This week, we discuss the butterfly strategy. In contrast to straddle and strangle, a butterfly is a low volatility strategy. A butterfly should be set up when you expect the underlying to move sideways.

## Three parts, low volatility

Picture a butterfly with a body and two wings- three parts in all. That is what the butterfly strategy entails. The strategy has two distinct characteristics. First, to set up a long position, you need three strikes (or parts) on the same underlying for the same maturity. These strikes should be equidistant from each other. For example, the 14900, the 15000 and the 15100 calls on the Nifty 50 index. Second, you should go long on the outer strikes (14900 and 15100 strikes) and short on the inner strike (15000 strike). This position has to be in the ratio of 1:2:1. For every contract long on each of the outer strikes, you should short two contracts of the inner strike.

The position generates maximum profit when the underlying trades at the inner strike at option expiry (15000 in the above example). This is because the lower call strike (14900) balloons to its maximum intrinsic value of 100 points whereas the short inner strike expires worthless, allowing the trader to keep the premium collected at contract initiation.

The maximum profit is the difference between the strike less net debit to set up the trade. In the above example, the maximum profit will be 91 points (100 less 9 points of net debit). If the underlying trades below 14900 or above 15100, the position will be worth zero. Suppose the underlying trades at 15300 at option expiry, the combined intrinsic value of the outer strikes (14900 and 15100) of 600 points will be cancelled by the intrinsic value of the two short contracts of the inner strike (15000).

The maximum loss on the position is the net debit. That is why many traders prefer this strategy to a short straddle or a short strangle when they expect the underlying to move sideways. Potential candidates for a butterfly strategy can be stocks that have entered into a consolidation phase with tight daily price range following an impressive uptrend. Note that tight daily price ranges indicate continual fighting between the bulls and the bears with no decisive winner.

It is typical to set up a butterfly with the inner strike as an at-the-money (ATM) option. So, one outer strike will the immediate in-the-money (ITM) and the other strike, an immediate out-of-the-money (OTM) option. In the case of the Nifty 50 Index, because the 50-strike options are not actively traded, you may want to consider strikes with intervals of 100.

## Optional reading

A trader has the choice of setting up a put butterfly or a call butterfly. If a trader decides to choose the 14900/15000/15100 strikes, the payoff on the put butterfly will the same as the payoff on the call butterfly, which is the difference between strikes. For this reason, the trader should choose either the call or the put butterfly, whichever has the lowest net debit.

Suppose a trader has a bullish bias on the underlying even though she expects the price to move sideways. Then, the trader can set up the butterfly such that the inner strike (short position) is an OTM option. So, even if the underlying moves up, the option has high likelihood of expiring worthless. Since the trader is setting up the position in anticipation of the underlying moving up, albeit marginally, the position is called bull butterfly. Similarly, if the trader has a bearish bias on the underlying, she can set up the butterfly with the inner strike as the immediate ITM option. Note that if the trader has no directional bias, then she should prefer the ATM option as the inner strike, as it has the highest time value.

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