Picturing Option Profits – Volatility Part 2

Russ Allen

For the last several weeks, I’ve been using a bearish vertical call spread on GLD as an example to demonstrate how option payoff diagrams help us visualize option profits. Today we’ll wrap up that example, finishing our discussion of volatility.

In last week’s article, which you can review , we looked at an option payoff diagram on that position, which showed profit/loss curves as of selected future dates. These lines show the projected profit on the position given a price of GLD.

Below, for the final time, are the price chart of GLD as of our October 10 start date; and also the option payoff diagram that we drew at that time on the November 130/135 bear call spread.

Figure 1 – GLD price chart


Figure 2 – GLD November 130/135 Bear Call Spread Payoff Diagram


At the end of last week’s article, I said:

Notice the blue, green and purple curved lines above. Each of them represents what the position’s P/L would be at a different selected future date – October 10 (blue line), October 22 (green line), or November 3 (purple line). Look at where those lines cross the vertical red line, where GLD’s price is $123.18. The black line at that point is at its maximum, which is + $80.50.

All the other curves, however, are lower.

How those P/L lines curve tells us a great deal about how the position will react to changes in expectations.

Now we’ll examine this further:

Remember that in this position, which we entered on October 10, we believed that GLD would be below $130 at the November 15 option expiration date. So we initially sold a November call at a strike price of $130, receiving $136 in cash. If we were right, that call would be worthless at expiration, and we would just end up keeping the money we got for selling it. That was the reason for the trade. We refer to this option as the anchor unit of the position.

We also bought a call with a $135 strike price, paying $55.50. We bought this one strictly for insurance, in case the price of GLD suddenly shot up. Adding that long 135 call to our short 130 call transformed the position from one with unlimited potential loss, to one with limited potential loss. That limitation of risk was the reason for buying the 135 call. We refer to this call as the offset unit of the position. It offsets an undesirable aspect of the anchor unit – in this case, unlimited risk.

Although we own this offset unit, we actually want it to expire worthless. The $55.50 we paid for it was just an insurance premium. Giving that up was part of the price we paid for keeping the bigger $136 premium from the 130 option. We bought $55.50 worth of time value so that we could sell $136 worth of time value. We were net sellers of $136 – 55.50 = $80.50 of time value. In other words, we were short time value.

Like any option trade that is short time value, this one makes money as that time value melts away. If the price of the underlying doesn’t move against us, all we have to do is wait for all of the time value to disappear. This happens little by little with each passing day until expiration. If GLD doesn’t move, both options drop in price every day, with the 130 call dropping faster.

In the interim, our position could be liquidated at any time – there’s no law saying that we actually have to wait until expiration. If we were willing to accept a smaller profit, we could get out by buying back (buying to close) the 130 call, and selling to close the 135 call. We can calculate ahead of time what our profit would be if we did get out early. That’s what the curved lines on the diagram show us.

Back to the diagram – let’s look at the blue curved line. It shows the amount of profit or loss our position would give us, at any price of GLD, if we closed out the position on October 10, when the options had 36 days to go. I’ve drawn a red vertical line on the chart at a GLD price of about $123. At that point, the  blue line’s P/L reading is about $20 (read the P/L number off the vertical axis at the left side of the diagram). This means that as of the date of the blue line, October 10, if GLD were at $123, and we closed out this trade, we would make about $20.

But if we stayed in the position and GLD stayed at that $123 price, then 12 days later our profit would be about $40, which is where the green line crosses the $123 price; another twelve days later our profit would be about $60 (purple line); and finally at expiration our profit would be the whole $80.50 (black straight line).

Here is a key point: All of these P/L curves are drawn assuming that implied volatility remains constant. They will give accurate estimates of the position’s profit at future dates and different prices of GLD as long that is true. But what if it isn’t?  What if the expectations on the part of the option-buying public change? They might be willing to pay either less or more for time value in the future.

In that case, the curves will have to be re-drawn, and their shapes will change.

If implied volatility goes up (meaning faster price movement has come to be expected), then time value will be more expensive. Every option will be seen to have a better shot at gaining value, with a faster-moving stock. The effect of greater price movement expectations will be a lot like giving each option a longer lifespan. It would make all options more valuable, with those that have more time value gaining more. An increase in implied volatility would flatten out all the P/L curves, so that the purple one would look more like the blue one, and the blue one would be even flatter. This would not be good for our position – we want time value to go away. Anything that increases it hurts us.

A decrease in IV would have the opposite effect. This would be like shortening every option’s lifespan, which would be good for us. If IV went down, then at any price of GLD below (i.e. to the left of) $132.50, our profit would be greater sooner. Decreasing IV would make both options drop in value faster, with whichever one had the most time value being affected the most. All the P/L curves would curve more tightly, and move closer to the black straight line.

On a payoff diagram, increasing IV flattens all interim P/L curves, moving them away from the apexes. This is similar to the effect of going back in time. Decreasing IV moves all the P/L curves toward the apexes. This is similar to the effect of the passage of time.

Note that if GLD rises above that $132.50 crossover point, this position switches from being short time value, to being long time value. For that reason, some people refer to this as the “theta switch point.” As GLD’s price rises above that level, all the Greeks except Delta reverse roles. Increasing volatility would thereafter help us, and time decay would hurt us. We can see this clearly by noting that all the P/L curves are now on the other side of the black at-expiration line.

In summary, for any position that is short time value, an increase in IV is the enemy; a decrease in IV will help us. The payoff diagram shows us the extent to which that is true by displaying the distance between the current P/L curve and the black at-expiration line. The further below the line our curve is, the greater the amount of short time value, and the greater the effect of the change in IV. If our P/L curve is above the line, then we are long time value. In that case the effects of time decay and volatility reverse.

Vertical spreads like this one appear deceptively simple. They can actually be quite complex when we realize that their character changes dramatically above and below the theta switch point.

Next time we’ll look at a new type of position, and see that some seemingly more elaborate positions are actually simpler in their reactions than the vertical spread.

For comments or questions on this article contact me at rallen@tradingacademy.com.

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