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Box Spread 4-legged

box-4-pontas

1. Definition

The Box Spread 4-legged, also known as Box Spread, is an operation in which only profits are expected, and involves dealing with four options at the same time: 2 Calls and 2 Puts, or a Bull Call Spread and a Long Put Spread. So, it starts with selling an OTM Call and buying an ITM Call, and then buying an ITM Put and selling an OTM Put, all of them with same volume and expiry dates.

Buying a Call In-The-Money: buying a Call at a strike price lower than current share prices. Buying a Call gives you rights of buying a share before the expiration date, at the strike prices.

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.

Buying a Put In-The-Money: buying a Put at a strike price higher than the current share prices. Buying a Put gives you rights of selling a share until the expiry date at the strike price.

Selling a Put Out-The-Money: selling a Put at a strike price lower than current share prices. Selling a Put forces you to buy a share until the expiry date at the strike price.


2. Objective

The 4-legged Box Spread is considered a fixed income operation and is not subject to any floats in the asset’s pricing. The investor already knows the expected profits to be made. That is widely used by the end of fiscal years, in order to reduce the capital exposure to income taxes. Also, taxation is pretty much the same than it is for fixed income investments. Brokerage costs must be observed to calculate profits, though. It was commonly called “alligator’s spread”, as profits might be biten by fees. The low liquidity of Puts in Brazil turn this operations hard to be set up, where only fluctuations in the market can bring significant gains, but “robot traders” are sometimes used, in order to set up the four legs at the same time, quickly.


3. How it works

In this strategy, an ITM Call is purchased, paying a premium, also, an OTM Call is sold, receiving a premium. Thereafter, an ITM Put is purchased, paying a premium, and an OTM Put sold, receiving a premium. The initial balance for the operation is negative, with premium paid exceeding those which were received. However, the strategy always result in a profit. The operation is graphically demonstrated as follows:

Buying a Call + Selling a Call + Selling a Put + Buying a Put = Box Spread

Buying a Call

gráfico Long call_clean

+

Selling a Call

gráfico Short call_clean

+

Selling a Put

gráfico Short Put_clean

+

Buying a Put

 gráfico Long Put_clean

 =

Box Spread

gráfico Box 4 pontas_clean

Caption:
Green = Profits

Earnings: this strategy always produces gains, although they are limited. No matter what was the change on prices for the underlying asset, the operation is profitable. Premiums paid must be deducted, though, as the initial results are always negative. Also, fees and taxes must be taken in account.

Losses: they are not possible. The problem with the strategy is just the low liquidity for Puts.


4. Example

Consider the following data:

Asset:

Petrobrás

Date:

09/10/2013

Maturity:

10/21/2013

Share prices:

18,94

Days before expiration

41

Number of options

1.000

To set up this operation, the investor buy a Call In-The-Money PETRJ17, paying a premium of R$ 2.02 per option, sell a Call Out-The-Money PETRJ18, receiving a premium of R$ 1.60, sell a Put Out-the-Money PETRV18, receiving a premium of R$ 0.40 and buy a Put In-the-Money, paying a premium of R$ 0.55 per option. See the summary below:

Summary:

Option   type

Asset

Series

Number of options

Premium

Exercise prices

Liquidation Value

Buying a Call

Petrobrás

PETRJ17

1.000

-2,02

17

R$ -2.020,00

Selling a Call

Petrobrás

PETRJ18

-1.000

1,60

18

R$ 1.600,00

Selling a Put

Petrobrás

PETRJ17

-1.000

0,40

17

R$ 400,00

Buying a Put

Petrobrás

PETRJ18

1.000

-0,55

18

R$ -550,00

Total

-0,57

R$ -570,00

By the expiry date, the results by share prices are the following:

Share prices on expiration

Buying a Call

Selling a Call

Selling a Put

Buying a Put

Results

R$ 17,00

-2.020,00

1.600

400

450

430,00

R$ 14,00

-2.020,00

1.600

-2.600

3.450

430,00

R$ 15,00

-2.020,00

1.600

-1.600

2.450

430,00

R$ 16,00

-2.020,00

1.600

-600

1.450

430,00

R$ 17,00

-2.020,00

1.600

400

450

430,00

R$ 18,00

-1.020,00

1.600

400

-550

430,00

R$ 19,00

-20,00

600

400

-550

430,00

R$ 20,00

980,00

-400

400

-550

430,00

R$ 21,00

1.980,00

-1.400

400

-550

430,00

R$ 22,00

2.980,00

-2.400

400

-550

430,00

R$ 23,00

3.980,00

-3.400

400

-550

430,00

R$ 24,00

4.980,00

-4.400

400

-550

430,00

R$ 25,00

5.980,00

-5.400

400

-550

430,00

Results:

Results from this strategy are always positive, no matter how prices behave. Profits from the operation always depend on the options prices. The higher are the premiums received minus those which have been paid, the bigger the profits will be. However, it is already settled while the operation is set up.

Box 4 Pontas Pronto

Caption:
Green = Profits

Earnings: the operations always produces profits, no matter what Petrobras quotations are by the expiry date. The following situations may happen:

Petrobras shares pricing by the expiry date: R$ 15,00.

PETRJ17: the option just expires, as the investor doesn’t want to buy Petrobras shares at R$ 17.00, while current prices reach R$ 15.00. Even so, losses reach R$ 2.02 from the premiums paid for the options.

PETRJ18: the option just expires, as the counterpart shall not exercise rights of buying at R$ 18.00, while current prices reach R$ 15.00. The investor, though, keeps the premium of R$ 1.60 received.

PETRV17: the investor will be exercised by his counterpart, and will be forced to buy shares at R$ 17.00, while current prices reach R$ 15.00. Part of his losses can be offset by the R$ 0.40 premium received per option, so the total losses here are R$ 1.60 per share.

PETRV18: the investor will exercise its right to purchase, and will buy the stock of Petrobras for R$ 15.00, where it costs $ 18.00. That profit, he will have to subtract the amount of the premium paid of R$ 0.55.

Results: – R$ 2.02 + R$ 1.60 – R$ 1.60 + R$ 2.45 = R$ 0.43

Petrobras shares pricing by the expiry date: R$ 22.00.

PETRJ17: the investor exercises rights of this Call, buying Petrobras shares  at R$ 17.00 versus current prices of R$ 22.00. From earnings, the premiums paid must be deduct. Net gains are equal to R$ 2.98 per option.

PETRJ18: the investor will be exercised and should be buying shares at R$ 18.00, versus current prices of R$ 22.00. Losses are partially offset by the premium received of  R$ 1,60 per option, and net losses are equal to R$ 2.40.

PETRV17: the option just expires, as the counterpart shall not be selling shares at R$ 17.00, versus current prices of R$ 22.00. In this case, the investor just keeps the premium of R$ 0.40 per share.

PETRV18: the option just expires, as the investor should not be selling shares for R$ 18.00, versus current prices of R$ 22.00. His losses reach R$ 0.55 per option, due to the premiums paid.

Results: R$ 2,98 – R$ 2,40 + R$ 0,40 – R$ 0,55 = R$ 0,43

This way,  results are always positive, with two options being exercised and the other two just expiring. It works as though the investor blocked prices at a level above the current pricing, deducting only the premiums paid.

Losses: the investor never accumulates losses. Obviously that brokerage costs and taxes must be carefully observed. Besides, the Puts liquidity is low and the operation should be preferably made by a Robot Trader, to perform four simultaneous orders, the best time to buy and more quickly.

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