Thursday, September 3, 2009

Over-Writes: A Delta Perspective Take Two

Yesterday's post explored two methods for lowering one's delta exposure on a long AAPL stock position. If you missed it, scroll down and read it first.

Today let's tackle shorting calls, the third potential negative delta trade. Although there are a myriad of calls available to short, the conventional approach for selling covered calls is usually to sell a short term, out-of-the money call option. Let's see the affect that has on our position delta, then we'll highlight an alternative.

Over-Write #1
With AAPL currently around $166, the Sept. 170 call would be the front month, first strike out of the money.

Original Position: Long 100 shares Delta = +100
Adjustment: Short Sept. 170 call Delta = -39
New Position: Long 100 shares and short 170 Sept. call Delta = +61

With my new position I've succeeded in cutting down my delta exposure. If AAPL were to drop $1, instead of losing $100 (as I would have with the original position), I merely lose $61. Now, at the same rate I also don't make as much money if AAPL continues to rise. That is the opportunity cost of hedging the position. You forfeit some upside to hedge off part of your risk.

It's also worth pointing out that unlike the protective put highlighted yesterday, a covered call is a negative gamma trade- meaning my net delta will actually begin to increase if the stock falls (my losses will accelerate) and it will decrease as the stock rises (my gains will decelerate).


Because my long stock position has a fixed delta of +100, but the short call option has a variable delta. Although the call is currently showing a -39 delta, its delta will get smaller and smaller as the stock falls, as well as larger as the stock rises. The "negative gamma" aspect of the trade causes the covered call position to experience accelerating losses as the stock falls, and decelerating gains as the stock rises. I've provided a visual to help drive the point home. Take note of the slope of the blue line in the risk graph below.

[Source: EduTrader]
Suppose I want to lower my net delta by more than 39 deltas. Could I find a call option to short that has a higher delta, thereby providing more hedge? Certainly. Let's take a look at selling a Sept. 160 call.

Over-Write #2
Original Position: Long 100 shares Delta = +100
Adjustment: Short Sept. 160 call Delta = -75
New Position: Long 100 shares and short 160 Sept. call Delta = +25

So what's the primary diff between both examples? Well look at the difference in net delta. By selling an in the money call with a higher delta, I was able to hedge my position delta to a greater degree than selling an out of the money call option (+25 vs. +61).

Another important distinction between using long puts vs. short calls to hedge is that while the former increase in effectiveness as the stock price drops, the latter actually lose there effectiveness.

Keep in mind the delta perspective when choosing strikes for covered calls.


VanceH- said...

Unless the covered call writer is a short term trader (fairly unusual I suspect), then I think it is easy to over emphasize the importance of delta in the position. If the position is held until expiration the situation is much simpler -- the delta is 0 above the strike price, and -1 below that. I don't see that worrying about delta accomplishes much of anything--for example delta hedges are unlikely to be worth the trouble. It seems like going for higher or lower strike prices should be more driven by the projection of where the underlying is likely to go rather than delta considerations.

Tyler Craig said...

Thanks for the comments VanceH-

As far as risk management goes, I can't manage positions based on what they will look like at expiration. I've got to assess the trade and make adjustments based on what it looks like TODAY. Consequently, I'm not worried about what the GREEKS will look like at expiration. I'm concerned about what they look like right here, right now and whether or not I'm comfortable with it.

In the example I gave we had owned AAPL stock for about 6 months and had amassed an unrealized gain of $4500. We were beginning to become uncomfortable with the delta of the position (+100). So, the whole point of the exercise was to show various methods whereby we could lower the delta. Selling a call option is one such legitimate method. Illustrating the hedging aspect of short calls necessitates emphasizing the affect on the positions Delta. So I'm not sure I was OVERemphasizing its importance.

I've got to disagree that "delta hedges are unlikely to be worth the trouble". You better believe their worth the trouble IMO. In the example, AAPL was at $165. Let's say we decided to lower our delta position by buying a 160 put. If after that AAPL drops to $155, am I going to be glad that I lowered my position delta before the drop? You bet! Whether I buy a put, sell stock, or sell a call- I'm certainly going to be glad I took action if AAPL proceeds to drop considerably

I agree 100% that the covered call (along with Delta & the other Greeks) looks much simpler at expiration, but so does every other option trade out there. That doesn't diminish the importance of managing option positions based on TODAY's risk-reward characteristics.

You're correct that choosing which strike you sell on a normal covered call could depend on where you think the stock is going to be at expiration. I use the same approach. The primary purpose of the post was to show how short calls can be used to hedge existing positions.