As a strategy, calendar or time spreads are rarely used yet often profitable.

The strategy involves the purchase of a longer term call (or put) option coupled with a simultaneous sale of a shorter term call (or put) option. Both options having the same strike price.

Gold stocks make interesting case studies in the current market environment. That is, if you believe that gold will trade in a range between US$1,000 and US$1,200 over the next six months.

With Barrick Gold (symbol ABX) trading at $39.59 per share, a calendar call spread might involve the purchase of the ABX April 40 calls at $3.75 ($375 per contract) combined with the sale of the ABX Nov 40 calls at $1.15 ($115 per contract). You are long and short calls with the same strike price, but different expiration months.

For margin purposes, the long call covers the short call. As well, a calendar spread is a debit spread, which with our ABX example means a debit of $2.60 ($260 per spread). Theoretically, the most you can lose from a calendar spread is the net debit.

I say theoretical, because you could be assigned early on the short option if the counterparty was say, interested in collecting a dividend. In that position, you would be required to buy back the shares – ex dividend - in order to meet the assignment notice. However, with stocks like ABX that do not pay a significant dividend, the risk of early assignment is relatively low.

The key to a calendar spread is the eroding time value. The option pricing formula calculates time value erosion with the “theta” derivative (often referred to as “Greeks”) within the formula. For more information on option pricing, see the MX Option Calculator at http://www.m-x.ca/accueil_en.php then click Options Calculator on the left side of the page.

When I input the following ABX data into the calculator on October 25th - stock price $39.59, strike price $40, volatility 31%, November 2009 expiration, 1% interest rate assumption, $0 dividend and 12/12/09 for the dividend date - the theoretical call price is $1.15.

The ABX November Calls’ theta is -9.124, which is an annualized number. Divide that number by 365 and we get -.0249, which means that the November 40 call should decline in value by 2.5 cents per day, assuming all other factors remain the same and the stock remains stagnant.

If we apply the same calculation to the ABX April 40 call theta comes in at -3.7, which translates into a -1.01 cent per day loss associated with time value. In other words the April call is losing time value at 40% of the rate of the short term call.

Mathematical Certainty
What makes the calendar spread interesting is that its success or failure is determined by a set of mathematical constants. We know with certainty that time value will decline to zero at expiration. We know that time value decays more quickly the closer the option is to expiration.

If ABX remains unchanged between now and the November expiration date, this position will most likely generate a profit. Why? Because at the November expiration, the April options will still have 161 days to expiry. If the stock is at $39.59, the April 40 calls should be worth at least $3.15 ($315 per contract). Since the initial debit was $2.60, a $3.15 value represents a profit of 21% (not counting transaction costs).

Next week, I will look at some of the risks associated with calendar spreads. Such as the impact of all things not being equal.