Jul 11, 2016

PUT vs WPUT Analysis

Earlier this year Oleg Bondarenko, professor at U of Illinois published an excellent empirical analysis of CBOE's PUT index and more recent WPUT (same as PUT but using weekly options). I will review some of the points in the paper comparing theoretical values with the ones that were empirically observed.

Here is a summary, and complete research paper.

Professor Bondarenko notes:
Selling 1-month ATM puts 12 times a year can produce significant income. From 2006 to 2015, the average monthly premium is 2.01%.
From 2006 to 2015, the average weekly premium is 0.75%.
Although smaller, the premium is collected more frequently. Intuitively, the premium of the ATM put increases as the square root of maturity. This means that a one-week tenor option rolled over four times per month will approximately generate 2.0x the premium of a one-month tenor option rolled over once per month (i.e., 1/2 premium times 4). 
Premium by itself, of course, does not guarantee profit. Let's take a look at some basic formulas (assuming ABM,  zero rates, and unit price for simplicity. All formulas were generated using Mathematica )

So, as stated, assuming 4 weeks per month, we would expect theoretically to collect 2x more premium. Since in reality we are collecting about 1.5x more premium, it means that weekly premiums are smaller than expected, which is pretty much what we would expect as vol term structure is in contango most of the time.

Similarly, expected vol arb (implied vs realized) PL suffers from contango.

In theory, for the same implied vol value we would expect 2x more profit for WPUT, while in practice WPUT has slightly underperformed PUT.
This implies an interesting relationship (not a statistical or theoretical, just merely an observation) if we simply re-arrange the terms, that value of weekly implied volatility is in between monthly implied volatility and realized volatility.

As an approximation I took VXST index (available since 2011), VIX, and SPX returns. Because of the period mismatch, the results are not exact - average value of VXST is 17.14, between  average of VIX of 17.47, and realized volatility of 15.54.

Now, let's consider another aspect of put selling - what is the risk? We can derive expected volatility of put selling strategy:

Just like in the formulas above, the expression is "per trade". That means that individual weekly trade will have half the volatility of monthly trade, but since there are 4 of them, and vol scales with the square root of # of trades, the expected volatility of PUT and WPUT should be the same. In reality, WPUT has somewhat smaller standard deviation (2.84% vs 3.32% ). Since expected volatility of put selling strategy only (theoretically) depends on realized volatility, the difference is quite surprising.

Finally we can derive a formula for sharpe ratio for selling ATM options, it is

We can see that sharpe ratio does not depend on frequency of put sales, but rather proportional to the percent difference in implied vs realized volatility. As expected, SR for WPUT is lower than that of the PUT.

Jun 9, 2016


I am travelling to Ukraine to visit family. If you are a Kyiv-based volatility trader and would like to chat, send me an email.

Speaking of, Ukraine has a tiny options market (here's front month options on the UX index futures) Open interest at the time of writing is 15K contracts.

Jun 6, 2016

Making Money In Volatility Is Difficult

Well - making money in anything is difficult, but volatility is both difficult and complex. I received an interesting performance table for a number of  volatility and options funds (Nelson Report from Soc Gen, cannot post here for legal reasons) .

Total of 48 funds across 38 managers with average fund being about 6 years old. Out of 48 42 have positive average returns, 18 have sharpe over 1, and only 5 have sharpe over 2. These 5 are

  • Structured Alpha 1000 from Allianz 
  • Bond VOL from Global Sigma, as well as their 
  • Global Sigma Plus program
  • Mint Tower
  • Twin Tree

I am not familiar with the last two names, if you have any interesting information please get in touch.

P.S. A reader emailed me: "In your latest post your mention a report from Soc Gen.  I have access to their markets portal, but can't find any recent report authored by or related to a Nelson or anything volatility.  I'm very curious to look closer though.  Can you help with any other identifiers of said report?"   My reply: "I don't have access to the research portal and received it from a colleague. Maybe this will help - it was not a pdf report, but a spreadsheet called SG Nelson Report (May 2016) . Inside the spreadsheet it is called "Newedge Nelson Report".

Jun 2, 2016

SEC Charges Karen "The Supertrader" Bruton With Fraud

The filing is available here, but the summary is as follows:
Ms Bruton is a self-taught options trader who allegedly earned millions in profit with fraud. She gave a number of interviews that are available on youtube, and apparently is a known name for retain options traders.

SEC alleges that she would realize gains and roll over losses, but charge fees on realized gains. What I don't understand is how is this possible using listed options (she was in the business since 2008, why didn't she go bust? was it  incoming funds that kept her afloat?) and mark to market accounting? Didn't any of the clients ask to see actual account statements from their broker?