more and more above the strike price of the call, the long call becomes more and more like a long stock position with a delta of +1.00. Also, as the stock price falls more and more below the strike price of the put, the short put becomes more and more like a long stock position with a delta of +1.00.

### 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. Since a bullish split-strike synthetic position consists of one long call and one short put, the price changes very little when volatility changes if the stock price is between the strike prices. In the language of options, this is a “near-zero vega.” Vega estimates how much an option price changes as the level of volatility changes and other factors are unchanged. However, if the stock price is above the strike price of the call, then a change in volatility will have a greater impact on the price of the call than on the price of the put. As a result, when the stock price is above the strike price of the call, the net price of a bullish split-strike synthetic position will rise when volatility rises and fall when volatility falls. Similarly, if the stock price is below the strike price of the put, then a change in volatility will have a greater impact on the price of the put than on the price of the call. As a result, when the stock price is below the strike price of the put, the net price of a bullish split-strike synthetic position will decrease when volatility rises and rise when volatility falls.

### Impact of time

The time value portion of an option’s total price decreases as expiration approaches. This is known as time erosion. Since a bullish split-strike synthetic position consists of one long call and one short put, the sensitivity to time erosion depends on the relationship of the stock price to the strike prices of the position. If the stock price is “close to” or above the strike price of the long call (higher strike price), then the net price of a bullish split-strike synthetic position decreases with passing of time, and the position loses money. This happens because the long call is closest to the money and decreases in value faster than the short put. However, if the stock price is “close to” or below the strike price of the short put (lower strike price), then the net price of a bullish split-strike synthetic position increases with passing time, and the position profits. This happens because the short put is now closer to the money and decreases in value faster than the long call. If the stock price is half-way between the strike prices, then time erosion has little effect on the net price of a bullish split-strike synthetic position, because both the long call and the short put decay at approximately the same rate.

### Risk of early assignment

Stock options in the United States can be exercised on any business day, and the holder of a short stock option position has 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 call in a bullish split-strike synthetic position 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. Therefore, if the stock price is below the strike price of the short put in a bullish split-strike synthetic position (the lower strike price), an assessment must be made if early assignment is likely. 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 strategy can be closed by selling the long call to close and buying the short put to close. Alternatively, the short put can be purchased to close and the long call can be kept open.

If early assignment of a short put does occur, stock is purchased. If a long stock position is not wanted, the stock must be sold in the marketplace. Note, however, that the date of the stock sale will be one day later than the date of the stock purchase. This one-day 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 stock position.

### Potential position created at expiration

There are three possible outcomes at expiration. The stock price can be below the lower strike price, at or above the lower strike price but not above the higher strike price or above the higher strike price. If the stock price is below the lower strike price, the call expires worthless, the short put is assigned, stock is purchased and a long stock position is created. If the stock price is at or above the lower strike price but not above the higher strike price, then both the short put and long call expire worthless and no stock position is created. If the stock price is above the higher strike price, then the long call is exercised, stock is purchased and a long stock position is created.

### Other considerations

A common mistake made by speculators is to think that a bullish split-strike synthetic position is a “zero-cost call option” (because the premium received for selling the put is used to pay for the call). Such thinking overlooks the risk of the short put, which is substantial if the stock price declines. Just like all other investment and trading strategies, a bullish split-strike synthetic position requires planning for both good and bad outcomes. If the stock price rises, when will the position be closed and the profit realized? If the stock price falls, when will the position be closed and the loss taken? These are subjective questions that every investor must answer personally.

Article copyright 2013 by Chicago Board Options Exchange, Inc (CBOE). Reprinted with permission from CBOE. The statements and opinions expressed in this article are those of the author. Fidelity Investments cannot guarantee the accuracy or completeness of any statements or data.

There are additional costs associated with option strategies that call for multiple purchases and sales of options, such as spreads, straddles, and collars, as compared with a single option trade.

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