ESP For Option Traders

A covered call strategy carries about 50% to 70% of the risk associated with a long equity position. We accept that thesis as a rule of thumb, but how does one square that position mathematically?

The simple answer is to evaluate the downside protection accorded by the premium. We receive more money and, by extension, more downside protection by selling at-the-money calls rather than out-of-the-money calls. More downside protection means less risk. The trade-off being the limitation on upside potential.

Following that train of thought, writing longer dated options at the same strike also enhances downside protection. But is it a less risky strategy? On the surface it would seem so. In reality, it is not. The reason is that movements in the underlying security are not time sensitive.

This comes together in the option pricing formula which takes into account the random nature of price changes in the underlying security. As such the options’ time value is not calculated using a linear model but rather follows an exponential curve. A three month at-the-money option carries about half the time premium of a nine month at-the-money option on the same underlying security. Three being the square root of nine. Similarly, two month options carry about half the time premium of four month options… two being the square root of four.

The option pricing formula is particularly relevant in terms of quantifying the risk in more complex strategies. Directional spreads, calendar spreads, straddles and ratio writes come to mind.

With complex option strategies risk is not related to downside protection but rather to the amount of leverage being employed. What separates success from failure when trading complex strategies is cash management. And that is directly impacted by the amount of leverage being employed within a specific position.

For example, let’s assume that you are beginning with a $50,000 portfolio. Cash management is about determining much money should one risk in a single strategy? And the only way to calculate that is to look at the risk associated with a specific strategy.

That’s where Equivalent Share Position (i.e. ESP) comes in. The objective is to use ESP to evaluate how much leverage is being assumed and then to use that information to assess how much capital should be committed to a specific position.

So what is ESP? It is a single number that tells us how many shares of the underlying stock we are being exposed to with a single position. For example, with a covered call strategy we own the underlying shares. We know that 100 shares of stock must be used to write a covered call. That’s the first step in calculating ESP.

We also know that delta – a derivative with the option pricing formula – tells us how much an option should move for every dollar gain or loss in the underlying security. Delta can also be used to calculate the ESP reflected in the option.

For example, if a call has a delta of say 0.50 we know that the call option is equivalent to buying 50 shares of the underlying stock. In a covered call strategy, we are selling the call which means the delta tells us that we have reduced exposure to the underlying stock by 50 shares. The ESP for our covered call strategy then is 60, which is calculated as long 100 shares less 50 shares for the short call. In this example, we theoretically have a position that carries about 50% of the risk associated with holding the underlying stock. For our purposes we are assuming that delta is static. The reality, is delta is not static. It changes – sometimes dramatically – based on time to expiration, volatility and the movement in the underlying security. At best it is a rule of thumb.

With that caveat out of the way, let’s apply ESP to more complex strategies using the following assumptions;

XYZ is trading at $50 per share
XYZ six month 50 call is trading at $3.00 with a delta of 0.60
XYZ six month 55 call is trading at $1.00 with a delta of 0.40

If we were to employ a bull call spread, we would purchase the XYZ 50 call at $3.00 and sell the XYZ 55 call at $1.00. The net outlay for this position $2.00 per share and the ESP for the position is 20 which is calculated as 60 shares for the long call less 40 shares for the short call.

If we multiply the 20 shares by the current price for XYZ ($50 per share) we have assumed $1,000 of exposure to XYZ for each bull call spread. If we buy 10 bull call spreads on XYZ we have assumed $10,000 in leverage or about 20% of the total cash available for option trading (based on our hypothetical $50,000 portfolio). That’s how you want to think about it when determining how much cash to employ for each position.

Obviously this is a conservative approach. If XYZ were a $100 stock, the linkage between ESP and cash management translates into 5 bull call spreads rather than the 10 contracts described previously. But the $2.00 per share risk (i.e. difference between the cost of buying the long call and the premium received from selling the short call) is the same regardless of the per share value of XYZ. While that may be true, cash management is a discipline. Within that context, a middle-of-the-road approach seems appropriate.

Next week I will look at how one can use ESP to examine equivalent option strategies across the option strategy spectrum.