What is Volatility?

Volatility is commonly understood as the degree of variation in the price of a financial asset, security, or market over a specific period. It measures how much prices move over a period of time and is often used as an indicator of risk. Market practitioners typically view volatility through the following three lenses:

1. Distributional Volatility: This is the volatility measure most people think about when financial markets are involved. This volatility or risk is measured by a statistic called a standard deviation. The larger the standard deviation the greater the volatility.
2. Up and Down Volatility: Generally called semi-variance. This is a statistic that measures the movement that will cause a loss versus the movement that will cause a gain.
3. Implied Volatility: This is a forecast of future volatility that is embedded in all option prices.

These types of volatility estimates do not always tell the same story. For instance, suppose token YOLO is down 60% over a one year period. And suppose that it got to -60% by declining 7.35% every month ( -7.35% compounded for 12 months closely equals -60%). Most people would say that this was a volatile period for YOLO and a directional measure such as the one year return would agree. After all -60% is not commonly seen in most financial markets. But the standard deviation, measuring directional volatility, would give a different answer. The standard deviation of one month returns would be zero since YOLO was down the exact same amount every month.

Another example of how these measures might not agree is a period where token MOON was down 50% followed by a +100% upward move. So MOON started at $100, declined to $50 and then rose back to $100. Most people would call this a volatile period but the calculated return over the entire period was zero since the price at the end of the period was the same as the price at the beginning of the period. But the standard deviation and semi-variance measured over shorter time periods would show a highly volatile investment.

Implied volatility might tell a different story than the standard deviation of recent asset returns. Implied volatility is a measure of future or expected volatility of an asset. But the recent past may have been atypically calm for this asset and this may result in large differences between the implied volatility (the volatility reflected in option prices) and historic standard deviation of recent returns.

1. Distributional Volatility

This is the type of volatility most of us think of when we hear or read that volatility was high in the financial markets. This kind of volatility causes prices to bounce up and down during some time period. The statistic generally used to measure this kind of volatility is called a standard deviation. The standard deviation uses historical price data to measure the spread of price returns around the average price return for the period. One standard deviation, plus and minus captures about 68% of the total market returns for the measurement period.

2. Up and Down Volatility (Semi-variance)

High volatility is generally considered a bad thing. However, if you are long YOLO then upside volatility is your friend, while downside volatility is your enemy. This one-sided measure of risk is called semi-variance. It attempts to quantify the particular one-sided (up or down) risk exposure of the investor. The standard deviation, the most common risk or volatility measure, is two-sided, including in the measure both the good volatility and the bad volatility. When the return distribution is symmetric, then using variance or semi-variance will yield similar outcomes. However, for investment portfolios with asymmetric return distributions, semi-variance gives a better measure of downside investment risk. Also, volatility on the downside is generally higher than volatility on the upside (this is generally true for traditional financial assets like equities but may not hold for cryptocurrencies, which often exhibit unique volatility patterns).

3. Implied Volatility

Implied volatility is a market-derived measure of expected future volatility that is embedded in option prices. For a given underlying asset, implied volatility represents the market’s forecast of future price volatility over the remaining life of the option.

Implied volatility is typically calculated by taking an observed market price of an option and solving backwards through an option pricing model (commonly the Black-Scholes model) to determine what volatility value would result in that market price. This is reverse-engineering the model — we know the market price, and we solve for the volatility parameter that would produce that price. All other option parameters remaining constant, higher option prices mean a higher implied volatility.