An important characteristic of a butterfly is that the three strikes used to set up the strategy must be equidistant from each other. But what if you create a position such that the distance between the higher strike and the middle strike is smaller than the distance between the middle strike and lower strike? This week, we discuss the characteristics of such a strategy.

Mod butterfly

With the Nifty Index at 19575, a normal butterfly strategy can be set up with one long 19600 call, two short 19700 calls and one long 19800 call. But what if you decide to use the 19750 strike instead of the 19800 call? Let us call this strategy mod butterfly, short for modified butterfly. The strategy can be setup for a net debit of 28 points as opposed to a net debit of 15 points for a normal butterfly. So, the maximum loss (net debit) on a mod butterfly is higher. This means the maximum profit for mod butterfly will be lower than that of a normal butterfly.

Note that the maximum profit on a normal butterfly occurs when the lower strike carries its highest intrinsic value subject to the condition that the short strike expires worthless. This argument holds for mod butterfly too. Therefore, the position’s maximum profit is 72 points, 100 (19700 less 19600) less 28 (net debit) as opposed to 85 points for a normal butterfly. Why setup a mod butterfly position if gains are lower?

To answer this question, let us look what happens to the position if the underlying moves past the higher strike. Suppose the Nifty Index trades at 19900 at the expiry of the options. The normal butterfly will have zero intrinsic value, with net loss equal to the net debit. This is true for any price that the underlying takes above the higher strike. The mod butterfly, however, will carry an intrinsic value of 50 points for a net gain of 22 points (50 less 28). Note that the net gain depends on the distance between the higher strike and the middle strike and the net debit. For instance, if you were to set up mod butterfly with 19600/19800/19900, the position will carry an intrinsic value of 100 points for the underlying above the higher strike. So, the net gain (intrinsic value less net debit) will greater than in the case of 19600/19700/19750 strategy.

Know the difference
Mod butterfly has a bullish bias compared to a normal butterfly, though both generate maximum gains when the underlying trades at the short middle strike
Optional reading

Mod butterfly has a bullish bias compared to a normal butterfly, though both generate maximum gains when the underlying trades at the short middle strike. Therefore, mod butterfly also profits from low volatility of the underlying asset, unless volatility drives the underlying price above the higher strike. In such cases, the intrinsic value of the position will be the difference between the middle and the lower strike less the difference between the higher strike and the middle strike. That explains why 19600/19800/19000 setup has a greater intrinsic value than 19600/19700/19750 setup.

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