Most of the time market volatility is not a hot topic – until it suddenly becomes relevant again. Even when it is not making headlines, though, learning about it clarifies your thought process for navigating markets.

I like volatility. First of all, it makes ‘stuff move’, which saves us from the relentlessly atrophying, boring market that seemed for far too long to have known only one direction. Second, and this might surprise you, volatility is a very reliable ‘customer’ in my world. Reducing it to the essence, it seems to have two positions: a progression of a sclerotic wasting disease which, in this case, helps us put bread on the table, or ‘full-on batshit crazy’ mode, supplying the champagne to wash the bread down. But before we dive into things, let us step back and agree what we are talking about when we refer to volatility.

## What Is Volatility?

There is not ‘one’ volatility definition. **There are many interpretations of the term volatility, and all of them mean different things to different people.** If you are quantitively inclined, you want to know how certain assets performed in the past. Just observing the price development (wow, this went up a lot!) would omit the rather important information – how our desired assets moved to their lofty heights or deep and dark valleys over time. Historic daily returns allow you to compute how the S&P 500, or any other asset, moved around its average returns in the past and then calculate a number (with a magical formula known as the ‘square root of time rule’, which justifies ridiculous salaries in the options world) everyone is using in polite market conversations to interpret the characteristics of an asset.

## Historical Equity Volatility Levels

For example, over the last 94 years, the S&P would have yielded an annual return of 5.9% while moving around this average by roughly 19%. In the last 50 years, that amounted to an average of roughly 7% with volatility still around 19%. This 19% is what we would call the historic volatility of the S&P 500, and it is a pretty good approximation of where volatility, on average, will find its most comfortable position.

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Keep in mind that ‘the average’ can increase substantially if you add the occasional basketball player to your book club – your bespectacled friends will not become taller. That means volatility will not magically find its way back to its average. Most of the time, it will trade below this level to average up in those nasty up moves that happen from time to time.

These historic observations are important because they provide us with a yardstick to measure the current environment versus what to expect in the long term. Sir John Maynard Keynes eloquently pointed out that ‘no derivatives trader desires to be dead in the long run’. So we tend to ignore the long-term data and trade the hell out of markets when we see fit, will say we guess how the asset will trade in the future, while having an eye on the ancient data in the rear-view mirror and discounting the madness of our fellow trading partners.

This newly formed educated guess about things to come is filtering into prices paid, based on the so-called implied volatility, mostly referred to when talking about ‘the Market’ in its incarnation called the VIX Index. It roughly indicates how market participants assume the S&P 500 will trade in the future. Here the uninitiated ‘civilians’ mostly misinterpret the published VIX Index Level. It is not a ‘Fear Barometer’. The VIX Index is a highly accurate market poll fed with the opinions of investors about their expectation of a future trading range, in which they can be right or wrong.

## Implied Volatility and Standard Deviation Explained

Let me run you through an example. A VIX Index Level of 20% tells you (after some square root of time rule magic buried in the index calculation) that investors and traders assume that the S&P 500 will, in a year’s time, in all likelihood, trade not higher or lower than 20% of its current level. Everything in between is a free for all, so to speak. All available data shows this is (mostly) true 68% of the time.

Out of which hat did I pull this number? The Index Level of 20% represents the One Standard Deviation, which simply is a 68% probability corridor for what might or might not happen in the future. Two standard deviations will give you a wider 95% corridor, three an even bigger 99% probability corridor. When volatility is on the rise, these corridors widen, facilitating all sorts of mad moves. When volatility contracts, the probability corridors narrow, making bizarre moves less likely. You can scale those numbers up or down to any time horizon you wish to observe – months, weeks, days or even minutes.

Why does it work so well? Because it is not a survey where some telemarketer calls you for your valued opinion on markets or world hunger. Rather, it is a tool that measures the views of those who voted in hard cold cash to buy speculative or defensive tools, calls and puts. The higher the traded volume, the more reliable this market poll gets.

Interestingly enough, this bidding process for options incorporates only one variable: the future expectation of volatility or ‘how much stuff moves’. Therefore, there should of course exist only one market expectation, read implied volatility, about what the individual asset will do in the future. Different exercise prices, for example lower put exercise prices or higher call exercise prices, cannot make a difference in expectations about how the asset ‘will have moved’ when all is over. It can only move the way it will have done once you turn around and look back. The likelihood of hitting different strike prices in one asset should not skew pricing. If you knew the future – the one path returns will have taken – your input to calculate probabilities would be this one volatility for all strike prices. You should not see different volatility quotes for different maturities or strikes.

## Options Skew, What Is That?

You do. These different expectations for one asset, while observing different strikes, are called the option skew. The relative price traders are willing to pay is, for example, higher in lower exercise prices when trading put options on the S&P 500, even though the asset itself will have made only one path into the future. The famous Black-Scholes Formula works under the reasonable assumption that ‘there can be only one’ future volatility, as argued above.

Mr. Black and Mr. Scholes plonked into their model something called the bell curve, an assumption about the probability distribution of future returns of assets solely described by the volatility of their average returns around its mean. However, the normal distribution, or bell curve, employed in the option model describes reality rather poorly. Also, it neither accurately predicts so called tail events nor reflects the non-randomness of markets.

