4. The VIX and the volatility risk premium

Derivatives 3: Volatility

It is the volatility number that appears in the press, the only one known to plenty of people who have never bought an option in their lives, and it comes accompanied almost always by the same unfortunate nickname. It deserves a whole module because understanding it properly sums up everything that came before.

What it measures exactly

The VIX is an index published by the Chicago options market which measures the thirty-day implied volatility of the S&P 500. Three points of precision about that sentence:

• It does not come from a single option. It is calculated by aggregating the prices of a broad basket of put and call options from the two expiries closest to thirty days, weighted so that the result does not depend on any particular strike. It captures the whole surface from the previous module, not one point on it.
• It is expressed annualized. A VIX of 20 means 20% a year, which divided by 16 is about 1.25 percentage points of typical daily move and around 5.8% over the month.
• It has a history. It was born in 1993 with a different benchmark index and a different method; the current methodology dates from 2003 and the series is reconstructed backwards to 1990.

Why calling it the fear index misleads

It makes a good headline and a bad description, for three separate reasons:

• It measures a price, not a state of mind. If a rule came into force tomorrow obliging funds to hedge part of their portfolios, the VIX would rise without anybody having felt any fear. Demand for insurance rises, its price rises, the index rises.
• It contains neither direction nor date. A high VIX does not say the market is going to fall, nor when. It says that moving a lot is expensive. There are long periods with the stock market rising and the implied elevated at the same time.
• It is contaminated by the skew. Because far out-of-the-money put options weigh heavily in its calculation, and they carry the mark-up from the previous module, it is in good part a thermometer of how much is being paid to hedge against a fall, rather than a clean forecast of amplitude.

An honest and boring name would be thirty-day price-of-insurance index on the American stock market. It does not fit in a headline, but that is what it is.

The volatility risk premium

Here everything from module two comes together with a concrete number. Comparing the level of the VIX on any given day with the volatility the S&P 500 realizes over the following thirty days, the former has exceeded the latter in the clear majority of periods over the last three decades, with an average difference of the order of three or four points. That gap is the volatility risk premium.

Its existence is no mystery. There are at least three underlying reasons:

• Aversion to large losses. People overpay to avoid disaster, just as with home insurance whose premium comfortably exceeds the expected loss.
• Correlation with the bad moment. Whoever sells volatility loses precisely when the rest of his portfolio is losing. An asset with that profile has to offer compensation to find anybody to take it.
• Capital constraints. Selling volatility requires posting margin, and that margin shoots up in moments of stress, when capital is scarce.

A small, frequent income and a rare, enormous loss

The series of results from selling volatility has a characteristic shape: a staircase that climbs slowly with a hole in it every so often. Most months produce a modest income; very occasionally a month arrives that takes away years of that income.

Both things are true at once, and the second explains the first: if that trapdoor were not there, there would be no premium to collect. How that asymmetry is managed from the sell side is the subject of a later level. What matters here is the phenomenon and its shape.

A real case: February 5, 2018

That Monday the S&P 500 fell 4.1%. A bad session, but nowhere near a historic catastrophe. The VIX, by contrast, more than doubled in value on the day and closed above 37, the biggest daily percentage rise in its history.

The consequence wiped out a set of exchange-traded products offering inverse exposure to the VIX, that is, which gained when volatility fell, and which had worked splendidly in the calm years before. The main one, a Credit Suisse product known by its ticker XIV, lost around 90% in hours and was redeemed early a few days later; its assets beforehand exceeded one and a half billion dollars. The stock market fell 4% and the product evaporated.

There was also a feedback mechanism worth retaining: those products were obliged to buy VIX futures at the close in order to rebalance, so their own hedging pushed the index even higher. The episode is known as Volmageddon.

A real case: August 5, 2024

A weak American employment figure coincided with the accelerated unwinding of yen-funded carry trades after a rate rise in Japan. The Nikkei fell more than 12%, its worst session since 1987. The VIX touched intraday levels above 60, not seen since 2020, and closed a good deal lower. The S&P 500 fell around 3% that day, and within a few weeks it was back near its highs with the VIX in the low zone.

That distance between an intraday peak of 60 and a fall of 3% says something no textbook explains better: a good part of that peak was an options book with no sellers first thing in the morning, not a forecast of catastrophe. The VIX announced nothing. It recorded what it cost to buy protection when almost nobody wanted to sell it.

All of the above is education about how these instruments' prices are formed, not a recommendation to buy or to sell volatility.