# Butterfly Strategy

Now, we will learn to implement a ‘**Butterfly Strategy**,’ which is a fairly complex strategy compared to other strategies that we have learned earlier. So let us begin.

A butterfly spread is **a neutral option strategy** combining bull and bear spreads together. It is a four legged strategy- which means the trader has to take positions in four different option contracts to implement this strategy.

The trader implements these four option contracts with the **same expiration in three different strike prices. **

One of the unique features of this strategy is that we can implement this by either using Calls or Puts

Let us first discuss it using Calls.

### When do we implement butterfly strategy?

A Long Call Butterfly is implemented when the trader is expecting slight or no movement in the underlying asset. The motive behind initiating this strategy is to rightly predict the stock price till expiration and gain from time value of an option premium by undertaking limited risk.

When the trader expects the underlying asset to trade in a narrow range and remain neutral on the direction front, then this strategy is ideal to be implemented.

Remember when we discussed Short Strangle or Short Straddle, we had the view that underlying asset will be in range bound, and the profit occurs if it remains in the range else we start incurring unlimited losses. On the contrary the advantage of a butterfly strategy is that, here the potential risk is also limited.

This is a **neutral strategy used for range bound markets and is undertaken during last few days or second half of the expiry to capitalize the time value of Premium.**

### How to construct a Long Call Butterfly?

A Long Call Butterfly can be created by:

- Buy 1 IN-THE-MONEY (ITM)Call
- Buy 1 OUT OF-THE-MONEY (OTM)Call
- Selling 2 AT-THE-MONEY (ATM)Calls.

We need to make sure that –

- The Call options belong to the same expiry
- All the option contracts belong to the same underlying asset.
- The strike prices are equidistant from each other, i.e. the difference between IN-THE-MONEY (ITM) , OUT OF-THE-MONEY (OTM) and AT-THE-MONEY (ATM) should all be same.
- All the legs of the strategy should be initiated simultaneously.

**Example:**

**Option Chain: **

**Strategy:** Buy 1 (ITM) Call, Sell 2 (ATM) Call and Buy 1 (OTM) Call

**Market Outlook:** Neutral on the market direction

**Spread:** Equidistant 100

**Lower Breakeven:** Lower Strike Price of buy call + Net Premium Paid 16220

**Upper Breakeven:** Higher Strike Price of buy call - Net Premium Paid 16380

**Maximum Loss:** Limited to Net Premium Paid 20

**Maximum Profit:** Limited and it is achieved when the underlying asset remains at the middle strike price on expiry 16300

**Calculation of Maximum Profit **(Spread - Premium Paid) 80

Now let us discuss a Long Butterfly strategy using Puts:

A long butterfly strategy can be implemented either by calls or Puts! The payoff from the strategy will be the same. The reason behind this is that we can create simple strategies using synthetic positions.

How synthetic options can be used to create a butterfly strategy using Puts?

**A Long Butterfly strategy can be devised by:**

- Buy 1 IN-THE-MONEY (ITM) Call,
- Sell 2 AT-THE-MONEY (ATM) Call
- Buy 1 OUT OF-THE-MONEY (OTM) Call
- All strike prices to be equidistant

Now one Long call synthetically can be created by Buying 1 put Option and simultaneously Buying 1 Lot of Futures contract (P+ and F+)

Short Call synthetically can be created by Selling 1 Lot of Put and simultaneously selling 1 Lot of Futures Contract. (P- and F-)

So we can re- write the Long Butterfly strategy using calls as:

C+ IN-THE-MONEY (ITM) = P+ , F- IN-THE-MONEY (ITM)

C+ OUT OF-THE-MONEY (OTM) = P+ , F- OUT OF-THE-MONEY (OTM)

2C- AT-THE-MONEY (ATM) = 2 P- , 2 F + AT-THE-MONEY (ATM)

If we solve the above equations, we are net 2 contracts of futures - **Buy** and simultaneously 2 Lots futures - **Sell**

Both the above futures lots get cancelled.

Final Equation:

**Buy 1 IN-THE-MONEY (ITM) Put , Sell 2 AT-THE-MONEY (ATM) Put and Buy 1 OUT OF-THE-MONEY (OTM) Put **

We need to make sure that –

- The Put options belong to the same expiry
- Belongs to the same underlying
- The strike prices are equidistant from each other i.e. the difference between IN-THE-MONEY (ITM) , OUT OF-THE-MONEY (OTM) and AT-THE-MONEY (ATM) should all be the same .

**Example**:

We consider the same Option chain as used in the above example.

**Strategy: **Buy 1 (ITM) Put, Sell 2 (ATM) Put and Buy 1 (OTM) Put

**Market Outlook:** Neutral on the market direction

**Spread:** Equidistant 100

**Lower Breakeven**: Lower Strike Price of Buy Put + Net Premium Paid 16218

**Upper Breakeven: **Higher Strike Price of Buy Put - Net Premium Paid 16382

**Maximum Profit: ** Limited and it is acheived when the underlying asset remains at the middle strike price on expiry 16300

**Calculation of Max. Profit:** (Spread - Premium Paid) 82