Beta is a measure of an investment's volatility relative to the market as a whole. For the stock market, that usually means a benchmark broad market index like the S&P 500. You can compute **beta values of stocks** yourself using a statistical formula and details about the price of the stock and the benchmark, or you can use an online **stock beta calculator** or beta lookup tool. Stocks with higher beta are more likely to have outsized returns, whether higher or lower than the market as a whole.

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**The stock beta definition** is the covariance of the stock's price and a broad market index's price divided by the variance of the index price. A stock more volatile than the market has a beta value greater than 1, and one that's less volatile than the market has a beta value less than 1.

## Understanding Beta Values of Stocks

The quantity called beta, sometimes written using the Greek letter as **β**, is a measure of the volatility of a stock or another investment. It's not an absolute measure of volatility but one determined based on the market as a whole.

It's used in what's called the **capital asset pricing model**, a formula used to explain that stocks that are more volatile, and hence riskier, can provide greater returns when they do well. Of course, they can also cause you to lose your money if they do poorly.

Beta is one of the many factors that you may look at it in deciding to make investments. You'll usually not want to pick a stock investment solely based on beta, since you'll also be interested in the fundamentals of the company behind the stock and how it's performing relative to other businesses in its same sector.

## Determining Beta Values of Stock

You can compute beta yourself if you have historic prices for a stock and a benchmark index such as the S&P 500 or another index that is relevant to the stock in question. For foreign stocks, you'd likely look at a stock market index from the country where the stock is traded.

Determine the variance of the index price over time using the standard statistical variance formula. This is the **sum of the squares of the differences between each price value and the mean, or average price, divided by the total number of price values you have**. You can also compute it using many software tools, including Microsoft Excel and plenty of statistical software. It's also the square of the standard deviation, which can be handy to know if you have a calculator or computer program that has a function to find the standard deviation but not the variance.

Then, find the covariance of the particular stock price and the index price. This is the **sum of the products of the differences between the corresponding individual and mean values of the two prices, divided by the total number of pairs of values**. Like the variance, the covariance can be computed directly or with the help of statistical or spreadsheet software. You can then **divide the covariance by the variance** to get the beta value.

## Other Ways to Find Beta

You don't need to recompute beta using the variance and covariance every time. You can set up a simple formula in Excel to do so when you feed in new stock and index prices or create a formula or script in another tool of your choice if you know how to do so.

You can also use an online beta calculator tool or look up a published beta value. Beta values are sometimes shared by investment firms, financial news and information sites and similar sources.

## Beta and Risk

Beta is often considered a measure of risk, so it can be helpful in determining how much risk you're exposed to in your portfolio. Generally, adding a high-beta stock will be increasing your risk of losing money (or of making good money), and adding a low-beta stock will decrease your portfolio's total risk.

Since beta only measures previous stock prices, it **may not fully capture risk inherent in a particular investment going forward**. If you know that a company has taken a risky decision, such as entering a new industry, or that it spun off or closed down a risky division, you might estimate risk to be higher or lower than the value you'd get from beta alone. Beta values can also be less useful if the risk of the market itself changes, since beta values are relative to market prices.

Also note that it can be **hard to directly compare beta values determined from two different indexes**. For instance, if you compute the beta value of a French stock using a French stock market index and a U.S. stock using the S&P 500, it can be hard to use those values to say one stock is more volatile than another since one volatility measure is relative to the French stock market and one relative to the U.S. stock market. Similarly, you can't directly compare beta values of stocks and bonds.

## Beta of the Index Itself

By definition, the covariance of a quantity and itself is the same as the quantity's variance. For beta purposes, that means that the beta formula for the index itself always comes down to the **variance of the index's price divided by itself**, which is always 1. While knowing that a particular stock's beta value is 1 tells you that it is roughly as volatile as the market itself, knowing that the index's beta value is 1 is not a useful piece of information, since it is always 1 by definition.

## Understanding Alpha Values

Another Greek letter that sometimes pops up in investment discussions is alpha, or **α**. Alpha is the return of an investment or investment above or below the return delivered by the market as a whole. It's often used to evaluate mutual funds and their managers.

It's usually measured in percentage points relative to a broad index like the S&P 500, so that an alpha of -2 would mean that the investment did 2 percent worse than the index, while an alpha of 3 would mean it did 3 percentage points better. You can easily calculate alpha if you have the rate of return of a stock and of the index of your choice for a given period of time simply by **dividing the stock's return by the index's return and multiplying by 100** to generate a percentage.

By definition, the index itself has an alpha of 0. Naturally, you will do well if you invest in opportunities that turn out to have high alpha, but determining which these may be is where the difficulty lies in investment. Past high alpha doesn't guarantee future high alpha, and it's not at all uncommon for a soaring stock to eventually return to more average or even negative alpha values.

## Linking Alpha and Beta Values

Since stocks with high beta are more volatile, they're more likely to have either **high positive or low negative alpha**. Like beta, alpha can't tell you if an investment made money or lost money unless you know how the underlying index did, since it's a relative measure. You also can't directly compare alpha values determined from different indexes.