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Long Butterfly

compra-buterfly

1. Definition

A Long Butterfly is a strategy that uses three options (Calls) in sequence. First two moves comprise Long ITM and OTM Calls and a third is a short ATM Call, with the double of amount, i.e., the position of sale would be the same amount as the two positions shown. All of them must have the same expiry date. The name “butterfly” is a reference to the correspondent graph, where the long calls figure as the butterfly’s wings and the short calls as the body.

Buying a Call In-The-Money: buying a call at a strike price lower than the current share prices. By doing that, the investor has the right to buy a share for an agreed price by the expiry date.

Selling a Call At-The-Money: selling double Call at a strike price as close as possible to the current share prices. By doing that, the investor is forced to sell a share for the agreed price by the expiry date.

Buying a Call Out-The-Money: buying a call at a strike price higher than the current share prices. By doing that, the investor has the right to buy a share for an agreed price by the expiry date.


2. Objective

It’s highly used by investors who think prices will change a bit and want to bet on this possibility with limited risks and a lower cost than for other strategies. Also, it is one of the few strategies that can be used with long term options (approximately greater than 1 month).


3. How it works

For this strategy, the investor buys an ITM Call, paying a premium. At the same time, an OTM Call is purchased, paying another premium. After that, an ATM Call is sold in the same amount, receiving a premium. The starting results are negative, as premiums paid exceed those received, even though the debts are relatively low if compared with other strategies with options. Graphs altogether figure as follows:

Call is bought + Call is bought + Call is sold = Long Butterfly

Buying a Call

gráfico Long call_clean

+

Buying a Call

gráfico Long call_clean

+

Selling a Call

gráfico Short call_clean

=

Butterfly

gráfico Long Butterfly_clean

Caption:

Red = loss

Yellow = slight loss

Green = Profits

Earnings: gains should be limited for this strategy, in which the object should change slightly, staying in the range between the first purchased Call and the sold Call. From results, premiums paid are to be deducted, as the starting position results in a debt.

Losses: losses are also limited. They never exceed the cost of the operation itself, in other words, the debts from the operation’s starting position..


4. Example

Consider the following data:

Asset:

Petrobrás

Date:

09/10/2013

Maturity:

10/21/2013

Share prices:

18,94

Days to the expiration

41

Number of options

1.000

To arrange this position, the investor needs to buy PETRJ17 ITM Call, paying a premium of R$ 2.02 per option, sell twice as much PETRJ19 ATM Calls, receiving R$ 1.00 of premium per each option (R$ 2,00), and finally buy another PETRJ21 OTM Call, paying a R$ 0.11 premium per option. Look at the summary below:

Summary:

Option Type

Asset

Series

Number of options

Premium

Exercise prices

Liquidation amount

Buying a Call

Petrobrás

PETRJ17

1,000

-2.02

17

R$     -2,020.00

Selling a Call

Petrobrás

PETRJ19

-2,000

2.00

19

R$     2,000.00

Buying a Call

Petrobrás

PETRJ21

1,000

-0.11

21

R$     -110.00

Total

-0.13

R$     -130.00

By the expiration dates, results depend on the share prices as follows:

Share prices on the expiry date

Long ITM   Call

Short ATM   Call

Long OTM   Call

Results

R$     17.00

-2,020.00

2,000

-110

-130.00

R$     14.00

-2,020.00

2,000

-110

-130.00

R$     15.00

-2,020.00

2,000

-110

-130.00

R$     16.00

-2,020.00

2,000

-110

-130.00

R$     17.00

-2,020.00

2,000

-110

-130.00

R$     18.00

-1,020.00

2,000

-110

870.00

R$     19.00

-20.00

2,000

-110

1,870.00

R$     20.00

980.00

0

-110

870.00

R$     21.00

1,980.00

-2,000

-110

-130.00

R$     22.00

2,980.00

-4,000

890

-130.00

R$     23.00

3,980.00

-6,000

1.890

-130.00

R$     24.00

4,980.00

-8,000

2.890

-130.00

R$     25.00

5,980.00

-10,000

3.890

-130.00

Results:

Results from the strategy are positive if prices change within R$ 17.14 and R$ 20.87. If shares reach less than R$ 17.14 by the expiry date or more than R$ 20.87, the investor loses money. The higher loss will be equal to all premiums paid minus the premium received.

Long Butterfly_Pronto

Caption:

Red = Max losses

Yellow = Limited losses

Green = Profits

Earnings: the operations generates gains if Petrobras shares by the expiry date reach more than R$ 17.14 and less than R$ 20.87. For this array we have the following situation:

If share prices are over R$ 17.14 by the expiry date, the option Call PETRJ17 will be realized and the investor will be able to buy shares at R$ 17.00, while market prices reach R$ 17.14. However, as he paid R$ 2.02 per option, losses reach R$ 1.88 per share (R$ 17.14 – R$ 17.00 – R$ 2.02 = R$ -1.88). The option PETRJ19 disappears and the investor keeps the premium of R$ 2,00 (as he sold twice as much options, premiums will be in double). Lastly, the option PETRJ21 also disappears, as well as the premium paid by the investor (R$ 0.11 per option).

Results: R$ 17.14 – R$ 17.00 – R$ 2.02 + R$ 2.00 – R$ 0.11 = R$ 0.01

Now, if Petrobras shares are quoted above R$ 20.86 by the expiry date, the option PETRJ17 will be exercised and the investor will buy shares at R$ 17.00. As he paid a premium of R$ 2.02, results will be:

Results: R$ 20.86 – R$ 17.00 – R$ 2.02 = R$ 1.84

But the option PETRJ19 will be exercised by his counterpart, and the investor will need to sell shares at R$ 19.00, accumulating the following losses:

Results: (R$ 19.00 * 2) – (R$ 20.86 * 2) + (R$ 1.00 * 2) = – R$ 1.72

Finally, the option PETRJ21 loses effectiveness, and the investor loses the premium of R$ 0.11. So total results are the following:

Results: R$ 1.84 – R$ 1.72 – R$ 0.11 = R$ 0.01

Losses: the investor will accumulate losses if share prices reach less than R$ 17.14 or more than R$ 20.86. Maximum losses are equal to all premiums paid minus those received, or R$ 0.13 per share in this case.

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