#### Measuring Volatility: Expectations vs Reality

By: Steve Smith

The price action in the weeks before and after the Brexit has been nothing short of breathtaking. This is not only in underlying shares, but also the related options. And both the implied volatility in anticipation of the event, but also the actual or realized moves in its wake.

The **VIX **saw some it’s largest 1-3 moves, in excess of 45% both up and down as stocks tanked then soared. But what is interesting to note is implied volatility of the **S&P 500 Index** options, on which the **VIX** is calculated, actually started to decline even as the index was hitting new lows on Monday, June 27.

This isn’t to say the **VIX** “predicted” the rebound, only that it had already started to price in the size of the move the market was undergoing. This concept of what options’ implied volatility levels are expecting or “pricing in” is crucial to profitably trading options. Especially during events such as this upcoming earnings season.

The Brexit event provides a good recent illustration. The graphic below shows the SPY’s 30-day realized volatility (the blue line) and the implied volatility (gold line). One can see the building expectations (implied volatility) build, ahead of the event, before declining even as the actual price move (historical volatility) spiked.

Expectations can diverge from reality for a while, but at some point the two must meet.

**Rule of 16**

Let’s look closer at the VIX to understand how implied volatility gets measured and what it means. The VIX was introduced by the **CBOE** in 2003 as a weighted measure of the implied volatility (IV) the **S&P 500 Index.**

As investors monitor the VIX on a daily and weekly basis, they’re simply watching a number that represents the IV of the SPX. Without getting into a long math discussion involving square roots, let me simplify an interesting aspect of the VIX: the number 16 (or more precisely, 15.87) is approximately the square root of 252 (the number of trading days in a year). This is where the Rule of 16 comes from.

While you let that sink in, let’s walk through some hypotheticals. If the VIX is trading at 16, then 68.2% (or two-thirds) of the time, it might trade up or down by less than 1%. The other 31.8% (or one-third) of the time, the SPX might trade up or down by more than 1%.

Now let’s go further. The VIX at 24 might equate to a 1.5% move in the SPX 31.8% (one-third) of the time. Finally, a VIX at 32 might equate to a 2% move in the SPX 31.8% (one-third) of the time.

These VIX levels and understanding the probability of movement in the SPX can give investors a measuring stick to test if the market movement and measured volatility are in line.

**Volatility Skew**

Now if your head doesn’t ache enough let’s tackle skew.

Skew shows up when out-of-the-money (OTM) put IV is at a higher level than OTM call volatility, causing higher premiums on the put side. This comes from the perception that stocks fall faster than they rise.

The option volatility skew illustrates which direction the implied risk lies in an underlying. There is, of course, a supply and demand variable that determines if there’s a skew and how severe that skew (or IV differential) is. Without this demand, skew would not exist, because supply and demand for options is the clearest driver of IV.

Recognizing the existence of skew is the first step to considering it in your trading. With extra premium in OTM puts and conversely lower premiums in OTM calls, strikes can be chosen to potentially enhance trades using the divergence that skew imposes on option markets. Skew allows investors to push the put strike further out than a corresponding call side, providing less downside exposure.

In rare cases (stock splits or potentially positive news events), skew can flatten or even slightly shift positive to the call side (OTM calls with higher IV than OTM puts). This is a rare but very informative set of circumstances in equity options.

This are something to keep in mind when expectation seem to be diverging from reality or vice versa. At some point the two must meet. This will help prevent you from overpaying for options that might seem “cheap” or selling something that seems “expensive. This will be especially useful as we roll into earnings season.