I never could have imagined the level of interest last week's VIX article generated from readers. Of course there was the long list of messages from those that expressed their gratitude for showing the characteristics of what has frequently been referred to as the "Fear Index", and those comments are always appreciated. But it was the other emails that I found most interesting. Summarizing last week's article, what I did was demonstrate how to use the VIX to read the pulse of the market, or if you'll pardon the analogy, how to tell time.
I had a number of emails asking for further details of how the VIX is created, or to continue the analogy, how the clock actually works. Here are a couple of the questions that came out of the list, which I think are fairly representative of the group.
"What I still don't understand is the connection between the put/call ratio and the VIX defined as the "implied volatility of the eight most heavily traded front month put and call options on the S&P 100" (from your par. 3). It is clear why p/c grows with declining markets and fear, but why does volatility (=variance) get higher with increasing p/c? What is the causal relation between the two?"
And then from another reader,
"I note that the VIX is calculated using the IV of the noted 8 call and put OEX options. Is the VIX calculated by averaging the IV of the 8 calls and puts? Does the put/call ratio directly affect the calculation of the VIX? For example,
1. When the market declines, put buying increases, the put/call ratio. Does this ratio directly affect the VIX? Or is it that the IV of the chosen puts goes up enough to affect the total IV of the combined 8 puts and calls?
2. In the opposite direction, when the market goes up and there is more call buying, does this not increase the IV of calls and why does that not also increase the VIX?"
WOW! Great questions, guys! My initial response was "Duuuhhh, I dunno!" To be honest, I had never really given the internals of the VIX much consideration, content with the information it provided me about current market conditions. I considered the VIX to be just another key indicator to be used in my day-to-day trading.
But my curious cohorts roused my normally-dormant alter ego, RocketMan. Long time readers will recall that I was a NASA engineer in a prior life, and "How does it work" musings launched me down the road to discovery once again. Care to join me and find the answers?
Since the VIX is created and maintained by the ever-vigilant folks over at the CBOE, I decided that contacting them would be the logical place to start. After several dead-ends, I got John Hiatt from the Research Department on the phone and am eternally grateful for the assistance he provided. After about 5 minutes of him describing how the VIX is calculated, I realized I was never going to wrap my throbbing brain around the concept without seeing the equations in print. Mr. Hiatt was kind enough to forward me a copy of a document (Derivatives on Market Volatility: Hedging Tools Long Overdue by Robert E. Whaley) that included the formulation for the VIX.
After reading the text 3 times, all I had to show for it was a pounding headache, so I'll throw in this disclaimer now -- "You are now entering the Theoretical Zone - proceed at your own risk!"
Just to get everyone on the same page, I'll quote from the article:
"The CBOE Market Volatility Index (VIX) is constructed from the implied volatilities of the eight near-the-money, nearby, and second nearby OEX option series. The implied volatilities are weighted in such a manner that VIX represents the implied volatility of a hypothetical thirty-calendar day (twenty-two-trading day), at-the-money OEX option."
Without going into a great deal of detail (mainly because it isn't a necessary waypoint on our journey of discovery), suffice to say that a proprietary approximation method is used for calculating the implied volatilities of the OEX options. This is necessary because the OEX is an American-style cash-settled index and the Black-Scholes model is insufficient for the task.
Coming back to the VIX calculation, we need a couple definitions before we proceed. As stated above, the VIX is constructed from the implied volatilities of the eight near-the-money, nearby, and second nearby OEX option series. The nearby series are defined as the front-month series, provided that there are at least 8 calendar days until expiration. Otherwise, the nearby series is defined as the next expiration month. The second nearby series uses the contract month following the nearby series.
That definition alone can be confusing, so let's simplify it with an example. Since we are currently more than 8 calendar days away from December expiration, the nearby month would be defined as December and the second nearby would be defined as January. If we were in the final week of the December expiration cycle, January would be the nearby month and February would be the second nearby month. Are you with me so far?
