An introduction to beta - What is the VIX:SPX beta?

In the investing world, beta is generally referring to an individual security's return in relation to the movement of the underlying benchmark.  Now on a technical level it's quite a complicated calculation of covariance, but since you're not going to be calculating it and it's unlikely that you'll be using this article as a foundation for building a complex diversified portfolio and require all the math, I'm going to be using beta in more of the layman sense.

In the simplest terms, beta measures how much one security changes in value in relation to another security.

So for example how much Apple stock, or Johnson and Johnson stock move in relation to the S&P 500.  Beta is a very useful metric to look at because a single beta value gives insight into two different aspects:

1) Direction. Positive or negative beta values tell us whether the security generally moves in the same direction as the comparison benchmark, or in the opposite direction. In our example, Apple has a positive beta value meaning it generally moves in the same direction as the S&P 500.

* Spoiler, the VIX index has a negative beta value because it generally moves in the opposite direction to the S&P 500.

2) Magnitude. Higher or lower beta values tell us whether the security generally moves more or less than the comparison benchmark. Beta values below 1 show the security generally moves less than the benchmark, and beta values above 1 indicate the security generally moves more than the benchmark. Apple has a beta of about 1.3 which shows it moves more than the S&P 500, and Johnson and Johnson has a beta of about 0.7 meaning it generally moves less than the S&P 500.

* Again spoiler, the VIX index has a high beta value because it generally moves a lot more than the S&P 500.

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Quantifying beta:

If we just use all daily return values for the VIX index and the S&P 500 going back to the introduction of VIX futures on Mar 26, 2004:

VIX:SPX beta = -4.94

So on first glance we can conclude two things. First, because it's negative it means the VIX index moves in the opposite direction to the S&P 500. When the S&P goes up the VIX tends to go down, and vice versa. Also, because the beta value is very high it shows the VIX index tends to move 4.94 times the daily movement of the S&P 500. It's a useful number right? Direction and magnitude.

We need to adjust it:

However, we have a little problem with this value. There are plenty of days when the S&P 500 moves very little, but the VIX index still moves quite a bit. That's the nature of volatility, it sometimes sees large changes even though the market isn't doing much. This can skew the beta readings.

For example, just recently on December 27th, 2019 the S&P 500 only went up 0.003%, basically unchanged. However the VIX index was up 6.17%. That's about a 2000x change in relation to the S&P.

So what I like to do instead is only measure the VIX:SPX beta on days when the S&P 500 moves at least 0.5% or more, and that means both positive and negative daily S&P movements.

VIX:SPX beta (when S&P moves +/- 0.5% or more) = -6.37

So again, direction and magnitude. It's negative because the VIX tends to move in the opposite direction to the S&P 500, and -6.37 because the VIX tends to move 6.37x the daily movement of the S&P 500 (on days when the S&P moves at least +/- 0.5%)

Monday's massive VIX spike:

So Monday February 24th, 2020 saw the 7th largest VIX index spike in its history going back to 1990. Quite a bloodbath in the market as the S&P 500 dropped -3.35% that day. So is that in line with historical values and what we would have expected? Well, it was definitely on the high end.

• VIX % change: 46.55%
• S&P % change: -3.35%

VIX:SPX beta on Feb 24, 2020: -13.89

That's more than double the long term average, but it's also more than triple the long term average when we filter for just days when the S&P 500 moved > +/- 3%. Filtering for just those big S&P 500 moves, the long term VIX:SPX beta is about -4.32.

So the move we saw recently on Feb 24, 2020 and an S&P 500 drop of -3.35% taking the VIX index up +46.55% was definitely an outlier, that seemed overdone. It's not the worst we've seen, that honor goes to Volpocalypse on February 5th, 2018 with an absolutely nutty 115.6% VIX index spike. However the move this past Monday was a big VIX reaction in comparison to history.

The last thing we can look at is the declining nature of VIX:SPX beta as the S&P 500 makes larger and larger moves. We can see below that VIX:SPX beta is higher when the S&P 500 is just moving +/- 1% or so, and it declines as those moves become larger.

We saw a lot of this in the financial crisis in 2008/09, the flash crash in 2010, and the European debt crisis in 2011. In those periods we saw some very large single day moves in the S&P 500, and the accompanying VIX index moves were more muted.

That makes sense right? When the stock market is crashing, the first several percent will see elevated hedging and naturally the VIX is going to overreact to the move. But as the S&P continues its decline, market participants can't just keep buying massive amounts of hedges or they would overtake the actual directional bias of the portfolio. So as the market continues down during significant drops, the VIX will start reacting less to the moves. Then when the market is sufficiently hedged, a recovery can take place.

That's what we saw this past Monday. Mid last week the S&P was at all time highs and we saw a pretty long period of calm. So when we get a -3.35% S&P drop, that first wave of hedging is going to shoot the VIX to the moon and it's normal to see an over-reaction. In this case a beta of nearly -14. But if the sell-off continues those VIX:SPX beta moves will start to drop, to the point where the VIX may only be moving 3-4 times the S&P moves.

Food for thought:

What if a person tracked the short term exponential moving average of VIX:SPX beta? If it was declining, wouldn't that mean..... I'll save that for a future article :)