Friday, June 12, 2009

Clash of the Greeks: Part Deux

In our first Clash of the Greeks post, I explored the inverse relationship between Theta & Gamma. If you missed it, you can view it here. I used a long straddle to illustrate a positive gamma, negative theta trade. In today’s post I’m going to review the nuances of a negative gamma, positive theta trade.

Negative gamma positions are positive theta positions.

Consider delta neutral trades such as iron condors or short straddles/strangles. They all make money as time passes (+theta), while looking for the underlying stock to remain relatively quiet (-gamma).

As mentioned in the original Clash of the Greeks post:

“We could say that when we enter trades that seek volatility, i.e. want the stock to move a lot or +gamma, we always have to fight time decay (-theta). Conversely, when we enter trades that profit from time decay (+theta), we constantly have to fight the stock moving too much (-gamma). Hence, there is a constant clash between Gamma and Theta.”

We can consider negative gamma trades, such as iron condors and short straddles, a race between time decay and underlying stock movement (realized volatility). For example, in the case of a short strangle we must make enough money due to time decay (+theta), to offset whatever money we lose due to the stock moving too high or too low (- gamma).

Suppose I enter a July short strangle on the SPY which is currently trading around 94. There are currently 35 days to expiration.

Short SPY July 98 Call for $1.15
Short SPY July 90 Put for $1.58

The net credit for the trade is $2.73. Both options are about $4 OTM, thus their premium is comprised of all extrinsic value. As long as the SPY remains between 98 and 90 at July expiration, both options will expire worthless allowing me to keep the $2.73 of premium.

The upside breakeven at expiration is 100.73. (98 + 2.73)
The downside breakeven at expiration is 87.27 (90 – 2.73)

With the breakevens at $100.73 and $87.27, all I need at expiration for the trade to produce a profit is the SPY to reside somewhere between these two points.

Viewing risk graphs helps to convey the trade-off between time decay and too much movement in the underlying. As a result of the time decay, SPY can move in a wider range as we approach expiration and still have the trade result in a net profit. In the case of the long straddle (used in last weeks Clash of the Greeks), we wanted the stock to move above or below the breakevens. Today's example is the opposite. As the risk graphs will portray, we want the underlying to remain in between the breakevens.
35 days to expiration
Breakevens = 91.50 and 94.75
18 days to expiration
Breakevens = $88.50 and $98.75
Breakevens = $87.27 and $100.73

As you can see, as expiration approaches, the break evens widen. This is a direct result of time decay. Thus, the longer we stay in this positive theta trade, the wider the range the stock can trade in and still result in a net profit. As is the nature with all delta neutral, positive theta, negative gamma trades, if the stock rises or falls too much the trade will lose money. Once again I've displayed a chart that juxtaposes the risk graph with the SPY price chart. In the first day or two, the SPY would have to remain within the two blue lines to result in a profit. With 18 days to expiration, the SPY would have to reside between the red lines. And finally at expiration the SPY would have to reside between the black lines to result in a profit.
I assumed implied volatility remained constant throughout the trade. In the real world, a rise in IV can hurt (shrink the profit zone) a short strangle, and a fall would help (widen the profit zone).



KrengelFamily said...

Hey Tyler,
Two quick questions for you on your management of (short) straddle trades.

1. What rules do you follow for exiting? Based upon your post, it almost looks like you may be looking at trailing the breakeven points for exits. Do you use them for exits? or have another rule ie strike prices for exits?

2. More out of curiosity, since the short straddle and Iron Condor share similar risk graphs, why would you choose the short straddle? My thought process is that the short straddle has much greater risk associated with it (in the case of a strong gap or move in one direction you dont have limited protection to either side), and can also carry a much larger margin requirement (naked put/call requirements on higher priced stocks compared to the $5-10margin requirement minus the net credit for an entire iron condor trade) thereby limiting your profit percentage. Just wondering what your thoughts are.


Tyler Craig said...


First off- the purpose of the post was primarily to show the trade off between positive theta & negative gamma. The simplest way to place a delta neutral, neg gamma, positive theta trade is by shorting straddles or strangles. I don't personally trade short straddles/strangles, but primarily stick to the iron condors (b/c of the advantages you mention in #2). So you're correct in stating that IC's are usually a better way to go. If I were to trade short strangles it would only be on cheaper stocks ($30 or less) to reduce the inherent risk and margin requirement.

My management for a short strangle would be similar to an iron condor-I would either delta hedge if the stock move too close to my B/E points or short strikes, roll further OTM, or merely close the position.



Interesting post

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