# Beta of options based strategy

This is probably a simple/dumb question, but I am not getting it.

As per GMO's recent Insight:

Second, as can be inferred from Exhibit 1, put writing strategies have a low beta to the equity market and they are able to collect elevated premiums during market sell offs due to enhanced demand for insurance in these periods.

This is mechanical: At-the-money put writing strategies have a delta of approximately 0.5, so a low beta to the market is guaranteed.

From that Exhibit, I can see pretty high correlation and close to 1 beta. How can a low beta to the market be guaranteed? how are the authors measuring the beta?

EDIT

Alex, as per your suggestions I tried to replicate the graphs and calculations. I took the monthly index values, generated log scaled returns and here are the equity curve and related statistics (skipped subtracting US 3M T-bills from both return series):

In log scale:

So, I think GMO's ATM 1M Put Writing strategy has a different profile. And as you can eyeball from the graphs, the original (GMO's) strategy has a beta close to 1. That was my initial concern.

Any further thoughts?

• Theoretically according to the Black Scholes formula a short term put with $S=K$ and $r=0$ has a Delta of $\approx 0.5$. If you do the calculation of Beta empirically for this time period using monthly data from the CME (try it), you find approximately 0.6. The chart you posted clearly shows a Beta less than one: from 1999 to 2003 the orange line goes down a lot, the blue line goes down only a little (about half as much), etc. – Alex C Mar 30 '18 at 13:51
• can you please give me the link to CME data? do I need to pay for it? – AK88 Mar 31 '18 at 6:48
• Sorry, CBOE not CME The general info page is cboe.com/products/strategy-benchmark-indexes/putwrite-indexes/… there is data at the bottom under "Data on Put Index" – Alex C Mar 31 '18 at 17:30
• I got that 0.6 beta, but I think CBOE's Put Index differs from GMO's ATM 1M Put Writing strategy – AK88 Apr 1 '18 at 6:51
• Sorry, what's GMO? – user217285 Apr 2 '18 at 1:26