The VIX is a unit of information within the financial market system that investment professionals use to make investment decisions. There are derivatives (options and futures) of that unit of information that investment professionals (and regular people) can use as tools to trade and/or invest within the financial market ecosystem.

What unit of information does the VIX track? the **volatility**^{1}** **of the S&P 500 index over the next 30 days, annualized. What does this mean?

__Volatility__ is a measure of the severity of the return of an asset, regardless of whether the return is positive of negative. Lets say that on Monday Apple stock goes down 6%, Tuesday up 5%, Wednesday down 7%, Thursday up 8%, and Friday down 10%. Since Apple stock typically moves under 2% per day, we can infer that this week Apple stock was **volatile. The higher the volatility of an asset, the riskier it is perceived.**

__The S&P 500 index__ is a stock market index composed of the 500 largest American companies that trade in public exchanges. It is probably the most common financial market index today.

So what the VIX tracks is what market participants are *implying *the S&P 500 Index volatility will be over the next 30 days. The VIX presents that number in percentage terms, which is then annualized. The higher the VIX percentage, the higher it is implied that the risk of the S&P 500 index is over the next 30 days. This is why the VIX is considered the *fear gauge. ***It informs market participants how risky it is to invest in the S&P 500 index in the near term.**

How market participants derive future implied volatility of the index and how the Chicago Board Options Exchange (The creators of the VIX) calculate the VIX is somewhat complex and beyond the scope of this post. You can read the VIX whitepaper ** here**. I would suggest also looking at

__The Black-Scholes Model__**formula for pricing options before looking at the whitepaper. I am happy to discuss in more detail the complexity of the VIX and options pricing in private.**

__You can read more about the VIX here.__

*This is not investment advice. For informational purposes only. I hold a long position on the VIX through call options.*

1 To be more specific, the VIX tracks the variance, or volatility squared. Non quantitative financial professionals use variance and volatility interchangeably, creating a bit of a confusion.

VIX tracks the

notvarianceof the S&P. (Slightly more subtly, it measures the variance in vol units). (This twitter thread does a decent job of explaining the difference and why it matters)volatilityI believe that you (and the Twitter thread) are saying something meaningful, but I'm having trouble parsing it.

I had thought of the difference between variance and volatility as just that one is the square of the other. So saying that the VIX is "variance in vol units, but not volatility" doesn't mean anything to me.

I think these are the critical tweets:

I was with him at "a variance swap's payoff is proportional to volatility squared". That matches my understanding of volatility as the square root of variance. But then I don't get the next point about realized volatility needing to be "compensated for".

Anybody care to explain?

Roughly speaking, it's about "when" you take square roots and what that means for the product you are trading. Here is a handy guide on a zoo of vol/var swap/forward/future products.

The key thing is less about what "volatility" and "variance" have been. (Realized volatility is the square-root of realised variance). We're talking about the

expectationfor the next month's volatility or variance.The "mathematician" way to think about this (although I think this is a little unhelpful) is E(√X)≤√E(X). If "X" is (future) realised variance (as yet unknown), then the former is "volatility" and the latter is "square root of variance" (what I call "variance in vol units"). Therefore "expected volatility" is lower than "square root expected variance". The difference is what needs compensating

The more practical way to think about this, is that variance is being dominated much more by the tails (or volatility of volatility). When you trade a variance, you need a premium over volatility to compensate you for these tails (even if they don't realise very often).

Another way to think about this, is there is "convexity" in variance (when measured in units of volatility). If you are long and volatility goes up, you much more (because it's squared), but if it goes down, you aren't making as much less.

I remember how much it irritated my advanced investment finance professors that variance and volatility were used interchangeably.

But even in the whitepaper the CBOE uses the term volatility. Considering the simplistic nature of the post, I will add a footnote to make the definition more clear.

Thank you.

