1 VIX

Outline

  • Why is it useful?
  • How stable has the vix been?
  • Any noteworthy regimes?
  • Can you get a “vix” like measurement for non-S&P things?
  • Does the vix do a good job of predicting future volatility?
  • What if you aggregated the “vix” by securities?
  • Or looked at options on sector ETFs?
  • Why fear gauge?
  • Estimation is only good as the model

“I’m going to insert some quote about the vix here I think.”

References to the VIX are pervasive in the financial news - especially during times of heightened uncertainty and turmoil. Simply search “Vix” on any financial news source and you’ll see a multitude of articles all purporting to derive some insight about current market conditions based on how the VIX Index has recently behaved:

So I’d like to explore the VIX myself to see what exactly it’s telling us, when it’s most useful, and potentially examine when it is inappropriate.

1.1 Background

First, we need to have at least a cursory understanding of what the VIX is, before diving into the details with an attempt to extract any sort of insight. The VIX Index was created in 1993, by the Chicago Board Options Exchange (CBOE) with the intention of providing a forward-looking estimation of the volatility of the S&P 500. The VIX has become recognized and referred to as the “fear index” by the media and financial practitioners because of it’s tendency to spike at the same time that the stock market is declining.

Definition: the expected volatility of the stock market, derived by calculating the implied volatility of traded S&P 500 options with a weighted average maturity of 30 days, using the Black-Scholes option pricing model.

With this simple definition adn background, there are already a variety of questions and insights that come to mind, and may be worth exploring in further detail:

  • The VIX is used to measure the future volatility of the S&P 500. Has it historically done a good job of predicting the S&P 500’s realized volatility?
  • We tend to think of the VIX as a measure of the entire stock market, but in reality, it only measures the expected volatility of the S&P 500. Is that an important distinction?
  • Based on the definition, we should be able to create a VIX-like estimate of volatility for any asset which has options traded on it, right?
    • We could calculate the expected volatility of individual sectors of the economy, as long as we we have options traded on sector-based ETFs.
    • Would it be worthwhile or interesting to construct a sort of “Aggregated” volatility index by calculating the implied volatility of all of stocks in the S&P 500 and rolling up the results?
  • The VIX, uses the Black-Scholes model to back out the implied volatility of the index, but what if we used another option pricing model?
  • What exactly is meant, by “weighted average maturity of 30-days”.Weighted by what? Volume?
  • Does the calculation use both call and put options?
  • To examine the validity of the VIX as a fear index, perhaps we can explore the correlation of the VIX and the S&P 500.
  • What is a typical value of the VIX?

I’ll likely come back to examine some of these questions in more detail later on, but I just think it’s interesting that right off the bat, before doing much investigation, we already have a host of questions to explore in further detail, simply from dissecting the definition.

1.2 Empirical Analysis

1.2.1 Download The Data

Now it’s time to grab some data and begin trying to examine the properties of the VIX, and hopefully answer some questions that we posed along the way. I think a first pass at understanding the VIX (or any new dataset) should involve some preliminary and plotting and summary statistics.

I’ll grab historical VIX data’ll grab the historical, daily VIX values from the St. Louis Federal Reserve’s Website. Now, because of the wonders of R Markdown, we can display a dataframe of the downloaded values, with the ability to filter and search the data (Note, there are a few more columns in this table that I calculated now, because I’m going to reference them later). It would be cool if there was an option to download the data in an excel file, but I haven’t found an option for that yet, stay tuned. Feel free to play around and explore the dataset.

1.2.2 Exploratory Data Analysis

Now that the data has been imported, it’s easy enough to plot the full history of the VIX and get a feel for how it has evolved over time. Note, in order to answer one of the initial questions posed above, I’ve added a horizonatal, red line to display what the long-term average of the VIX has been.

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## i The deprecated feature was likely used in the plotly package.
##   Please report the issue at <]8;;https://github.com/plotly/plotly.R/issueshttps://github.com/plotly/plotly.R/issues]8;;>.

Well I would say that we already have a few interesting takeaways, just by examining the plot.

  1. The VIX is often well above its longterm average of 20ish.
  2. There are volatility regimes. When the vix spikes, it tends to stay elevated for awhile, and it also looks to go through periods of dampened volatility. Said differently, there appears to be autocorrelation in the values of the vix. This feels intuitively correct: When there is high uncertainty in the economy or financial markets, we wouldn’t expect the uncertainty to last for one day only, and the markts will probably maintain high volatility estimates for quite some time, until things become a bit more predictable.
  3. Sometimes the vix gets ridiculously high: In late 2008, during the financial crisis, and during the pandemic in 2020, the VIX jumped above 80. I’d argue that this is a pretty ridiculous level from both a statistical and fundamental perspective. (Need to talk about why standard deviaiton of 80% is nonsense and that this is pricing in an armageddon.)

1.2.2.1 Examining the Auto-Correlation

Clearly, the correlation is high.

Below looks like a simple random sample:

1.2.3 Bringing In the S&P 500

1.3 Trading Strategies