Those of us who have not yet received a Nobel Prize for their filed work on efficient markets (Eugene Fama) and instead spend more time trading those inefficient realities had to take notice of these shortcomings. And, in 1987, traders took notice, changing how we look at volatility. Before the ‘Big Crash’, options where roughly priced under the assumption that all options on one asset with different exercise prices should be calculated under the assumption that ‘there can be only one future’.

## Volatility Smile

Maybe a little volatility ‘smile’ could be observed at lower and higher strikes, but all in the world seemed fine, until it was not. The S&P 500 dived 22% one day in October, and the S&P Future took an intraday dive of roughly 30% before recouping the excess losses into the closing.

Nothing of that kind could be, or was expected, by market participants or by the assumptions the bell curve provided about likely scenarios under the assumption of randomness. Jack Schwager calculated in his book, Market Sense and Nonsense, the probability of an event like this at 10-160 and gave the analogy that such a large crash was as likely as picking a random atom from all atoms in our universe twice in a row.

This is not very likely, but it happened, and traders and investors adapted. They started making up prices for the ‘shitstorm events’. If you wanted to protect yourself against madness on the downside or upside of markets, you had to pay for it, not giving a damn about the beautiful explanation given earlier about ‘only one path into the future’ and the probabilities the bell curve attached to it. The volatility skewed since this 1987 event and no longer resembles a subtle smile. It now rather looks like a stroke victim having a bad day. However, the magnitude of these events is still not priced into markets and provides endless fun seeing ‘civilians’ chasing assets like Gamestop, Tesla, Natural Gas, Oil and many others on their way up and/or down.

So, what can a smart investor do in these unlikely events once you are caught with your trousers down? Again, this might surprise you: sit it out. If, and that is a big ‘if’, you can service your margin calls, relax. Volatility always comes down to its long-term average and then most likely some more, for longer.

As markets are traded by humans, they will eventually display the same time-tested behavioural patterns.

## Real-World Examples

An analogy I like to use with my students goes like this. Let us assume for whatever reason we are taking a dislike to each other, but we must share the same room, house or ranch. For a while, we can ignore each other. But inevitably, we end up slapping each other’s faces over some imagined minor or major difference we might have and get really, really angry. As this is not a very pleasant situation – it hurts – after a cooling down phase, we eventually will forget or forgive the reason for our dispute, we will stop being silly and end up having a cup of coffee, a nice cigar, and some good cake, wondering what all the fuzz was about.

Now ask yourself, on which activity will we spend more time? It is in our nature to favour pleasant scenarios more than unpleasant ones. And we favour those pleasant scenarios for longer. Throw in the terms ‘high volatility’ and ‘low volatility’ or crash and recovery and you get the picture about magnitude and time.

However, if you do not want to be caught in a face-slapping contest, biding your time and convincing risk management that ‘all will be fine’, what should you do?

Here is my third and last surprise for the day and one of the reasons I like volatility: trust the bell curve, even if it does not work as it should. You would not give up driving your Ferrari just because it gets a bit unstable at speeds above 300km/h. Yes, it by no means represents reality, and the predictions are edgy once you leave the comfort of three standard deviation events. But hey, why would you?

Option markets offer a plethora of instruments with which you can comfortably trade in the predictable universe, below maximum speed. All the nasty tail events do not need to be your hidden calamities. Bilal Hafeez likes his ‘Grey Swans’. I don’t. It is like predicting earthquakes or meteor strikes. Eventually, they will happen and offer great opportunity or peril. Meanwhile, I will lose money waiting for these tails.

I prefer cutting off my risk at 99% and never speculating on the 1% profit chance. That seems to have worked for me for the last 30 years, so I mostly shut up venturing an unspectacular opinion and let someone else, probably younger, more aggressive and untainted by a long memory, worry about picking up those pennies in front of the proverbial steamroller or going all-in to break the bank.

If you are interested in a more comprehensive analysis on what volatility can do, please look at my article on volatility ‘How Hot Can It Get?’, which I wrote after Covid-19 hit in March 2020.

## FAQ

### What does volatility mean?

Volatility is simply how much and how quickly something changes. In finance, volatility is how much a trading price series varies over time. We normally measure volatility by the standard deviation of logarithmic returns.

### What is historical volatility?

Historic volatility is the degree of variation in trading price over a past time series. We measure it by calculating the average deviation from the average price of a security or market index over a specific period. Implied volatility, on the other hand, is forward-looking.

### How is implied volatility calculated?

Implied volatility is the market’s forecast of the probably movement in a security or index’s price over a specified timeframe. One way of calculating implied volatility is to enter the market price of the option into the Black-Scholes formula and backsolving for the value of the volatility. There are, however, other ways to calculate implied volatility, including an iterative search.

### Why are equities volatile?

Equities are volatile because of changes in their supply and demand. These changes come about from investor decision-making, or whether investors want to buy or sell an asset. In a world of rational investors, demand and supply would only depend on alterations in the intrinsic value of businesses. However, human biases, irrational behaviour, and animal spirits can decouple stock prices from their intrinsic values and contribute to equity volatility.

Thorsten Roland Wegener spent twenty years trading equity derivatives and was a partner at Bear Stearns. Currently, he teaches as well as cooking, driving, and cleaning lots.

**spent twenty years trading equity derivatives and was a partner at Bear Stearns. Currently, he teaches as well as cooking, driving, and cleaning lots.**

Thorsten Roland Wegener

Thorsten Roland Wegener