Box spreads - Options "Holy Grail"

Introduction


The box spread is an option strategy, which can offer risk free profits and has a special place amongst all other options strategies for this reason. Box spreads are interesting to options users and potentials as they provide an appropriate test of the efficiency of the options market, are a means of uncovering risk and neutralising it and as a borrowing and lending mechanism. 

Learning objectives
After reading this article you should be able to:
• Test of the efficiency of options markets
• Calculate the borrowing and lending rates used in the options market

What are box spreads


A box spread is considered a flat position with no directional risk and a way to get square or flat. It involves two strikes and can be perceived as:

1. A combination of synthetic long stock at one price and synthetic short stock at another

If the strike price of the two options is the same, a Long Call/Short Put position is equivalent to a Long Stock position. And if the strike price of the other two options is the same, a Long Put/Short Call position is equivalent to a Short Stock position.


box spread graphic

 

2. A conversion at one strike and a reversal at another with the underlying shares cancelling out

A conversion consists of a long underlying stock position combined with a short call and a long put, whereby both options have the same exercise price and same expiry. A reversal or a reverse conversion consists of a short underlying stock position(U/L) combined with a long call and a short put, whereby both options have the same exercise price and same expiry. The conversion and reversal strategies are synthetics. Synthetics can consist of a combination of options or a combination of options with the underlying stock to form positions that have approximately the same profit/loss characteristics as the target strategy
 

 box spread graphic

*   + U/L = long underlying stock, - U/L = short underlying stock


3. Bull spread in calls and a bear spread in puts or vice versa
A Vertical Spread (A.K.A. - Bull Spread or Bear Spread depending on the options selected) involves buying a Call option (or a Put) and simultaneously writing another Call option (Put) with the same expiration but a different strike price.
Depending on which option is purchased and which written, a vertical spread can be either a bullish or a bearish spread.

Bullish Spreads:                                                Bearish Spreads:

Long Call strike< Short Call strike            Long Call strike > Short Call strike
Long Put strike < Short Put strike             Long Put strike > Short Put strike


box spread graphic

 
Box spreads as a test of pricing efficiency


In this examination of efficiency we use European exercise style index options over the S&P/ASX200 because the early exercise feature of American exercise style options results in a risky box spread strategy where one or more options can be exercised unwinding the box.
To construct the box spread strategy, one needs four European options characterised by 1) the same underlying asset; 2) the same expiry date; 3) two different (low and high) exercise prices. When constructed as follows:
1. Long in the low exercise price call option
2. Short in the high exercise price call option
3. Long in the high exercise price put option
4. Short in the low exercise price put option
The strategy always requires an initial investment.
Using the 4125 and 4175 strikes the cost of the box must come in at less than 50 points because that is all it will be worth on expiry.

XJO Click screen image

Source: Derivatives Trading Platform  Prices 10.30am, 11 April 05


Buying at the offer and selling at the bid we have (102-67) + (87-63) = 35 +24 = 59; clearly overpriced. However if we are able to buy at the bid and sell at the offer we get (96-72) + (82-67) = 24 + 15 = 39. As these boxes are priced around the present value of the difference between the strikes, the present value of 50pts is equal to 50 pts x $10 per point, minus the cost of carry for $500. At 5.5% for 66 days, the present value of the box is $495.05, for a cost of carry of $4.95. At 6% for 66 days, the present value of the box is $494.61, for a cost of carry of $5.39. Both values are higher than the mid point of 49 pts (box bid 39 / box ask 59) however when transaction costs are taken into account – ($40 x 4) x 2(in and out) $320 for an average retail trader any opportunity to buy the box spread for less than fair value of 49.5 pts is eroded. To make the trade worthwhile a large capital outlay will be need to pick up the small basis points gain in a box spread. As XJO index options are category 1 options market makers must be prepared to bid and offer a minimum of 10 contracts at all times. In the screen shot we can see a minimum of 25 contracts on the bid in the 4125 puts so the box spread could be executed for at least this size. If we traded for 49 points, 25 times the box costs $12,250 ($25 x 49 x $10 per point) plus $320 in transaction costs for a total of $12,570. As the box has a fair value of $12,500 doing the spread 25 times and paying $320 in brokerage would result in a loss of $70. We can therefore conclude that the pricing of XJO options is efficient at the mid point between the bid and ask prices. 

Implied Interest Rate on a Box Trade

The implied interest rate calculation on a box trade is very similar to that of the conversion/reversal. Take the discount on the box and divide it by the cost of the box, multiply the result times 365 days a year, and divide
it by the numbers of days left to go.

Box Discount   x     365           = Implied interest rate
Box Price               Days left   

If the box in the last example had a market of 39–59 the trades would yield the implied interest rates as shown below.
Long Box                                                                 Short Box
 11      x 365   = Lending at 155%                         -9.0 x 365    = Borrowing at -84%. * 
 39         66                                                                  59      66

.                                                                                                                                    
 *  A negative represents being paid to borrow

Obviously, this is a very wide market relative to the risk and if the prices were achieved would represent a bonanza to anyone that bought at the bid and sold at the offer. An annualised return of 155% to invest in the equivalent of a risk free bond and actually being paid to borrow for 66 days is absurd.  A more realistic market on the 50 pt box would be 49.25– 49.75 given its fair value of approx 49.5 pts.

Long Box                                                                   Short Box
0.75   x 365   = Lending at  8.42%                         0.25 x  365  =  Borrowing at 2.78%
49.25     66                                                                 49.75     66

                                  
      
Because the XJO is a European-style exercise it makes it attractive to use for financing the rest of the products traded on the ASX without the fear of or benefit of the early exercise.

With electronic trading options markets are becoming more efficient

Two recent studies into index options markets -Tel Aviv 2005 and Hong Kong 2004, concluded that both are highly efficient. The Tel Aviv study concluded, “It takes about one second for an arbitrage gain to vanish, but it takes less than that time to detect and exploit the opportunities.” This contrasts an earlier US report into  the efficiency of S&P 500 index options covering the period 1986-1996 that found, “.. frequent and substantial violations of the box spread relationship in particular, even though the analysis reflects transaction costs.”

References

Benzion U, Danan s, Yagil J. “Box Spread Strategies and Arbitrage Opportunities.”  The Journal of Derivatives, 1 (2005), pp 47- 62
http://www.thefinancialreview.org/abstracts/FinancialReviewAbstractsAugust2004.html#5-Fung