On any given day when the stock market is open, if the broad market indices are down a percentage point or two, you’ll undoubtedly hear about “stock market volatility.” But what exactly is meant by this phrase? Does stock market volatility just describe the market when stocks decline? Or does it refer to a specific measurement that describes how stocks are moving up and down? In this article, we’ll cover all of the above. We’ll look at the different ways the phrase stock market volatility is used then look at how we can manage our investments when volatility is high.

## General stock market volatility

Let’s start off with the more general usage of the term volatility. Everyday investors often refer to volatility when the stock market is in turmoil a bit, maybe during a correction or a crash. We saw a significant drawdown in stocks during March 2020 with the major indices all down 30% and more. This was definitely a “volatile” time.

How concerned should we be as investors about general stock market volatility? Well the reality is, not much. Unless you’re a retiree and susceptible to sequence of returns risk, most investors can simply focus on long-term goals and not get too wrapped up in the volatility of the moment. I know, easier said than done.

But, let’s look at some history. This history should perhaps calm your nerves during market volatility.

I first saw this chart over at the Bogleheads message board, and I think it’s a really great overview of the stock market and regular volatility. This chart shows the annual return each year for the S&P 500 and the largest drawdown that occurred during that year. So, in 2008 for instance, at one point the S&P 500 was down 49%, but it finished the year itself down 38%. *Note that 2020 is obviously incomplete at the time of writing and when this graphic was made.*

What can we learn from this chart? Let’s note a few observations:

- The S&P 500 was up 30 of the last 40 years
- Despite finishing up 75% of the time, the S&P 500 averaged a 13.8% intra-year drawdown. That’s pretty remarkable!
- In the 41 years of stock market action shown in the chart, 23 years had a drawdown of at least 10%. 56% of the years had a stock market correction of at least 10%.
- If we define stock market crashes as drawdowns of at least 30%, this happened five times during this span of time. Interestingly, when this occurred, the S&P 500 finished much higher than the lows of the crash intra-year. For example, in 1987, despite a 34% drawdown, stocks finished up 2% on the year. In 2002, stocks were down 34% at one point, but finished a bit higher at -23%. In the crash of 2008, the index was down 49% but finished down 38%. While 2020 is still underway, stocks are already much higher off the lows of the March 2020 coronavirus-related crash.

To sum up, we should expect stock market volatility, and we should expect a rebound from any significant drawdown (often within the same year!). This data should have a profound impact on your view as an investor and give you confidence to stay the course with your long-term strategy regardless of how ugly things might be in the moment.

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## Measuring stock market volatility

In a strict world of analysis, volatility often refers to risk, and risk is usually defined via the statistical tool known as standard deviation. Standard deviation is a statistical measurement that sheds light on how spread out the historical returns of an investment are from its average or mean (or expected return). Simply put, if an investment usually returns 8% each year, but the actual returns over time have a huge range going from -40% to +50%, then the standard deviation is going to be high. Compare this to a much more “stable” investment that still returns 8% each year, but typically never varies from a range in the 5% to 11% range.

Let’s look at an example of how to calculate standard deviation for a particular stock. Here are recent annual returns for Tesla (TSLA):

- 2011: 7%
- 2012: 19%
- 2013: 344%
- 2014: 48%
- 2015: 8%
- 2016: -11%
- 2017: 46%
- 2018: 7%
- 2019: 26%

#### How to calculate the standard deviation of annual returns

To calculate the standard deviation, let’s first get the mean of the annual returns. We do this by adding up the values then dividing by the number of values. Mean = (7 + 19 + 344 + 48 + 8 – 11 + 46 + 7 + 26) / 9. The mean is 54.89.

Now we need to calculate the deviation of each value from its mean, then square each value. So, in 2011, we had a 7% annual return. The deviation away from the mean is determined by subtracting the mean from it, or 7 – 54.89. That would lead to -47.89. Then we square it to get 2,293.45. Let’s do that for each annual return:

- 2011: 7% –> 2,293.45
- 2012: 19% –> 1,288.09
- 2013: 344% –> 83,584.59
- 2014: 48% –> 47.47
- 2015: 8% –> 2,198.67
- 2016: -11% –> 4,341.49
- 2017: 46% –> 79.03
- 2018: 7% –> 2,293.45
- 2019: 26% –> 834.63

Now if we take the mean of these values, it gives us the variance. We get the mean, once again, by adding them up then dividing by the number of terms. Mean = (2,293.45 + 1,288.09 + 83,584.59 + 47.47 + 2,198.67 + 4,341.49 + 79.03 + 2,293.45 + 834.63) / 9. The mean is 10,773.43. The variance is 10,773.43.

