Gamma Rent Breakeven Calculation

T

twentyquid

Hello,
I'm new to elite trader. I have a question that I hope will prove useful for everyone here.

How do I calculate the break-even gamma rent or "fair alpha" for an options position, given a specific underlying price and implied volatility?

Nassim Taleb discusses this in chapter 10 of his book Dynamic Hedging, but I'm quite confused by his numbers.

I want to be able to look at the gamma/theta ratio of a short iron condor for example, and see if I'm getting paid enough theta to compensate for my gamma exposure. On the flip side, it'd be great to see if I'll be able to gamma scalp a long gamma position profitably (at least as greeks are this moment).

Would love to hear thoughts and discuss!

-twentyquid
 
First of all, realize that you're going to need to be able to hedge this position on a daily basis (at minimum) if you want to really use Taleb's strategy. Which means it can be capital intensive (esp when doing it for options on stock, vs using futures). Anyways, this is your quick & dirty way to calculate your "gamma rent" that pretty much all traders use:

Take the implied vol of the option (really probably just stick to using near ATM options for scalping gamma, unless it's a spread), and divide by 16. Why 16? Because it's roughly the square root of 252, which is the # of trading days in a year. (To be more exact, can use 15.87, but it's not going to make much of a difference in your strategy in the end).

That is the daily average % move/range you need to capture in the underlying to realize the implied vol.

Last step just translate that % move into a $ move and now you know what kind of buy / sell limit orders you need to look to get hit on.

EX:

SPX march ATM implied running about 13.5 right now. That's a 0.85% daily range that you need to capture to break even on the theta. With SPX @ 1140, that's about a $9.5 of SPX points per day you need to scalp vs your gamma.

You can obv do this any way you want: hedge @ eod, try to pick the top/bottom, make small scalps over and over. But the point is this 'quick & dirty' calculation gives you a good idea of what kind of range you need to see in the day to break even on a long gamma position (works for short too, just flip everything).

Best of luck.
 
Excellent reply Dr Sean. If you're running a complex book of options it may be easier to make those micro adjustments and not hedge yourself to death.
 
After looking at the situation, it appears that you would need multiple scalps per day in order to capture that much movement on a day over day basis.
 
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