# How To Quantify The Volatility Of Your Portfolio

When times get scary, one approach to financial protection is to build a portfolio around solid, low-volatility, low-risk stocks. Sometimes, identifying volatility can be as simple as looking at a chart.

For example, take a look at this chart comparing Apple Inc. (NASDAQ: AAPL) to biotech company Dynavax Technologies Corporation (NASDAQ: DVAX).

All it takes is a quick look at the “choppiness” of Dynavax’s share price compared to Apple’s to see that Dynavax is a more volatile stock. However, sometimes the contrast is not so obvious, and “visual choppiness” is not a very well-defined means of differentiation.

Related Link: Understanding Stock Market Cycles

### How can volatility be quantified?

The S&P 500 index is a composite of all of its component stocks, meaning that when the S&P 500 moves x amount, many of its component stocks have moved greater than x amount, and many of them have moved less than x amount. One way to define volatility for a stock is “a measure of how much more or less than the overall index a particular stock moves on the average day.”

Scientists are always trying to determine how things are related to each other. They collect a bunch of data about two variables and then look for a pattern. After collecting data, the next step is looking for a pattern. The data might look like this image.

That looks like a mess. However, they could instead end up with something like this image.

That image appears to have a pattern to it. The pattern indicates that the two variables likely have some sort of effect on each other, much like time has an effect on share price. The next step is to determine the strength of the effect.

### Regression Analysis

The idea behind regression analysis is to take a data plot and add a trend line to the plot, then determine how closely all of the data points fall to the trend line. The closer the data points fall to the trend line, the stronger the effect, or correlation, between the two variables.

Stock traders have a beautifully-defined “trend line” to use for regression analysis: the S&P 500 Index! To determine the volatility of a stock, the key is to look at how closely the stock’s price fluctuations correlate to the changes in the S&P 500 Index.

This correlation between a particular stock and the S&P 500 is called beta. If you watch CNBC at all, you’ve probably heard about “high-beta” or “low-beta” stocks. These terms refer to volatility.

### Calculating Beta

Here’s an overview of how beta is calculated:

1. Determine the variance of the stock and the variance of the S&P 500 over a given period of time (one year, for example). The variance is a measure of how closely the movements of the charts resemble a linear trend line.

2. Determine the covariance between the stock and the S&P 500 over the same period. Covariance measures how much the stock and the S&P 500 move in tandem.

3. Divide the covariance by the variance, and that’s beta.

### Understanding The Result

Almost any website that includes stock metrics will include a measure of a stock’s beta.

A beta of 1 means that the stock has moved, on average, exactly the same amount (in percentage terms) on a daily basis as the overall market has over the past year. A beta of less than 1 means that the stock is less volatile than the overall market, and a beta of greater than 1 means that the stock is more volatile than the overall market. The higher the beta, the more volatile a stock’s share price has been.

Disclosure: Author owns shares of Apple and Dynavax.

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