Wednesday, February 10, 2010

Mail Time- Clarifying Theta

I received an interesting question from Greg in response to yesterday's post:

I'm still unclear as to why in your SPY put ratio spread negative theta is a bad thing. I may be wrong, but when one sells options, one hopes that the time value premium will decay quickly so as to make the option less likely to be assigned (all other things being equal). Therefore, a negative theta would imply that there's a lot of time decay. Since in your spread you sold 2 puts and only bought one, negative theta- in this case- means time is on your side?

Thanks for the question Greg. Let's begin with clarifying positive and negative theta. If a trader owns a position that is negative theta, he will be losing money due to time decay. It doesn't matter what the position consists of. It could be something as simple as owning a put option or something as complex as being simultaneously long and short options of different expiration months and strikes. If the aggregate theta is negative, the position will be losing money overall due to time decay. So, negative theta never means time is on your side.

Consider the current value of the position highlighted yesterday:

Long (1) Feb 104 put @ $.67
Short (2) Feb 100 puts @ $.27

If we were to fast forward to expiration and assume these puts remain out-of-the money, I would lose $67 on the long put and gain $54 on the short puts. Net-net I'm losing money. Hence the trade is currently negative theta. Time is not on my side.

One other quick clarification. Negative theta does not necessarily imply there's a lot of time decay, it simply implies you're losing money due to time decay. How much you're losing depends on the size of the position. You could be losing $1 a day, you could be losing $1000 a day.

7 comments:

greg said...

Thanks for the clarification. Keep up the good work. I enjoy reading & learning from your blog.

Tyler Craig said...

Your welcome Greg. Glad you're enjoying the blog. Let me know if you have any other questions down the road.

Tyler Craig said...
This comment has been removed by the author.
Anonymous said...

Hi Tyler,

I did the same reasoning as you (fast forward to expiration) to realize that the position lost money as time goes by. But there is still something that I do not understand. When I calculate the theta of the position from the theta greeks that gives my broker I obtain a positive number :

(today)
Feb 104 put Theta = -0.07
Feb 101 put Theta = -0.05

I'm doing the following calculations :
(1 long put 104) -0.07 - (2 short put 101) 2* -0.05 = 0.03

What I'm missing ?

Thanks for your time,
Siull

Tyler Craig said...

Siull,

Very good question. To be quite honest I don't know the best answer. With the 101 puts currently around $.20 and about 9 calendar days remaining until expiration, the theta on those has to drop b/c they can't lose $.05 a day. At $.50, the 107 put could almost lose $.07 a day, so although an option chains shows the position is currently positive theta, it should turn negative quickly.

Why isn't it already negative? Truth is I don't know, but by looking at a risk graph as well as the amount of extrinsic value remaining in both options, it is easy to see the position will lose value if the puts remain OTM.

greg said...

shouldn't you be adding together all the thetas?

Tyler Craig said...

Greg-

The answer is yes. That's what Siull did. The long put was theoretically losing $7 a day (-.07), the short puts were theoretically making $10 a day (+.10).