## What You Don’t Know About Volatility Can Hurt You

*Editor’s Note: **As one of the traders who was instrumental in creating the precursor to the VIX, we asked Shah to write about the truth behind our understanding of volatility, and how it applies to today’s volatile markets. *

The wild swings we see in the stock market aren’t the result of volatility.

Volatility results from the wild swings, not the other way around.

One thing investors don’t understand is, the VIX (the CBOE Volatility Index, sometimes called the market’s “fear gauge”) isn’t predictive. It isn’t a leading indicator; it isn’t telling us what the future holds. It’s misleading.

If you didn’t know that, chances are you may not understand what’s really causing wild market swings.

Here’s your quick fix on the VIX, and how to avoid falling into the fear gauge’s trap…

### Back to Volatility Basics

There are two kinds of volatility:

- Realized volatility
- Implied volatility

Realized volatility, more often called historical volatility, is a measure of past volatility.

One measure of how things move is standard deviation, or how far from the “mean” (its average) something moves. A one standard deviation move is tame, a two standard deviation move is less so, and so on. Historical volatility is the average of how many standard deviations something moves (in either direction) over a period of time.

We know how volatile something *has been*, like a stock or the stock market as measured by the S&P 500, because we can measure how volatile it has been over historical time periods.

Implied volatility, on the other hand, is the measure of volatility that’s derived from the actual market price of an option, or a stock, or the market.

To calculate implied volatility, you would have to throw out the theoretical price of what something (like an options contract) should be, since that is calculated by using the Black-Scholes options pricing model which incorporates historical volatility.

To figure out what something’s implied volatility is, you’d plug in all the numbers that comprise the Black-Scholes model (except the historical volatility number), substituting the actual market price for the theoretical price (which is what the model solves for), and instead solve for a new volatility number.

Implied vol is the expected volatility buyers and sellers of that option are pricing it at, in the real world.

In other words, implied volatility is what the market expects volatility to be.

### Origins of the VIX

The Black-Scholes options pricing model (the one that uses historical volatility as part of its equation to calculate theoretical options prices) was plugged into the computers we used at the CBOE back in the early 1980s when I was a market-maker on the Floor.

If you wanted to buy or sell an option, you might look at what the theoretical price should be, to see if you could buy it cheaper than what it was supposedly worth or sell it for more than what it was theoretically worth.

However, what was obvious to a bunch of us was that theoretical prices derived by formula were quite different from the prices at which we were buying and selling.

Necessity is the mother of invention, and we were trying to make money. So, to figure out why there was such a difference between theoretical prices and actual prices, a handful of us started playing with the Black-Scholes model.

It didn’t take us long to figure out that if we used the formula to solve for volatility, instead of some theoretical price, we got markedly different volatility numbers.

We were trying to figure out if the implied volatility that we were calculating, which represented what actual buyers and sellers were expecting and pricing accordingly (without knowing it), could help us price other options more efficiently.

It did.

I was an OEX (the S&P 100) market-maker, in the pit, trading OEX options when they were launched in 1983. A group of us immediately extrapolated out what we knew about implied volatility. We used near-month, at-the-money puts and calls (because they were the most active) on the OEX to come up with what implied volatility was on the whole market, as measured by the S&P 100.

That ended up becoming the VIX, which is now the implied volatility of the S&P 500.

### The VIX Does Not Predict the Future

The VIX takes prices of puts and calls on the S&P 500 and extrapolates backward what the implied volatility is on all those individual options, and weighs them to determine where the market (buyers and sellers of options on the index) is pricing-in volatility, implied volatility.

If the VIX is at 10, it means the market is pricing a potential 10% move, either up or down, in the next 30 days.

What most people miss is that implied volatility is already priced into options, because it comes from realized trading. The VIX does not predict the future; it predicts what has happened, what expectations have been, and what they are currently.

If you thought the VIX was supposed to be a measure of what future vol is supposed to be over the next thirty days, you’re only partly right. It’s supposed to be, but is not.

When expectations change like they did last week, and panicked investors started buying puts on the S&P 500 to hedge themselves against the falling market, they bid up the price of S&P puts. That lifted the VIX, very quickly. That’s not expected volatility in the future being priced-in, that’s panic buying creating a higher VIX now, in real-time, reflecting what might happen tomorrow or any day now.

When the VIX got to 50 last week, it was because the put buying at higher and higher prices pushed it up. The VIX wasn’t saying the market expects a 50% move in the S&P in the next 30 days, even though that’s technically what it’s supposed to be saying. The “expected future” had just happened.

If the market really expected there to be a 50% move in the next 30 days, the VIX would have remained at or above 50. It didn’t. It dropped to 30 in the blink of an eye.

If you wait until the VIX is at 50 to panic and buy puts, you’ve already missed the move. Investors have already bid them up. The time to buy market protection is before the VIX rises.

Of course, that can get expensive if the VIX is at 10 for months (or years) on end, and you’re buying puts that you don’t need.

The VIX should constantly be monitored. When you see volatility breaking out of a sideways pattern, that’s the time to take action.

You can see that with the volatility index of the VIX, the CBOE VIX Volatility Index known as VVIX. It’s the vix of the VIX.

If you were following VVIX over the past months, you would have seen the volatility of the VIX picking up. You couldn’t see it in the actual VIX, which was meandering around 10, but the VVIX was moving up, signaling something was likely to happen.

Of course, it did.

Volatility is a good thing if you’re on the right side of it. In fact, volatility is an asset class all its own. You can trade volatility eight ways to Sunday, if you like.

But if you don’t know what volatility is, and if you don’t know the difference between historical and implied volatility, you might end up like all those investors who made a bundle selling volatility until last week, when the funds they were using imploded taking everyone’s open positions down with them.

On Friday, I’ll tell you how to trade volatility – the right way.

Sincerely,

Shah