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Box Spread – 3 legs

box-3-pontas

1. Definition

The Box Spread 3-legged, also known as “Conversion”, is an operation where there are just profits, similar to the 4-legged Box, but involves buying an asset. The operation requires cash buying an asset while mounting the operation, and selling an ATM Call and buying an ATM Put, both in the same quantity and with same expiry dates.

Selling a Call At-The-Money: selling a Call with strike prices as close as possible to the current share prices. Selling a Call forces you to sell a share until the expiry date, for the strike price.

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


 2. Objective

The Box Spread 3 legs, such as the 4-legged Box, works just like a fixed income investment, and is not exposed to the influence of the underlying asset prices, no matter how strong the volatility can be. The investor knows how the pofits shall be in advance, as all positions are closed. This strategy usually works well when Calls are overpriced, and creating a synthetic position will result in a more advantageous sale than the actual Call prices by the expiry date.


 3. How it works

In this strategy, the asset itself is purchased upfront, cash buyer. After that, na ATM Call is sold and a premium received. Then, na ATM Put is purchased, paying a premium. The initial results are a debt, considering the purchase of the asset, Graphically that results as follows:

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

Buying Asset

Compra Ativo

 

+

Selling a Call

 gráfico Short call_clean

 

+

Buying a Put

gráfico Long Put_clean

 =

Box Spread 3 legs

gráfico Box 3 pontas_clean

Caption:

Green = Profits

Earnings: in this strategy, there will be always gains, although they’ll be limited. Price changes for the underlying asset don’t matter, as the operation always results in profits. Premiums paid and taxes must be disconsidered, as the initial value in the assembly operation is a debit, but still, profits are guaranteed.

Perda: None. The key issue is the lower liquidity for Puts, so it becomes more difficult to assemble this strategy.


 4. Example

Consider the following figures:

Asset:

Petrobrás

Date:

09/10/2013

Maturity:

10/21/2013

Share prices:

18,94

Days before expiration

41

Number of shares

1.000

To set up this operation, the investor needs to buy Petrobras shares at R$ 18.94, selling a Call At-The-Money PETRJ19, earning a premium of R$ 1.20 per option and buying a Put At-The-Money PETRV19, paying a premium of R$ 0.80 per option. Look the summary:

Summary:

Option type

Asset

Series

Number of options

Premium

Exercise prices

Liquidation Value

Purchased asset

Petrobrás

-

1.000

-

18,94

R$ -18.940,00

Call sold

Petrobrás

PETRJ19

-1.000

1,20

19

R$ 1.200,00

Put purchased

Petrobrás

PETRV19

1.000

-0,80

19

R$ -800,00

Total

0,40

R$ -18.540,00

By the expiry date, we can reach the following results, depending on the share pricing:

Share prices on expiration

Selling a Call

Shares

Buying a Put

Results

R$ 14.00

1200

-4,940.00

4200.00

460.00

R$ 15.00

1200

-3,940.00

3200.00

460.00

R$ 16.00

1200

-2,940.00

2200.00

460.00

R$ 17.00

1200

-1,940.00

1200.00

460.00

R$ 18.00

1200

-940.00

200.00

460.00

R$ 19.00

1200

60.00

-800.00

460.00

R$ 20.00

200

1,060.00

-800.00

460.00

R$ 21.00

-800

2,060.00

-800.00

460.00

R$ 22.00

-1800

3,060.00

-800.00

460.00

R$ 23.00

-2800

4,060.00

-800.00

460.00

R$ 24.00

-3800

5,060.00

-800.00

460.00

R$ 25.00

-4800

6,060.00

-800.00

460.00

R$ 26.00

-5800

7,060.00

-800.00

460.00

R$ 27.00

-6800

8,060.00

-800.00

460.00

R$ 28.00

-7800

9,060.00

-800.00

460.00

Results:

This strategy’s results will be always positive, no matter what happens with share prices. Profits will always depend on the options’ prices. The larger is the amount received in premiums and the lower is that paid in premiums, the larger will be the profits. However, it’s blocked for the operation.

 box 3 pontas_new

Caption:

Green = Profits

Earnings: profits are guaranteed no matter how Petrobras prices can change. The following events may happen:

Petrobrás’ prices by the expiry date: R$ 15.00

Asset: the investor sells the asset having paid R$ 18.94, with losses of R$ 3.94 per share.

PETRJ19: the option just expires, once the counterpart is not exercising the purchase at R$ 19.00 per share, once it cost R$ 15,00 at spot market. The investor still takes the premium of R$ 1.20 per option, though.

PETRV19: the investor exercises its selling rights, paying R$ 15.00 per share rather than the current R$ 19.00. However, he deducts the premium of R$ 0.80 from profits.

Partial Results: R$ 19,00 – R$ 15,00 – R$ 0,80 = R$ 3,20

Total results from the operation are:

Results: – R$ 3,94 + R$ 1,20 + R$ 3,20 = R$ 0,46

Petrobras prices by the expiry date: R$ 22.00

Asset: the investor will be selling Petrobras shares at R$ 22.00, having paid R$ 18.94, which leads to earnings of R$ 3.06 per share.

PETRJ19: the investor will be exercised by its counterpart, and will be forced to sell shares at R$ 19.00, while current prices stand at R$ 22.00. However, part of the losses are compensated by the R$ 1.20 premium that has been received. Thus, total losses for this part of the operations reach R$ 1.80 per share.

PETRV19: the option expires, as the investor shall not be exercising rights of selling shares for R$ 19.00, once it cost R$ 22,00 at spot market. Because of that, he loses the premiums of R$ 0.80 per share paid to the counterpart.

Results: R$ 3,06 – R$ 1,80 – R$ 0,80 = R$ 0,46

Having that said, the investor will be always getting some earnings, with one of the options being exercised and another expiring. It’s like he locked the purchase price to a price level and locked the selling price at a higher level, where should discount the premium paid.

Losses: losses are not happening unless the brokerage fees and additional costs exceed the profits from the operation. The low liquidity of Puts make it difficult to set up the operation, which uses to be conducted by a “robot trader”, in order to get all three moves set up simultaneously, with the best timing and much faster.

An important aspect to be observed is the profit margins to be generated from the operation. If margins are equal or lower than any traditional fixed income investment, so the operations is not worth.

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