# How to Calculate Beta From Volatility & Correlation

When investors speak of "Beta," they are referencing a unique term that is associated with the volatility or risk present in a specific investment asset. The Beta of a given security also plays a critical role within the capital asset pricing model, or CAPM, an often used formula that helps investors derive the anticipated return from an asset.

In order to calculate Beta, analysts can utilize a variety of market data that is easily accessible, including the current volatility of the stock and/or market as well as the specific correlation between the security in question and the market as a whole. Although producing an accurate measure of volatility and correlation requires its own specific set of mathematical formulas, it is possible to effectively and accurately produce a resulting sum that is representative of current Beta.

### Tip

Beta is a mathematical product derived from the standard deviation of a security and the market as a whole. Using this information, investors can better determine how a given stock compares to greater market trends in terms of volatility, risk and return. The process of calculating Beta will allow investors to gain in-depth knowledge of the recent price history for assets and indexes at large.

## Exploring Standard Deviation and Volatility

In order to accurately assess the Beta of a given security, it is first necessary to calculate the current volatility of the stock and the market as a whole. The term volatility is, in fact, synonymous with the standard deviation of a particular asset. In order to do this, analysts must compute the standard deviation of the historical price record for both the stock in question and the market. With this information, a correlation between the security and market can quickly be created.

Broadly defined, standard deviation can be thought of as the extent to which the price of an asset varies relative to the price average over the given time period. More specifically, the standard deviation of a stock is calculated through a series of mathematical processes.

## Calculating Standard Deviation

First, the mean, or average of all prices must be derived; this can be gathered by adding together all of the prices within the designated time frame and then dividing by the total number of price points gathered. So, if there are 25 price points being used, the formula would be (where P equals Price):

**M = (P ^{1 }+ P^{2 }... + P^{25}) / 25**

It is then necessary to subtract the mean from each of the price data points gathered and then multiply the result by itself, a process referred to as "squaring."

**(P ^{1 }- M)^{2}**

Once these values have been obtained, the average of the previously squared results must be calculated. Finally, investors can take the square root of the previous average to determine the standard deviation.

**(P ^{1 }- M)^{2} +^{ }**

**(P**

^{2 }- M)^{2}+ ...**(P**

^{25 }- M)^{2 }/ 25This same process must be undertaken for both the specific asset in question and the market as a whole. Once the standard deviations have been generated for both, correlations can be drawn.

## Calculating Asset and Market Correlation

Relative to the steps required to produce a standard deviation, the process required to determine the level of correlation between the particular stock being assessed and the market is similarly complex. Once the standard deviations have been obtained, you must then calculate the difference between a specific price point for both the market and stock and the mean price point for the entire time duration of the market and the stock.

These two differences must then be multiplied together, and the entire process must be repeated for each available price point. Once this has been completed, all of the resulting values must be added together and then divided by the product of the two standard deviations.

As a last step, take the answer derived in the prior step and divide it by the total number of data points minus 1. This should give you a figure between -1 and 1, which will act as the correlation value between the two entities.

## Assessing Stock's Beta Value

Now that the correlation coefficient has been obtained, it is possible to accurately assess the Beta value of a given stock. Using a standard regression model, the correlation between asset and market is largely synonymous with Beta. This is due to the fact that values for correlation and volatility are bounded to a range of -1 to 1. With that in mind, investors or analysts seeking to obtain Beta within the confines of the standardized regression model can use the correlation value calculated in the previous steps as a representation of Beta.

In this model, the market as a whole is assigned a value of 1 on a scale of -1 to 1. As the correlation coefficient moves closer to the value of 1, this implies that the stock moves largely in line with market forces. A movement away from 1 implies that the stock's pricing is increasingly "erratic" relative to the movement of the market.

Outside of the standard regression model, it is possible to use the standard deviation of the stock compared to the standard deviation of the market to more broadly assess Beta. Simply dividing the standard deviation of the stock by the standard deviation of the market could lead to a value greater than 1, which can signify that the stock often exceeds the highs and lows witnessed in the market. Consequently, investors should prepare for a higher degree of risk. Using this model, it is not uncommon to experience Beta values above 1 for in-demand, "hot" stocks such as those found in the technology sectors.

## Closing Thoughts on Beta

For beginning investors, the calculations mentioned here may initially seem somewhat daunting. This is due in large part to the fact that much of the deeper market analysis possible in today's world of investing relies upon the investor having extensive knowledge of current market conditions and the various mathematical formulas required to manipulate and reorganize this information.

Because of this, it is strongly recommended that investors with less experience continue to explore Beta and various other Beta coefficient examples drawn from market analysis before beginning to leverage this knowledge in real-world trading. In many situations, novice investors could stand to benefit greatly from consulting with financial advisers or investment professionals to validate their own investment strategies and determine whether or not their conclusions concerning market activity are as accurate as they hoped.

All investments carry a degree of risk. Using the Beta calculations available to investors, it is possible to gain a better idea of just how much this risk exposure stands to hurt or benefit an investor who has their sights set on a particular asset. With practice, the process of calculating Beta becomes significantly less difficult and more streamlined.

References

Tips

- Volatility measures the stock’s total risk. Beta measures one component of total risk: the stock's systematic risk. If the beta you calculate is greater than 1, then the stock has more systematic risk than the broad stock market. If the beta you calculate is less than 1, the stock has less systematic risk than the stock market.
- Beta tells you how much the stock return is expected to move on average for a 1 percent move in the broad market return. For example, if the stock’s beta is 2 and the market return increases by 1 percent, your stock is expected to increase by 2 percent. On the other hand, if the market return decreases by 1 percent, your stock is expected to decrease by 2 percent.

Warnings

- There are some boundaries that your statistics must fall within. If they do not, your starting data is not correct. The correlation coefficient is bounded by minus 1 and positive 1. The volatility statistics must be positive. Your calculated variance must be positive. The covariance and beta are not bounded, but negative values are rare.

Writer Bio

Ryan Cockerham is a nationally recognized author specializing in all things business and finance. His work has served the business, nonprofit and political community. Ryan's work has been featured on PocketSense, Zacks Investment Research, SFGate Home Guides, Bloomberg, HuffPost and more.