Quick Note on CBOE's Buy-Write Indexes

Last month CBOE expanded their portfolio of benchmark indexes, adding 10 more new ones. Link to the press release. I would not be surprised that some people will look at these benchmarks as complete trading strategies, however one should be careful as such benchmark indexes are often just an exercise in overfitting until desired result (pretty chart) can be produced.

Such datamining error is especially easy with options. Short strategies tend to produce "good" results that seem like a legitimate alpha, when in reality it is just the median returns are high, and average returns looks much worse, i.e. the strategy negatively skewed. Even when one is using a long dataset, for example including the crisis of 2008, it is too easy to add a moving average filter, or change parameters in such a way as to create good results.

Separating legitimate alpha, especially short volatility alpha from what is generally referred to "volatility risk premium" is difficult. I believe if one is facing such task, the process should be both quantitative and qualitative, checking that the strategy makes sense on the logical level. Here I will not try to perform any thorough analysis but will just add a few notes and ides on the new benchmarks.

As I mentioned above there were total of 10 new strategies, 9 based on SPX, and one based on VIX. Complete list of CBOE benchmarks is available here. I will start with buy-write indexes, but will write about other benchmarks in later posts.

"The CBOE S&P 500 Multi-Week BuyWrite Index is designed to track the performance of a hypothetical weekly covered call strategy with staggered short positions in call options expiring in consecutive four week options.  The BXMW Index is constructed as a combined portfolio of four mini BuyWrite indexes.  Expirations are staggered so that the BXMW Index sells four-week options on a rolling weekly basis. "

This is a very recent index, and CBOE obviously tried to generalize the "original" Buy Write by using weeklys. In-samples statistics are robust - the benchmark delivers about 2% annualized alpha, with 0.6 beta to SPX.  Of course it is more interesting is writing weeklys is better than writing regular monthly options, so let's compare BXMW to BXM.

And indeed the weekly buy write outperforms BXM - alpha (to BXM, not SPX) is 3% annualized with beta of about 0.9. Most of the outperformance comes from two periods: in the end of 2012 and most recently in October of 2014. The drawdowns seems to be about the same, however BXMW has stronger rebounds than BXMW.  Below are all three indexes for comparison.

"The CBOE S&P 500 30-Delta BuyWrite Index is designed to track the performance of a hypothetical covered call strategy that holds a long position indexed to the S&P 500 Index and sells a monthly out-of-the-money (OTM) S&P 500 Index (SPX) call option. The call option written is the strike nearest to the 30 Delta at 10:00 a.m. CT on the roll date.  The BXMD Index rolls on a monthly basis, typically every third Friday of the month. "

BXMD writes a call that is father OTM than the original BXM. Not surprisingly alpha is higher - or let's say full premium is collected more often, alpha in the regression is higher, not necessarily true alpha. Beta is higher, as expected. Another very similar index is BXY, which uses 2% instead of 30-delta rule. BXY does just a tiny bit worse than BXMD, but the difference is not significant, so I will not include the chart.

"The CBOE S&P 500 Conditional BuyWrite Index is designed to track the performance of a hypothetical covered call strategy that holds a long position indexed to the S&P 500 Index and sells a monthly at-the-money (ATM) S&P 500 Index (SPX) call option. The written number of ATM call options will be either ½ unit or 1 unit and will be determined by the level of the CBOE Volatility Index (VIX Index) when the call option is written on the roll date.  The BXMC Index rolls on a monthly basis, typically every third Friday of the month. "

BXMC writes more or less options depending in the VIX level. It is not a surprise that adding this rule improves performance with alpha of 4% and beta of 0.7. 

Symbol	Start Date	Annualized Alpha	Beta	Alpha t-stat
BXM	30-Jun-86	3.8%	0.66	3.88
BXMC	31-Jan-90	4.5%	0.69	4.75
BXMD	30-Jun-86	4.1%	0.83	4.60
BXMW	29-Jun-12	2.3%	0.61	1.57
BXY	1-Jun-88	4.3%	0.76	4.40

There is really nothing surprising about these summary stats - beta < 1, alpha > 0 (otherwise there would be no benchmark), and ones with more rules make more alpha. However selling otm index calls (against the skew) is obviously risky in the run-away bull market like we had in the past few years. So let's see how the benchmarks fared over the most recent period (same as BXMW which has the shortest history)

Symbol	Start Date	Annualized Alpha	Beta	Alpha t-stat
BXM	29-Jun-12	-0.9%	0.65	-0.51
BXMC	29-Jun-12	-0.4%	0.80	-0.32
BXMD	29-Jun-12	-0.9%	0.81	-0.59
BXMW	29-Jun-12	2.3%	0.61	1.57
BXY	29-Jun-12	-1.8%	0.85	-1.17

I guess this is really the main reason for introduction of the BXMW - it is the only benchmark to beat SPX! To be honest, I am not sure why this is so - why is monthly sale worse than 4 weekly sales? What is it in the skew that would explain this outperformance? I don't know - and I would not really put much trust that this recent performance by BXMW is robust. I do not believe that there is sufficient evidence that buy-write indexes are delivering true alpha - or enough alpha to justify beta risk. 

For further reading (and more optimistic view) I recommend this recent article.