# How to Calculate the Beta Coefficient for a Single Stock

### Calculating volatility to structure your investing strategy.

Sep 10, 2015 at 11:44PM

A stock's beta coefficient is a measure of its volatility over time compared to a market benchmark. A beta of 1 means that a stock's volatility matches up exactly with the markets. A higher beta indicates great volatility, and a lower beta indicates less volatility.

Calculating beta for a given stock is not too difficult, despite the intimidating jargon. To calculate it, all you need is some market data over a period of time and a spreadsheet program.

Why calculate beta yourself?
There are many online resources to find a given stock's beta over various time frames and compared to various market benchmarks. Those are great tools, but oftentimes they limit how much control you have over the calculation. For example, your stock may be highly concentrated in a foreign country. In that case, it may make sense to forgo the standard market benchmark, the S&P 500, and instead use an international market index.

Time frames are also highly important and should be customized to your specific investment horizon. If you're a buy and hold investor, you should use a longer time period to calculate beta, maybe five or even 10 years. If you're a trader, buying and selling frequently, you should use a beta over a much shorter time frame, potentially just a few weeks, days, or even less.

Lastly, there are a few different methodologies for calculating beta -- from the simplistic and effective like we'll use here, all the way to highly academic models using calculus, interest rates, and expected return estimations. Many online calculators use these more sophisticated tools, which, in my opinion, only add complexity and uncertainty to the result.

Calculating beta yourself gives you full control over how you determine the beta for your investment. Online tools have their place, but nothing gives you a better understanding of a stock than doing the math yourself.

Doing the calculation
To calculate the beta coefficient for a single stock, you'll need the stock's closing price each day for a given period of time, the closing level of a market benchmark -- typically the S&P 500 -- over the same time period, and you'll need a spreadsheet program to do the statistics work for you.

In the first column, insert the date range to be used to calculate the beta. In the second column add the corresponding closing price data for the stock in question, and in column three, insert the closing level for the index you will be using. In this example will calculate the beta for the Coca-Cola Company compared with the S&P 500 in August 2015.

Next, we need to calculate the daily price change for both the stock and index as a percentage. To do that, subtract the more current price from the previous day's, then divide by the previous day's price. Multiply by 100 to show the result as a percentage.

Lastly, we'll compare how the stock and the index move relative to each other with a covariance formula and then divide that result by the variance of the index alone. In non-math terms, we're going to compare how the stock and index move together relative to how the index moves by itself. The result is the beta.

This results in a beta of 0.57 for the Coca-Cola Company compared to the S&P 500 for August 2015. Coca-Cola, therefore, was less volatile than the S&P for this month.

Whether you're calculating a beta over a one month or one decade time frame, or if you're using the S&P 500 or the Shanghai Stock Exchange Composite index, the process is the exact same. There are other, more academic methods for calculating a company's beta, but this technique is statistically sound and much simpler for the typical investor. Armed with this tool, you can now calculate your own betas, custom tailored to fit your stocks, your investment horizon, and with the perfect index to match.

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Jay Jenkins has no position in any stocks mentioned. The Motley Fool recommends Coca-Cola and has the following options on it: long January 2016 \$37 calls, short January 2016 \$43 calls, and short January 2016 \$37 puts on. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.

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