BOX

SPREADS

RECALL: BULL CALL SPREAD

Executed when investors think that stock prices

will go up.

RECALL: BEAR PUT SPREAD

Executed when investors think that stock prices

will go down.

THE BOX SPREAD

Combination of a Bull Call and a Bear Put

Involves 4 options and 2 strike prices

WHY THE BOX SPREAD WORKS

The investor refuses to make a bet on the

movement of the stock price, but knows that

there is a market inefficiency.

There is no need to invest in the underlying

stock.

The investor wants to lock in a riskless profit.

This strategy results in no possible losses and

limited profits.

EXAMPLE 1:

Given:

Today is February. The stock price of ABC is

trading at $38. Its options are:

Mar 30 put: $1.50

Mar 40 put: $5

Mar 30 call: $6

Mar 40 call: $1

Risk free rate for all maturities: 8%

TESTING THE PUT-CALL PARITY

Conclusion: The Put-Call Parity does not hold andthere is a market inefficiency in option prices

Tip! Set K2 as the option with the higher strike price It will help in the next slides

Stock price: $38

Mar 30 put: $1.50

Mar 40 put: $5

Mar 30 call: $6

Mar 40 call: $1

Risk Free Rate: 8%

HOW DO YOU TAKE ADVANTAGE OF THIS?

You now know there’s a market inefficiency. The

next thing to do would be to know how to position

your options.

First Step: Set up the ff equations: (Remember

our tip before where K2 is the bigger strike

price?)

This equation reduces to:

Note: K2 is the bigger strike price so that the discounted payoff

is positive and thus, comparable to market value

HOW DO YOU TAKE ADVANTAGE OF THIS?

Rearranging:

Next: Determine the market price and compare it

with the discounted payoff.

strategy: Long Box Spread

strategy: Short Box Spread

LONG BOX SPREAD

Market Price: $8.5

Following this equation:

Strategy would be:

Long on Mar40 put

Short on Mar30 put

Short on Mar 40 call

Long on Mar30 call

Note: follow the signs to determine your strategy if positive,

long. If negative, short

PROFITS AND PAY-OFFS

Stock Price at Exercise Date

Payoff From Call Options

Short on March 40 call

Long on March 30 call

Payoff from Put Options

Short on March 30 put

Long on March 40 put

Total Profit

20 25 30 350

1

-6

10

1.5

-5

1.5

0

1

-6

10

1.5

-5

1.5

5

1

-6

5

1.5

-5

1.5

0

1

-6

10

1.5

-5

1.5

PROFITS AND PAY-OFFS

Stock Price at Exercise Date

Payoff From Call Options

Short on March 40 call

Long on March 30 call

Payoff from Put Options

Short on March 30 put

Long on March 40 put

Total Profit

40 45 50 5510

1

-6

0

1.5

-5

1.5

10

1

-6

0

1.5

-5

1.5

10

1

-6

0

1.5

-5

1.5

10

1

-6

0

1.5

-5

1.5

GRAPH OF A LONG BOX SPREAD

Profit

Stock Price

Call Options

Put Options

EXAMPLE 2

Given:

Today is September. The stock price of EFG is

trading at $45. Its options are:

Oct 40 put: $2

Oct 50 put: $7

Oct 40 call: $7

Oct 50 call: $1.5

Risk free rate for all maturities: 8%

EXAMPLE 2:

The Put-Call Parity was violated.

Compare the market price and the discounted

payoff.

Determine your strategy

Short Box Spread

SHORT BOX SPREAD

Market Value: $10.5

Modify this equation:

New equation:

Strategy would be:

Short on Oct 50 put

Long on Oct 40 put

Long on Oct 50 call

Short on Oct 40 call

__

PROFITS AND PAY-OFFS

Stock Price at Exercise Date

Payoff From Call Options

Long on Oct 50 call

Short on Oct 40 call

Payoff from Put Options

Long on Oct 40 put

Short on Oct 50 put

Total Profit

35 40 45 500

-1.5

7

-10

-2

7

0.5

-5

-1.5

7

-5

-2

7

0.5

-10

-1.5

7

0

-2

7

0.5

0

-1.5

7

-10

-2

7

0.5

PROFITS AND PAY-OFFS

Stock Price at Exercise Date

Payoff From Call Options

Long on Oct 50 call

Short on Oct 40 call

Payoff from Put Options

Long on Oct 40 put

Short on Oct 50 put

Total Profit

55 60 65 70-10

-1.5

7

0

-2

7

0.5

-10

-1.5

7

0

-2

7

0.5

-10

-1.5

7

0

-2

7

0.5

-10

-1.5

7

0

-2

7

0.5

GRAPH OF A SHORT BOX SPREAD

Stock Price

Profit

RECAP:

Determine if there’s an inefficiency in the

market.

Find the discounted payoff and compare it with

the market price of the box spread today.

Long Box Spread

Short Box Spread

Determine how to establish the bull spread and

bear spread.

Enjoy the riskless profits while they last! The

market will soon clear out this arbitrage

opportunity

Note: this is the ‘follow the sign’ strategy

LIMITATIONS

It is hard to spot and take advantage of such

arbitrage opportunities.

The price differences quickly balance off, making

it hard to take a position.

This is not an ideal strategy for small investors

because the commission will eat up the profits.

It can be difficult to justify the small profits given

the high commissions paid.

THE ENDCua, Meredith

Te, Aimee

Wong, Leigh