Transfixed by the VIX: How the Popular Gauge Works

People dealing with volatility learn quickly and/or abruptly to allow it to provide them with a meaningful way to think about the market – though not necessarily giving them an answer regarding which way the market is headed.  You’ve most likely discovered that in most cases the world doesn’t really behave in exactly the way you planned—that models, financial advice, volatility, and the VIX are more often than not a mediocre approximation of reality. You constantly remind yourself that you are immersed in an industry that involves the behavior of humans and that data alone doesn’t speak—you need to deliberate and draw conclusions. You must remember that no one truly knows what volatility is and everything you learn, devise, or contrive concerning the topic, while certainly helpful, is merely an introduction.

The concept that volatility plays a significant role in determining asset valuation has long been a pillar of finance. Volatility measures, generally defined, are considered to be valuable tools for consolidating how opinions of uncertainty about economic fundamentals are apparent in prices. Derivative prices, where volatility plays a major part, are therefore especially relevant for unraveling the connections between uncertainty, the dynamics of economy, preference, and prices.

For decades, options traders have been obsessed with implied volatility along with additional measures of volatility, including historical volatility, realized volatility, or even the volatility surface, that are resultant of the options price quoted on the trading floors around the world. Now, it appears there is a brand new fixation, the VIX, or the volatility index on the Standard & Poor’s 500 stock index. This wholesale talk of VIX has caused me some concern as I’m afraid most people who talk about it perhaps don’t truly understand what it is or even what it is supposed to measure. When discussions go down the path of anything mathematically hazy—especially when the topic turns to volatility—I often remind myself of something Albert Einstein said, actually I’m told Einstein engraved this onto his desk at Princeton: “Not everything that can be counted counts, and not everything that counts can be counted.”

Definition of the VIX Index

The VIX is an implied-volatility index that calculates the market’s expectation of 30-day S&P 500 volatility embedded in the prices of near-term S&P 500 index options. However, the majority of investors, including some exceedingly seasoned ones; view VIX as merely the “fear gauge.” Some people suppose that an elevated VIX simply implies increasingly justified worries by the option traders  and, a reasonably low or falling VIX level sometimes dupes the mainstream into thinking that options prices are indicating that a significant bull market is under way. To complicate things further, there is a contrarian mind-set that believes a relatively high VIX reading is a buy signal for equities, and conversely, a relatively low reading is a signal pointing to a pending correction. The reason for this, I think, is the somewhat flawed interpretation on the part of these traders and the far-reaching public in the financial markets that VIX by hook or by crook solely measures the expected volatility in the S&P 500 index. They mistakenly believe that VIX somehow sums up the expected movement of the market in the next day, week, or month. Although it is true that the VIX theoretically measures the expected volatility of the S&P 500 stock index, there is more—much more—to the story.

VIX is an index, like the Dow Jones Industrial Average (DJIA) or the Goldman Sachs Commodity Index (GSCI), calculated in real time throughout the trading day. The key difference is that VIX measures the movement in the options’ implied volatility—not the price path.

In an attempt to truly understand VIX, it is critical to stress that VIX is an attempt—a mere snapshot of looking ahead—assessing volatility that we look forward to see. It is not in any way backward-facing, looking at volatility that has been recently observed as some of us are taught. It may prove helpful to think in the abstract and conceptualize the VIX the same way as you would a bond’s yield to maturity. A yield to maturity is the discount rate that equates a bond’s price to the present value of its promissory payments. A bond’s yield is therefore “implied” by its current trading price. And that price characterizes the expected future return of the bond over its residual life. Similarly, the VIX price is inferred or implied by the current prices of S&P 500 stock-index options and thus provides a portrayal of sorts of expected future volatility over the next 30 days.

It would be easy to fill the pages with all types of highbrow math to justify the VIX, however, I feel what is so often is missing is a clear explanation of what this number actually means. To be clear, I’m of the conviction that VIX is an indicator of sorts—it means what you want it to mean. In other words, this talk of the VIX is trying to interpret something that most likely can’t be interpreted. It’s severely limiting as it’s an expectation of an expectation. It works until it doesn’t work.

How the VIX Works in Practice

The VIX is quoted in percentage terms and predicts the expected movement in the S&P 500 stock index over the next 30-day period, which is then annualized. For example, if the VIX is 20, this represents an expected change of 20% in either direction over the next year with a 68.2% certainty. To break that down to a shorter time period, we multiply the annualized number by the square root of time.  In this case, that means we multiply 20% by the square root of (30 / 365), and come up with 5.73%.  More precisely, due to the math of the probability distribution, S&P 500 index options are priced (if the VIX is 20) with the assumption of a 68% certainty (one standard deviation) that the magnitude of the S&P 500’s 30-day return will be less than 5.73%.

The VIX and Perhaps the Biggest Misnomer of All!

I’m shocked by the number of traders and risk managers who still believe that because VIX results from liquid option prices on the S&P 500 stock index it in some way reflects the implied volatility of at-the-money S&P 500 options. This is dangerous thinking as nothing could be further from the truth. Although the VIX is computed from liquid options prices on the S&P 500 index, it is neither in relation to implied volatility resulting from these option prices nor is it in relation to expected volatility of the S&P 500 stock index.

The best way to decipher the VIX, which is connected to S&P 500 option prices across a substantial series of strikes, considers the level of volatility “smile” at any one given point in time. In a chart of volatility values, if the VIX goes up, the S&P 500 index appears to have a broader smile. This is because options contracts that are in-the-money and out-of-the-money will have a higher implied volatility than at-the-money contracts. Hence the smiley face curve. A lower VIX value makes the S&P 500 volatility values more somber, at least in the diagram. In real life, many traders and investors welcome a VIX value that draws a less cheerful face on the markets. VIX values can be used to predict likely risk, and while this method is not as accurate as frequently thought, it does serve well when guiding the trader and investor to make prudent decisions when trading derivatives.