Long Gamma/Long Theta

Long Gamma/Long Theta Jan 10, 2014 4:50:21 GMT

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Post by gammashort on Jan 10, 2014 4:50:21 GMT

Hi,

I am very interested in equity derivatives trading and I would have a question regarding how to create a long gamma/long theta position. Namely, I have read somewhere that this would be done via a risk reversal strategy, however, I tried many different versions of a risk reversal and I just can't manage to get a long gamma/long theta position, where "long theta" means that I "receive theta".

Let's say, we look at a bullish risk reversal with Short OTM Put (95) and Long OTM Call (105) with same expiries while we have the "usual" volatility skew with higher implied vol for lower strikes and lower implied vol for higher strikes. Btw, in this case I would be Short Skew, as I am shorting higher implied vol and going long lower implied vol, correct?

My gamma, in this case, should be negative since the gamma from Short Put is higher than gamma from Long Call as Gamma for higher OTM options > Gamma for lower OTM options. Would this assumption be correct?

On the other hand, I should "receive" Theta as Theta from short put (with higher vol) > Theta from long call (with lower vol), right?

=> Hence, I would be Short Gamma, Long Theta.

In the case of a "reversed" skew, meaning lower implied vol for lower strikes and higher implied vol for higher strikes, I would get the opposite effect.

Specifically speaking, Long Gamma as Gamma from long call > gamma from short put (due "reversed" skew) and I would need to "pay" theta as theta from long call > Theta from short put (due "reversed" skew).

=> Hence, I would be Long Gamma, Short Theta.

Would you with these conclusions for the above two examples?

Apparently, I thought that I need to try something else to get a long gamma/long theta position, so I looked at a Bearish Risk Reversal.

Namely, Long OTM Put (95) and Short OTM Call (105), again same expiries.

Then again, in case of "usual" skew, I would have:

- Long Gamma as Gamma long OTM Put > Gamma short OTM Call (due "usual" skew)
- "Paying" Theta as Theta from long put position > Theta I receive from short call position

=> Long Gamma, Short Theta.

Ultimately, in the case of a "reversed" skew, I would get:

- Short Gamma as gamma from Short call > gamma from Long Put
- "Receving" Theta as Theta I receive from short call > Theta I pay from Long Put

=> Short Gamma, Long Theta.

Hence, In all 4 cases, I just couldnt manage to set up a long gamma/long theta position.

I really spent quite a lot of time on this, and I just dont understand why this wouldn't be possible. Since you are an experienced trader, I thought that maybe you could help me with my problem and maybe also briefly tell me whether I was right with my conclusions/assumptions mentioned above.

Thank you very much for your time, I am looking forward to hearing your thoughts on this!

Best
gamma_short

Long Gamma/Long Theta Jan 12, 2014 0:45:04 GMT

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Post by Admin on Jan 12, 2014 0:45:04 GMT

The long gamma/receiving theta is a possibility under a risk reversal scenario but its never something that is practical or tradable. More something which is an intellectual exercise.

The thing with your net gamma on a skew position is that your dGamma/dVol flips at a certain point. So ATM, the your dGamma/dVol is negative (the higher the vol, the lower your gamma), and way OTM your dGamma/dVol is positive (the higher the vol the higher your gamma). So the question is, at what does the dGamma/dVol flip. If you are close enough to ATM where your dGamma/dVol is negative, then the risk reversal of short the high vol option and long the low vol option does technically give you a risk profile of receiving theta and being long gamma.

The other thing to keep in mind, you might have less gamma, but then again you expect the vol to be higher. I.e. since the lower strike option is a higher vol you expect the spot/vol correlation to be negative (as spot goes down you have bigger moves and vice versa). So the B-S gamma that is kicking out might be a smaller number than from the low vol option, but at the same time you are getting paid more because you expect the stock to be more volatile on the downside.

A good way to think about this is consider two stocks: A is a 40% vol stock, and B is a 20% vol stock. You sell an ATM straddle on A and buy an ATM straddle on B. Net you are receiving premium, great, and you have positive gamma. But the issue is that stock A is expected to move 2.5% per day and stock B is expected to move 1.27% per day. So even though you have less gamma on B, your expected move is bigger. In the end, the ratio b/w gamma and decay is fixed by the implied volatility so that the implied move is the break-even move on any day. So you can apply this concept to doing a risk reversal as well.

Let me know if that makes sense.

Good exercise, if you have 1m gamma% (therefore your delta$ changes by 1m per 1% move), and the impvol is 20%, whats your decay bill?