You can always get the standard deviation from the variance by simply taking the square root of the variance. The square root of 10,773.43 is 103.8. Therefore, our standard deviation is 103.8.

This is pretty big! This also shouldn’t be a surprise since the Tesla returns are pretty much all over the place. That single year of 344% really throws it off.

Now to calculate stock market volatility using the standard deviation, you could look at this process for a broad index such as the S&P 500. Typically, we also would use daily returns rather than annual returns. Taking the standard deviation of daily returns is a very common way to measure risk and volatility.

#### Understanding risk-adjusted returns

Once you get a feel for the concept standard deviation and how it works, you can better understand the concept of risk-adjusted returns. While most people talk simply about returns, the idea of risk-adjusted returns is actually quite important especially for people such as retirees. Risk-adjusted returns essentially describe the returns along with the degree of risk that must be accepted to meet such returns.

The Sharpe Ratio is a common way to calculate risk-adjusted returns. Developed by William F. Sharpe, the Sharpe Ratio in its simple form is calculated by dividing the average return by its standard deviation. By putting the standard deviation in the denominator, you can already tell that investments with a higher standard deviation will result in a lower Sharpe Ratio assuming the average returns are equal. So, the ideal investment is one with satisfactory average returns with a very low standard deviation. The Sharpe Ratio of such an investment would be quite high in comparison to most investments.

## Understanding the volatility index (VIX)

The Volatility Index (often referred to as “the VIX”) is one of the most commonly cited barometers of overall market volatility. The VIX is also sometimes called the “Fear Index” or “Fear Gauge.” The VIX was created by the Chicago Board Options Exchange. It is an index based on options activity that tends to provide an indicator of market volatility and market sentiment. During major stock market crashes, you may have noticed the VIX get a lot more attention with the VIX spiking higher from previous values.

#### How is the VIX calculated?

The VIX is calculated using a formula that averages the prices of a variety of put and call options that are trading in the market. When investors are more aggressively buying a range of options and thus driving up the prices on these options, it typically results in an increase in implied volatility and the VIX will go up. If you want to get into the technicals of the formula, you can read through the CBOE white paper that details how the VIX works.

## What causes stock market volatility

The stock market moves up and down on a wide range of variables and forces, and therefore, volatility can be caused by a wide range of items as well. Major moves lower in the stock market can be caused by a correction to overvalued stocks (e.g. think of the 2000 dot-com crash), it can be caused by a major blow to the financial system (e.g. the 2008 financial collapse) or it can be caused by major global events such as a pandemic as we saw in March 2020 with the coronavirus pandemic.

But it’s not always just major events that cause volatility. As we noted above, a 10% correction happens regularly. Since the stock market is a market of millions of transactions, individuals and entities buying and selling stocks every day the market is open, it can cause movement in prices. Sometimes, the movement gets momentum and traders attempt to front-run the momentum. If stocks sell off one day, traders might sell even more assuming that it might continue. Because the market is dynamic, these momentum driven moves are not unusual.

## How should you manage your portfolio?

There are two major implications to what we’ve discussed in this article on stock market volatility. First, let’s address how we should react to general market volatility that leads to major moves in the overall market. Second, let’s discuss how we might limit portfolio volatility.

As we saw above, the most important thing you can do as an individual investor is stay the course when you experience broad stock market volatility. In fact, you might get used to such moves that you learn to take advantage of them and rebalance into equities or put more money into play when the market is down quite a bit. By staying the course during volatile events and market drawdowns, you’ll do very well long term.

Now, portfolio volatility is a different animal than stock market volatility. The reason is the volatility of your portfolio is dependent on how you’ve constructed your portfolio. For example, if you have 100% of your assets in Tesla, you’re going to have a much more volatile portfolio than, say, a portfolio of 60% stocks and 40% bonds made up of index funds and ETFs. And as you understand the concepts behind standard deviation and the Sharpe Ratio, this can really inform how you set up your portfolio. Volatility is one of the reasons we previously spelled out rules for buying individual stocks. These rules can help mitigate single stock risk.