# Box spreads – An Easy Options Arbitrage Strategy

The idea is, that these two vertical debit spreads, each of which is designed to profit when the price of the underlying moves in either direction, create a “box” around the current trading price. A bull call spread normally profits when the underlying moves upwards, while the bear put spread does so when the prices falls.

So if you create two vertical debit spreads which, for want of a better expression, “face each other” on either side of the current market price of the underlying (the puts above and the calls below), you have effectively “boxed in” profits with options.

The thing to remember about debits spread however, is that profits are always limited to the difference in strike prices at expiration date, so the trick is to ensure that the cost of one of the debit spreads is sufficiently cheaper than the other, so that a profit can be realized.

There are times when option contracts are under-priced, usually due to current perceptions about the expected future price movement of the underlying market – for example, whether a trend has been exhausted and a reversal is imminent. So puts might be much cheaper than calls – and this is the ideal time to consider using box spreads.

Price distortions create opportunities which are known as “arbitrage”.

Most investors use this arbitrage strategy in cases where the spreads are under-priced in comparison to their values at the options expiry dates. The box spreads often combines two options pairs and it derives its name from the idea that prices are derived from a rectangular box in 2 columns of a given quotation.

Essentially, an arbitrageur is buying as well as selling equivalent spreads at the same time, on the proviso that the price paid for that given box is considerably below the combined value at expiration of the given spread, in which case a profit which is risk-free can be immediately locked in.

Expiration Value of the Box = Higher Strike Price less Lower Strike Price

Risk-free Profit = Expiration Value the of Box less Net Premium Paid

## Some Assumptions Used in Box Spreads

1. The trader is risk averse
2. The trader prefers more wealth to less
4. The transaction and operation costs are zero
5. The investor has the ability to easily enter and exit the market and the market is efficient.

## Box Spreads – An illustration

Suppose we are in December and a stock is currently trading at \$45 and the current options prices for the month are:

JAN 40 put –  \$2.50
JAN 50 put –  \$8.45
JAN 40 call – \$6.55
JAN 50 call – \$5.50

Buying A bull call spread includes purchasing the JAN 40 call for \$655 at the same time selling the Jan 50 call for \$550.

The bull call spread costs: \$655 – \$550 = \$105

Buying a bear put spread includes purchasing the JAN 50 put for \$845 at the same time selling the JAN 40 put for \$250.

The bear put spread costs: \$845 – \$250 = \$595

The total cost of the box spread will be \$105 + \$595 = \$700

The expiration value of the box is calculated to be: (\$50.00 – \$40.00) x 100 = \$1000.00

Since the total calculated cost of box spread is much less than the expiration value, a risk-free arbitrage is probable with a box strategy implemented. We can observe that the value at expiration of our box spread example, is the difference between the strike prices of the options available during the trading period.

If ABC stock price remains unchanged at \$45 at expiration date, then the JAN 40 put as well as the JAN 50 call expire worthless while both the JAN 40 call as well as the JAN 50 put expire in-the-money with a \$500 intrinsic value each. Therefore, the total accumulated value of box at the date of expiration is: \$500 + \$500 = \$1000.

Alternatively, suppose on the date of expiration in January, ABC stock price rallies to \$50, so that only the JAN 40 call expires in-the-money with \$1000 intrinsic value. Therefore, the box will still worth \$1000 at the date of expiration.

What will happens when ABC stock plunges to \$40? The same situation occurs but this time, it is the JAN 50 put which expires in-the-money with \$1000 in intrinsic value while all the other available options will expire worthless. Remember still, the box spread is worth \$1000.

As the trader you have only paid \$700 for the whole box, so your profit will be \$300.

Once you find these opportunities, you can just set and forget them  until options expiration date. Unfortunately, the difficulty is in finding them. Floor traders often use them because they don’t pay broker commissions but for the retail trader, it is much more difficult. For this reason, the three legged box is a much better alternative.

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