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Source: Oleg on Pexels.

How Can the VIX go up When the Market Goes up?

What exactly is the VIX and how the calculation works

We’ve seen the VIX hit marks as high as 80 in the last few months. The last time the VIX got this high was during the Great Recession in 2008–2009.

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Source: Chart courtesy of stockcharts.com.

Very few people understand the inner calculation of the VIX, however. Even further, fewer people understand what actually causes the VIX or spike up or down.

The VIX is calculated using this formula, given on their website here:

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Source: VIX website

This only looks scary. If you look closely, the N_i values and the T_i values are actually just time components.

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Source: VIX website

and

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Source: VIX website

From glossing over the VIX generalized formula, we understand that the one dynamic component that moves independently of the time is the variance — or, sigma-squared.

That formula is given at the beginning of the white paper and is defined as this:

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Source: VIX website

Again, this only looks complicated, until we break it down and define the components:

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Source: VIX website

From our glance, we know immediately that the second half of the right side is fairly irrelevant to the total calculation. Since F divided by K_0 is approximately 1 and the division outside is some tiny number, we know that the VIX isn’t moving due to this portion of the equation. These are not the values that cause large, sweeping variations in our calculation that we have seen in the past.

We can narrow down that it’s something in the initial sum that’s causing the VIX’s movement. If we look at the definitions, we will see that Q(K_i) is defined as:

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Source: VIX website

This is the heart of the VIX. Every strike division weight is multiplied by the corresponding midpoint of the bid-ask of the S&P’s option with the specific strike in question. Each of those sums in the equation above is essentially multiplied by a midpoint that is either larger or smaller depending on how much investors are willing to pay for the S&P’s option premiums.

If the strike point’s options have larger prices that investors are willing to pay, whether they are puts or calls, then those corresponding midpoints are also larger.

In reality, the VIX isn’t a measure of true volatility or of fear. Fear would make it so that nobody is willing to pay for the option and volatility would make it feel like there is no way to tell which direction it’s going to go. In reality, the VIX is generally high when the day to day trading is frantically up or frantically down in large gaps. If the S&P went up 10% tomorrow and then down 10% the day after, and followed that routine for a good while, the VIX would be up whether it is on a green day or a red day.

In essence, the VIX moving up is simply signaling that the premiums for the out-of-money S&P options are moving up. The premiums are a “cover” or hedge against those large varied movements of the S&P 500.

The most important figure in the VIX is calculated using those midpoints of the bid-ask spread in the weights of the sum. And, that number gets bigger if those bid-ask midpoints are bigger. This doesn’t necessarily mean that the S&P has to be up or down for that to happen.

The VIX is low when those midpoints are smaller than they are now. However, for that to happen, investors need to be willing to not pay whatever the current premiums are. In other words, if the market begins to calm down in its variation as investors lose on both sides of the options, investors will be less willing to pay out large premiums going forward.

Written by

UC Berkeley, mathematics. Los Angeles. Long-time runner. Top writer on Quora, 100M+ total content views. New to Medium. Inquiries: Moumj@berkeley.edu

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