Iron Butterfly Max Loss & Max Profit Calculation

Iron butterfly is a short volatility option strategy with limited profit and limited loss. This page explains the calculation of iron butterfly maximum loss and maximum profit (and explains how they relate to break-even points).

Factors Which Affect Iron Butterfly P/L

If held to expiration, total profit or loss from an iron butterfly position is the difference of two things:

Total iron butterfly profit or loss is what you receive at position entry minus what you lose at expiration.

Iron Butterfly Max Profit

Let’s start with maximum profit, because it is very simple.

Ideal outcome is when underlying price equals the middle (short) strike at expiration. In such case, all options expire worthless and there are no losses at expiration. Total P/L from the trade equals net premium received in the beginning (initial cash flow when opening the position).

Iron butterfly max profit = net premium received

Net premium received is the premium received for selling the short call and short put (the middle strike options), minus premium paid for buying the long call and long put (the outer strike options).

Iron Butterfly Max Loss Logic

When underlying price is anywhere else than exactly at the middle strike, some options are in the money. Because we are short the middle strike call and the middle strike put, the amount by which one of these options is in the money (they can’t be both itm at the same time) is the amount we lose at expiration. The further away underlying price gets from the middle strike, the more we lose.

But the losses are hedged by the long call and long put options. When underlying price rises above the long call strike, any further losses from the short call are offset by gains in the long call. Similarly, when price falls below the long puts strike, further losses from the short put are offset by gains in the long put.

As a result, total loss no longer grows above the long call strike or below the long put strike. Maximum possible loss from an iron butterfly position occurs at or below the long call strike and at or below the long put strike.

Iron Butterfly Max Loss Calculation

The worst possible outcome of iron butterfly is when underlying price is at or above the upper long call strike, or at or below the lower long put strike.

The size of maximum loss depends on how far the losses can grow before they start to be offset with gains from the long call or long put. In other words, iron butterfly maximum loss is proportional to the distance between the short call and long call strike, or the distance between the short put and long put strike. This is known as wing width (as butterfly wings).

A classic iron butterfly position should have the same wing width on both sides (difference between the call strikes should be the same as difference between the put strikes).

Therefore, the maximum loss formula is:

Iron butterfly max loss = wing width – net premium received

It is the same as iron condor max loss formula. Only difference is that in an iron condor, the short call strike is different (higher) than the short put strike and there is a window of maximum profit between these two strikes; in an iron butterfly maximum profit is reached at only one point, as the short option strikes are equal. But the logic and the formula for maximum loss is the same for both strategies.

Example

Consider an iron butterfly position involving the following options:

  • Long 120 strike put, bought for $2
  • Short 130 strike put, sold for $5
  • Short 130 strike call, sold for $4
  • Long 140 strike call, bought for $1.50

Net premium received, or initial cash flow, is the premium received for the short options (5 + 4 = 9) minus premium paid for the long options (2 + 1.50 = $3.50). It is $5.50, which is also the maximum possible profit from this iron butterfly.

The short put and short call strike is the same (otherwise it would be an iron condor).

The distance between the put strikes (130 – 120 = 10) is the same as the distance between the call strikes (140 – 130 = 10). This the wing width, which we need to calculate maximum loss.

Using the max loss formula:

Iron butterfly max loss = wing width – net premium received

… we get:

Iron butterfly max loss = 10 – 5.5 = $4.50

The most we can lose from this iron butterfly position is $4.50 (per share). It happens when underlying price is at or above 140 or at or below 120 at expiration.

With max profit $5.50 and max loss $4.50, the risk-reward ratio is 4.50 : 5:50, or 1.22 in the reward-to-risk format (maximum possible profit is 1.22x greater than maximum possible loss).

Max Profit, Max Loss and Break-Even Points

There is a close relationship between maximum profit, maximum loss, and break-even prices (the underlying prices where the outcome turns from profit to loss or vice-versa).

Because the relationship between underlying price and payoff at expiration is linear (the payoff diagram is always a straight line), the ratio of break even distances from the short (max profit) and long (max loss) strikes is the same as the ratio of maximum profit to maximum loss – in our example, it is 5.50 : 4.50.

Therefore, the break-even points must the $5.50 from the short strike and $4.50 from the long strikes: at $124.50 and $135.50.

Iron butterfly break-even point formulas are:

Iron butterfly B/E #1 = short strike – net premium received

Iron butterfly B/E #2 = short strike + net premium received

Again, it works the same as iron condor break-evens, with the only difference that in iron butterfly the two short strikes are the same.

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