Is Volatility the Same as Risk?

Does Volatility Equal Risk? Are They the Same Thing?

This question represents one of the most popular misconceptions in today's investment industry and public.

A whole book would not be enough to answer this question.

The short answer is:

Volatility is probably the most popular way of expressing, understanding, and quantifying risk of investments. In that sense, volatility is the same as risk.

However, there are some problems with that.

The Problems with Volatility as a Measure of Risk

Volatility is Non-Directional

Volatility, at least in its mainstream meaning in finance, is non-directional. It simply means how much something (a stock, bond, or portfolio) tends to move, regardless of the direction of the moves being up or down.

Risk, on the contrary, is usually understood as the possibility that something unfavorable happens. In investing it is the odds of your investment losing money.

One example – consider two stocks:

Stock A moves up 0-1% every third day, down 0-1% every third day, and more than 1% up or down every third day (this is not unlike many stocks in the real world).

Stock B moves up 0-1% every other day, up 1-5% every third day, and up approximately 10% every sixth day on average (yes, I would also love to have this stock in my portfolio, but it's fiction).

Which stock is more volatile? Stock B, definitely, because it moves 10% every sixth day, a big move. If you calculated historical volatility of such stock, you would get a number that is higher than most stocks that exist in the real world.

Which stock is more risky? In other words (as most people understand risk): Which stock would you be more afraid to invest in? Which stock has greater risk of losing money? Stock A of course.

Although stock B is more volatile, it can't lose money, because it never goes down. Therefore it is not risky at all.

I know that this example is as far from the real world as you can get, but the purpose is to make a point:

  • Volatility and risk are not the same thing.
  • When a stock is volatile, it means that it tends to make big moves (up or down).
  • When a stock is risky, it means that it can lose money (go down).

You don't lose money on stocks that go up, even if they are volatile and the up move is really huge. Unless of course you are a short seller. For short sellers, a stock that never goes down would be risky and a stock that always goes down would be zero risk. Volatility, on the other hand, is the same for everybody, regardless of direction, regardless of your position being long or short.

Volatility Can Underestimate Actual Risk

The most popular way of calculating and understanding volatility is standard deviation of returns. There are other ways, but standard deviation is by far the most common. If you need more details on the logic and the calculation, see:

There are hundreds of models and papers on that. Nobel Prizes have been awarded for them. And I don't say that these models and papers are wrong. Nevertheless, there are some limitations. One of the most serious drawbacks is that...

Volatility, when understood as standard deviation of returns (or something with a similar logic), does not take extreme events into consideration (enough). This idea always gets to greater public awareness after some extreme events in the markets when lots of investors lose money on something that was estimated to occur once every X thousands of years, but in reality happened to occur just during our lifetime.

The problem is that something that has low volatility (it has low standard deviation of returns and its moves are usually very small), but once in a while makes an extremely big move (usually to the downside), is in fact very risky, but many investors are not aware of the risk because of the low usual volatility. Typical examples of such securities are various credit instruments – highly rated corporate bonds or mortgage or credit derivatives which infamously started the big financial crisis of 2007-20??.

Note: This is not to say that credit instruments are bad investments. They are bad only when they are mispriced to the wrong side (when you are getting too little return for too much risk).

This is of course a complex issue that can't be discussed on one (or a few pages).

Volatility Is Only One Measure of Risk

Let's conclude that volatility is only one of the possible measures of risk. There are other tools and measures of risk which address one or both of the issues above with more or less success.

The problem of volatility being non-directional is addressed by measures that adapt the standard deviation concept or other common tools to the one-directionality of risk. Examples include downside deviation, Sortino Ratio, or Value at Risk (VAR). Most of them still fail to address the second problem (they underestimate the risk of extreme events).

If you want to measure risk without the risk of underestimating low-probability extreme outcomes, the only way to do it is by looking as maximum theoretical loss rather than some expected value implied by a return distribution model that you have created based on historical observations. Although 0.01% probability of something looks like zero, it isn't. Although once every 10,000 years means unlikely, it could also mean tomorrow.

Of course this does not mean that you should never invest in anything uncertain or anything volatile (because you wouldn't make any money). It means that while volatility is a useful measure of risk, it is not perfect and it should not be relied upon blindly.

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