There is an ETF that corresponds to the VIX:

https://www.justetf.com/de/etf-profile.html?isin=LU0832435464

This means you can "buy" VIX if you think the market is underestimating the risk.

This was mentioned by Zvi here:

https://www.lesswrong.com/posts/eWdh7pjMRKiF8Jzwt/hanson-and-mowshowitz-debate-covid-19-variolation

The VIX isn't tradeable.

There are futures which are based off of the VIX. And there are ETFs which own have portfolios of those futures. These products are very different from "buying" the VIX and I would being very careful when "trading" or "investing" in these products. There are lots of products in this space, and they won't necessarily behave like you think they will.

That's why I added the quotes. But I'd like to learn more about how these products are implemented and what effects that has. Can you provide some further links?

The behavior of the VIX is a lot more predictable than something like a stock. It tends to hang out at a certain level, and occasionally spike. If you could trade it directly, this suggests a simple strategy: Buy when it's steady, and then sell when it spikes. Even if you can't time the spikes perfectly, you'll make a lot of money.

So can you do this with the futures? No, because someone has to take the other side of the trade, and they know it might spike, so they'll price that in! It's like buying insurance. You have to pay a "risk premium" to the market to hold a long vol position. If you plot a logrithmic chart of an ETF that tracks VIX futures, like VIXY, you'll see that there are frequent sharp payouts for the spikes, but over the long term, the trend is pretty steeply negative. Plot that on the same graph as the VIX, and you'll understand why we say you can't trade the VIX. Unless you can predict the spikes pretty well, you'd be better off taking the opposite trade (like SVXY) to collect that premium yourself, though it would have to be leveraged down. During the quiet periods, VIXY will cost you the premium, because it's the wrong side of risk.

It's actually more subtle than this. There are two things going on (which I believe you understand based on "Wrong side of risk") but you have conflated here:

Buy when it's steady, and then sell when it spikes"You have to pay a "risk premium" to the market to hold a long vol position"The reason you have to pay a "risk premium" to hold a long vol position is because the "spikes" are negatively correlated to the market portfolio / other assets / the economy. This means that if the expected value for holding a long vol position was zero (or positive) you could improve your portfolio risk-adjusted returns (and hence by leverage total returns) by simply adding a "long vol" position to your portfolio. Another way of saying this is "You are only compensated (positive return) for systemic risks, and long vol as is inversely correlated to systemic risk so must have a negative return".

If there was an analogous index where the spikes weren't uncorrelated to the broader market, the futures would

stillhave some term structure such that you couldn't exploit future spikes and expect to make money. However, you wouldn't see the long term decay you see looking at (long) VIX ETFs that you do now.As I've said elsewhere, I think collecting vol risk premium is a poor strategy for retail investors. Vol risk premium should exist and adding expected negative return assets to your portfolio can enhance your returns. Equivalently, adding a positive expected return asset to your portfolio can

reduceyour returns.Caveat emptorThank you.

I had already noticed this and wondered where the catch is.

The simplest product (at least from an understanding point of view) would be VIX futures. These are futures which are (to a first approximation) cash settled to the VIX Index. (You can view the specs here).

One thing to notice is that they expire. This means that if you buy a future to gain exposure, when it expires you lose your exposure. (The same is true options - when they expire, you lose your optionality. (Actually, you lose some optionality on a daily basis which is par of why you can't own / replicate the VIX Index)). This means you have to come up with a strategy to "roll" your exposure before it expires. You can have a look at the term structure of VIX futures here.

Another thing to notice is that VIX futures are the expected value of the index - NOT the index. Typically when vol explodes, the VIX Index goes very high, the front future goes high, the next future less high and so on... Depending on which futures you own, you will make money, but not as much as the index will have moved.

Typically retail investors tend to trade the VIX via ETFs. These tend to formalise a strategy of buying and rolling VIX futures. Generally you can find the details in the ETF docs.

Thank you. That confirms my understanding of the ETF.