**1. ****Definition**

**Definition**

The short butterfly, or Short Call Butterfly, is a strategy that comprises three Calls from different strikes. The first move involves selling an ITM Call. After that, an OTM Call is also sold. A third move involves buying an ATM Call with intermediate price, twice as much as the first two options. All options must have the same expiration date. The sold Calls form the “wings” in the graph, while those which were purchased form the”body”.

**Selling a Call In-The-Money:** selling Call at prices below the share prices. Selling a Call forces you to sell a share until the expiry date, for an established price.

**Buying a Call At-The-Money:** buying double Call with strike prices as close as possible to the current share prices. Buying a Put gives you rights of buying a share until the expiry date for the strike price.

**Selling a Call Out-The-Money:** selling a Call at a strike price higher than the current share prices. Selling a Call forces you to sell a share until the expiry date at the strike price.

**2. ****Objective**

**Objective**

This strategy is used by investors who believe prices will change hugely, with limited possibilities of both losses and gains. It is used when the underlying asset is expected to show huge changes in a few days. The strategy is not really popular, if compared with straddles or strangles, and provides lower expectations in terms of gains, with a slightly lower risk.

**3. ****How it works**

**How it works**

In this strategy, an ITM Call is sold, receiving a premium. Simultaneously, an OTM Call is sold too, receiving another premium. After that, the same amount of ATM Calls is purchased, paying a premium. The initial position is positive, as premiums received exceed those to be paid. The graphs result as follows:

**Selling a Call + Selling a Call + Buying a Call = Short Butterfly**

**Selling a Call**

**+**

**Selling a Call**

**+**

**Buying a Call**

**=**

**Short Butterfly**

**Caption:**

Red = Losses

Yellow = Reduced losses

Green = Profits

**Earnings:** in this strategy, gains are limited with the underlying asset changing up or downwards. The maximum profits is equal to the premiums received minus those which were paid.

**Losses:** losses are also limited, and happen when prices stand on the butterfly’s “body”. If share prices are above the ITM Call level or below the OTM Call sold, the investor shall have losses. Premiums received will partially offset losses, though.

**4. Example**

Consider the following data:

Asset: |
Vale |

Date: |
09/10/2013 |

Maturity: |
10/21/2013 |

Share prices: |
32,15 |

Days before the expiration |
41 |

Number of options |
1.000 |

To set up this operation, the investor sells a VALEJ30 ITM Call, receiving a premium of R$ 3.91 per option, and buys in double VALEJ32 ATM Calls, paying a premium of R$ 2.12 x 2 = R$ 4.24, and finally sells a VALEJ34 OTM Call, earning a premium of R$ 1.39 per share. Check the summary:

**Summary:**

Type of option |
Asset |
Series |
Number of options |
Premiums |
Exercise price |
Results |

Selling a Call |
Vale |
VALEJ30 |
-1,000 |
3.91 |
30 |
R$ 3,910.00 |

Buying a Call |
Vale |
VALEJ32 |
2,000 |
-2.12 |
32 |
R$ -4,240.00 |

Selling a Call |
Vale |
VALEJ34 |
-1,000 |
1.39 |
34 |
R$ 1,390.00 |

Total |
1.06 |
R$ -1,060.00 |

On the expiry date, the results depend on prices for the underlying asset, as follows:

Prices on expiry date |
Selling a Call |
Buying a Call |
Selling a Call |
Results |

R$ 26.00 |
3,910.00 |
-4,240 |
1,390 |
1,060.00 |

R$ 27.00 |
3,910.00 |
-4,240 |
1,390 |
1,060.00 |

R$ 28.00 |
3,910.00 |
-4,240 |
1,390 |
1,060.00 |

R$ 29.00 |
3,910.00 |
-4,240 |
1,390 |
1,060.00 |

R$ 30.00 |
3,910.00 |
-4,240 |
1,390 |
1,060.00 |

R$ 31.00 |
2,910.00 |
-4,240 |
1,390 |
60.00 |

R$ 32.00 |
1,910.00 |
-4,240 |
1,390 |
-940.00 |

R$ 33.00 |
910.00 |
-2,240 |
1,390 |
60.00 |

R$ 34.00 |
-90.00 |
-240 |
1,390 |
1,060.00 |

R$ 35.00 |
-1,090.00 |
1,760 |
390 |
1,060.00 |

R$ 36.00 |
-2,090.00 |
3,760 |
-610 |
1,060.00 |

R$ 37.00 |
-3,090.00 |
5,760 |
-1,610 |
1,060.00 |

R$ 38.00 |
-4,090.00 |
7,760 |
-2,610 |
1,060.00 |

**Results:**

Results from this strategy will be positive if prices move outside the range between R$ 31.06 and R$ 32.94. If shares prices are lower than R$ 31.06 or higher than R$ 32.94, he makes profits. The maximum earnings are equal to all premiums received less the premiums paid.

**Caption:**

Red = Max losses

Yellow = Reduced losses

Green = Profits

**Earnings:** the operations generates earnings if Vale’s prices are lower than R$ 31.06 or higher than R$ 32.94. For those situations, we have the following:

If Vale’s share worth R$ 30.00 on the expiration, the option VALEJ30 just expires. However, the investor is given premiums of R$ 3.91 per option. The option VALEJ32 also expires, and the investor will have a loss of R$ 2,12 per options from buying them. The option VALEJ34 will also expires, and the investor will have a profit of R$ 1,39 because he sold the option. Then, we have the following results:

Results: R$ 3.91 – (R$ 2.12 * 2) + R$ 1.39 = R$ 1.06

This is the maximum profits – the sum of the premiums received less the sum of the premiums paid. If shares are over R$ 34.00, profits will be pretty much the same.

**Losses: **the investor loses money if Vale’s prices exceed R$ 31.06 and stand below R$ 32.94. For any price in the array, premiums gained are not enough to compensate losses with the operation. Maximum losses happen when Vale’s shares are at R$ 32.00. In this case, VALEJ30 will be exercised by the counterpart, and the investor will need to sell Vale’s shares for R$ 30.00. However, he still makes profits, as premiums received exceed the losses. The results are the following:

Results: R$ 30.00 – R$ 32.00 + R$ 3.91 = R$ 1.91

VALEJ32 won’t be exercised, as share prices are exactly on R$ 32.00. In this case, he loses the premiums paid, of R$ 2.12 * 2 = R$ 4.24.

The option VALEJ34 just expires, and the investor keeps the premium of R$ 1.39. So the final results are:

Results: R$ 1.91 – 4.24 + R$ 1.39 = – R$ 0.94

Thus, the maximum losses are R$ 0.94 per option, as the amount spent in buying the options VALEJ34 exceeded the profits.