Setting the at-the-money level of the OEX options at the current cash-settled value of the OEX, we would then pick a Put and a Call just above that level and just below that level for each of the expiration months for a total of 8 options -- 2 December calls, 2 December puts, 2 December puts and 2 January puts (since there are more than 8 calendar days to expiration). That is the basis for the calculation. So taking the current value of the OEX at 578, here are the options we would use for the calculation:
December - 575 Call, 575 Put, 580 Call and 580 Put January - 575 Call, 575 Put, 580 Call, and 580 Put
The first step in the calculation involves averaging the implied volatilities in each of the 4 groups of options as follows:
IV1 = (IV of the DEC 575 Call + IV of the DEC 575 Put)/2 IV2 = (IV of the JAN 575 Call + IV of the JAN 575 Put)/2 IV3 = (IV of the DEC 580 Call + IV of the DEC 580 Put)/2 IV4 = (IV of the JAN 580 Call + IV of the JAN 580 Put)/2
Ok, I know it's getting deep here, but bear with me. We're getting close to the end. The remainder of the calculation involves interpolation between the nearby implied volatilities (IV1 and IV3) and the second nearby implied volatilities (IV2 and IV4) to create hypothetical "at-the-money" implied volatilities for each expiration month. I won't bore you with the details of the calculation, as it would likely raise more questions than it would answer.
Simply put, IV1 and IV3 through interpolation yield a value for implied volatility for December (IV-DEC). IV2 and IV4 yield a value for implied volatility for January (IV-JAN) through a similar interpolation process.
The final step is to interpolate between the IV-DEC and IV-JAN implied volatilites to create a thirty calendar-day (or 22 trading day) implied volatility.
Exiting the Theoretical Zone
So now that I have put everyone to sleep except for those that actually raised the questions listed above, does all of this theory help to answer their questions? Well yes, at least partially.
Let's take them one at a time, shall we?
Q: I note that the VIX is calculated using the IV of the noted 8 call and put OEX options. Is the VIX calculated by averaging the IV of the 8 calls and puts? A: Yes, absolutely. First the implied volatilities are averaged together, and then interpolation is used to average between the front month implied volatility numbers to arrive at a theoretical at-the-money implied volatility for December. Repeat the process for January, and then use the results to interpolate one more time, arriving at a theoretical 30-day at-the-money implied volatility for the OEX, which is the VIX.
Q: Does the put/call ratio directly affect the calculation of the VIX? A: Interestingly enough, the answer here is No. The ratio of puts to calls does not figure into the calculation of the VIX; only the implied volatilities of each of the individual options are pertinent to the calculation.
Q: It is clear why p/c grows with declining markets and fear, but why does volatility (=variance) get higher with increasing p/c? What is the causal relation between the two? A: This question really cuts to the heart of the matter, and to be honest, I really don't know. I think it is a bit of a chicken and egg scenario -- which comes first? The change in the put/call ratio or the change in implied volatilities that are used to create the VIX? It would seem that the increase in put buying that comes with increasing fear in the markets would increase the implied volatility of the puts, while the decreased buying of calls would decrease the implied volatility of the calls, keeping the VIX relatively constant.
I think the real answer is that in a falling market, traders become more uncertain and implied volatility of both calls and puts rises, which in turn causes the VIX to rise. Conversely, a rising market deflates the implied volatilities of both puts and calls, resulting in a falling VIX.
It seems to me that the VIX and the put/call ratio are different indicators that do the same thing - measure fear in the markets. Each have their own rules of application and corresponding extremes, which can guide vigilant traders through a minefield of information, hopefully to the end goal of trading profits.
Needless to say, I don't have all the answers, but I hope this excessively complex discussion helps to illuminate the issue for those with inquiring minds. While I did indeed learn from the process, I now need to give my brain a rest. An icepack and a cold margarita ought to do the job nicely!
See you next week!