The differences between a bull call spread and a collar runs deeper than just being a philosophical argument amongst traders. There are capital or margin concerns as a collar carries long stock, which in turn requires a good deal more cash in the trading coffers to carry the equivalent position size. And while I’m not an accountant, there can be widely varying tax implications when comparing the one limited risk / limited reward spread to the other as well.

The variances don’t stop there either. There’s the Greek rho or interest rate risk, albeit a very tiny variable these days, to think about. A bull looking at the two strategies might also wish to think about the stock’s dividend stream potential or lack thereof before seeing one as potentially more attractive than the other. And of course, how a trader might expect to hedge and adjust their position as it matures, for better or worse, can also present very different possibilities and monetary conclusions.

Nonetheless and at their core, the bull call spread and collar are one in the same on a risk / reward graph. This commonality means we can compare the synthetic pricing of one versus the other and should be able to reach the same pricing conclusion of equality. To illustrate and show how the math behind this arbitrage relationship works, we’ll look at mid-market option pricing in up-and-comer semi outfit NXP Semi (NXPI) from last week. With shares of NXPI at $26.40 during Friday’s session, the following call and put markets were quoted:

Without knowing the value of prices based on implied volatility, which happened to be quite uniform between 44% and 45%, a trader can still compare the value of the bull call spread or bull vertical to the collar by understanding the working synthetic relationship between the two spreads.

The collar is built around equal parts or quantities of long stock, a protective long put and higher strike, short call used to help finance the cost of the position’s limited risk feature courtesy of the put. At the same time, the combination of long stock + long put = long call on a synthetic basis. This pricing truth means the collar can be viewed as a lower strike synthetic long call and short call at a higher strike.

Does that sound or look familiar? It should as it’s the same as the bull call spread’s long call and short call makeup. As we know the two are the same at the synthetic level,  what remains to confirm this truth is pricing out the synthetic long call and subtracting the short call in order to come up with the dollars at risk for the collar, which in turn, can be compared to the bull call spread’s debit cost.

To do this, the simple math involves: purchased stock + cost of put – strike price of put = price of synthetic long call. By then subtracting the credit received from the sale of the short call the trader has found the risk per one lot collar which can then be compared to the pricing of the bull call spread.

Referencing the quoted markets in NXPI and using mid-market prices, the long 25 strike synthetic call works out to: $26.40 + $0.70 – 25 = $2.10. Subtract a call sale of $0.85 and the collar’s risk of $1.25 is determined for each spread executed. Relative to the 25 / 27.5 bull call spread’s price of $1.25 ($2.10 - $0.85) we’ve found exactly what we were looking for; i.e. pricing which makes sense and cents during some very excited March Madness.

And what if that relationship between the two spreads doesn’t hold true? We’d suggest it’s a situation of “buyer be wary.” Any pricing anomalies are likely the result of unwanted liquidity issues and / or a hard-to-borrow situation involving high short interest. Our advice, instead of seeing a free lunch courtesy of Wall Street, traders should tread a bit more carefully than otherwise as profits and limiting one’s losses with relative ease are typically a good deal more difficult and most often not worth the effort.

Chris Tyler
Senior Options Writer, former Market Maker & fulltime Option Hedge Hog Advocate
Optionetics.com ~ Your Options Education Site
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The information offered here is based upon Christopher Tyler’s observations and strictly intended for educational purposes only, the use of which is the responsibility of the individual.