The folks at AQR are top-notch researchers and have written a ton of great papers.

Some of their more famous papers are the following:

Size Matters If you Control Your Junk (my favorite title of any paper ever published)

In this post, I wanted to highlight a number of lesser known papers by the fine folks at AQR that deal with the volatility premium primarily through covered call selling. Specifically, the papers help us understand 1) how covered call selling relates to the volatility premium, 2) how to harvest the volatility premium, 3) how to create a volatility premium factor and understand if other strategies or investments actually capture the volatility premium.

I am going to assume some working knowledge of options and option pricing for the remainder of this post.

### Volatility Premium

The first step in understanding covered calls (or cash secured put selling, which are

The volatility premium is the historical tendency for the implied volatility of an option to be greater than the realized volatility of the underlying security. Since the implied volatility of the option is greater than realized volatility (historically and on average) then an investor who sells an option (volatility) should expect to make a profit (on a delta hedged basis) as they are selling a dollar bill for more than a dollar.

This concept is driven home by a great Exhibit 4 in

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

What Exhibit 4 shows is that for the S&P 500 from 1986 through 2014 the implied volatility (

The key takeaway from the Embracing Downside Risk paper is that one can potentially improve investment returns by effectively harvesting the volatility premium in their portfolio.

### Covered Calls Uncovered

The folks at AQR wrote another great paper on covered calls and the volatility premium called

- Beta of 0.5 to the underlying asset (in this paper it is the S&P 500) called Passive Equity by the authors.
- At-the-money short straddle called Short Volatility by the authors.
- Timing bet on the underlying asset called Equity Timing by the authors.

The component pieces can be easily visualized by Figure 1 in the paper, below.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

### Equity Timing in Covered Calls?!

The CBOE BuyWrite Index each month sells a call option that is closest to the current price of the S&P 500. This means that when the option is sold, the delta (i.e. beta to the S&P 500) is approximately 0.5. As the price of the S&P 500 moves around between when the option is sold and the expiration of the option, it will have a different delta (beta to the S&P 500). Finally, as the maturity of the option approaches, the delta of the option starts to become more binary as it either moves to 0.0 (option expires out of the money) or 1.0 (option expires in the money).

The authors show this phenomenon in Figure 4 in the paper, below:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not...

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