Beta Definition and Investment Modeling Tutorial

Beta coefficient for investment analysis

Intermediate

Beta is a measure of market-related risk. It is the slope of the line of best fit from a single-variable linear regression of the asset returns (y-axis) versus the Market (x-axis). Beta is a key component of the Capital Asset Pricing Model (CAPM) and is used in asset valuation and for calculating the cost of capital in corporate finance.

Synonym: beta coefficient

For context, beta provides a measure of backward-looking sensitivity of a stock to a benchmark. It is the result of a regression of monthly observed rates of return typically. While any regression will return a slope coefficient, it may be irrelevant as the R-squared approaches zero.

To illustrate, imagine a scatterplot that looks like a random pattern, akin to a shotgun pattern. In this case relying on beta to make estimates about its return expectations and risk is questionable. So it is incumbent on the researcher to find a better estimate for beta. Most investors don't take this step however, instead electing to accept the beta provided by service providers.

A diversified portfolio's beta differs from a stock's beta in that it typically has a much higher R-squared. For example, a stocks's R-squared customarily fits in the range from 0.10 to 0.50, while for a portfolio relative to an appropriate benchmark, a range from 0.50 to 0.95 is more common. This has a profound impact on its applicability.

In a Sentence

Bev: Ann, when we report our beta we really should include R-squared to see how valid beta is, right?
Ann: I think so. But I guarantee Kay and Jim in Sales will say it's overkill.

Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

Beta definition for investment modeling (4:11)

Video Script

The script includes two sections where we visualize and demonstrate the calculation of beta.

Visualize

We're sitting right here in Excel, and this is a snippet from our boot camp course.

Here we plotted 60 monthly returns on the stock Merck on the y-axis. And 60 monthly returns on the Market on the x-axis, for the same time period.

So for this one month the Market was up 10% and Merck was up 14%.

This line of best fit minimizes the differences between the line and each of the points. That's what linear regression does.

The slope of this line, in the formula here, is 1.2274. That is beta. And the formula for the line, given in y = mx + b format, reads like this: to estimate the monthly return for Merck, multiply the Market return by 1.2274 and then subtract 0.0074.

Again, beta is a measure of market related risk. Notice it isn't an absolute measure of risk like volatility, also known as standard deviation. Beta is used to see how Merck's returns relate to movements in the Market (ie, relative to the Market).

And for cost of capital calculations, this is highly simplified, but if you expect equities to go up by 6%, then the cost of capital for Merck was 6% * 1.2274 or 7.36%. Next, let's demonstrate.

Demonstrate

There are four ways to generate regression statistics in Excel. First, you can use the chart output, but that isn't the easiest.

A lot of people use the Data Analysis method, with output like this, and beta is down here in the coefficient column.

Third is the function method, where you use the function called =SLOPE(). Input the stream of returns for the y-variable first, then comma, then the x-variable and hit Enter.

Fourth is the =LINEST() method which gives added functionality but is too advanced to cover here.

Quiz

Click box for answer.

A stock's beta was 1.25, the expected return on the market was 6.29%, what would you expect for the stock's return? (assuming a 0% risk-free rate) | 5.03% or 7.86%?

7.86%

A portfolio's R-squared is generally higher than that of an individual stock because a portfolio has lower specific risk? | True or False?

True

Questions or Comments?

Still unclear on beta? Leave a question in the comments section on YouTube or check out the Quant 101, specifically How to find the expected return on a stock using the CAPM Model. Also see examples of betas for thousands of US-traded stocks in our Stocks section.

Related Terms

Our trained humans found other terms in the category risk-adjusted performance.

Beta Definition and Tutorial