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How does theta change through time when selling strangles? SPY, META, IEF

What is Theta?

Theta is amount of value that an option position changes each day due to the passage of time.  

For example, SPY closing at 411.99 and Implied Volatility (IVOL) 22.58%

SPY 9/16/22 (47 DTE)



Strikedeltapricetheta
376P-0.153.12-0.09
440C0.151.97-0.07

The above table shows that the 376 Put has a theta of -0.09.  This means the option will lose $9 a day (each contract represents 100 shares so -0.09 x 100 = -$9. To standardize, the theta/price is a ratio that can be used.  In our example  -$9/411.99 => -0.02%.

Table of Theta for 15 delta Strangles for SPY, META, and IEF

Theta for 15 delta Stranges for SPY META and IEF

Information was pulled from market data on 7/31/2022 taking the initial strikes and seeing how the data changes for different upcoming Days to Expiration (DTE).  (15 delta Strangles for SPY correspond to 376P and 440C).

SPY is the most active ETF for S&P 500.

IEF is an ETF of 10 year Bonds.

META is the ticker for the company formerly known as Facebook.

Analysis

1) Theta is stable as time passes, especially from 47 to 19 days to expiration.

This means that day to day, especially with a couple weeks or more left, the theta stays fairly stable.  This is important as you can use this to estimate the change in a position or portfolio making it easier to target for long volatility strategies how much is being spent daily;  or for short volatility strategies that can estimate premium capture as a percentage of theta.  For example, if you estimate you can capture 25% of the theta, then selling SPY 376P and 440C with a theta of $16 means you would expect to keep $4 (the rest of the $12 is buffer against potential losses).

2) Theta roughly scales for different implied volatility levels.  For example, SPY implied volatility is roughly 2x that of IEF and so is the corresponding Theta.  Also, SPY is about 1/2 the volatility of Meta with also the 1/2 the amount of Theta.

This means you can take different amounts of risk with the same capital used.  For example, you can buy or sell 2x the number of IEF options than SPY or 1/2 the amount of META options than SPY.  If you are targeting a specific amount of options and have a limited amount of capital, then looking at implied volatility or theta can help calibrate the actual risk being taken.  This also can be used if you have an opinion on the relative volatility differences to see how the market is pricing the risk.

Takeaway

Theta is a major attribute of option portfolios.  Understanding its stability and relationship as time passes is very helpful when managing a portfolio of options, especially since time is a major component.  Seeing that theta seems to scale linearly with implied volatility it can be helpful when adding new positions as looking at the implied volatility and the current portfolio can help give a quick estimation of the change in theta (in short, higher volatility means higher theta).


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