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Rolling Regression is an analysis of the changing of relationships among variables over time, specifically of measures generated from a linear regression. Visualizing regression outputs like correlation, r-squared, beta and the standard error over time can be helpful in the analysis of risk for stocks, portfolios and factors.
Synonym: moving-period regression, rolling window regression
For context, recall that measures generated from a regression in Finance change over time. As an example, recall each stock has a beta relative to a market benchmark. Imagine a stock with a beta of 1.50, which means it is more sensitive to the ups and downs of the market. What if that company merged with a stable company with a historic beta of 0.60? In this case it may take months for the time series of observed monthly returns to change the beta. In this case it could be incumbent on the analyst to change the beta.
Beta offers a good example because it is used in many calculations in Finance. The weighted average cost of capital (WACC) in corporate finance utilizs beta, as does the CAPM calculation of the expected return. The single-index model relies on beta as well. A rolling regression of beta will highlight changes over time and offer the wise analyst information on what beta to use for future periods.
Ann: With this rolling regression of alpha, notice
how it all came in 1 year?
Jim: Great insight Ann, keep 'em rolling.
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Rolling regression definition for investment modeling (4:44)
The script includes two sections where we visualize and demonstrate the concept of a rolling regression.
We're sitting here in Excel and this is a snippet from our boot camp course (Quant 101).
Here in blue we have 24 monthly returns on a stock Merck and a Market portfolio. Think of this as a 2-year window over which we generated the regression statistics: alpha, beta, standard error, correlation and R-squared.
Now imagine sliding that window down one month, the window now goes from May 2003 to April 2005 and the statistics change.
Our goal is to make our investment models more realistic and accurate, so they adapt to changing relationships, and that we also know about upcoming changes.
Beta, for example, comes from a regression and is used to set expectations on the return and risk of stocks. Notice how the beta changed over time, from 1.43 to 1.28? That's a pretty big move for six months. Let's chart it.
What happened? Well granted this is only a 24-month period, nonetheless we'd have to look at the periods that rolled on here, and rolled off here.
Let's solidify this by creating the rolling regression.
There are four ways to generate regression statistics in Excel, and we'll use the function method here.
First for alpha, or the intercept, use
=INTERCEPT, open parenthesis, the
y-variable Merck, comma, the x-variable the Market, closed parenthesis
and Enter, for an alpha of -0.0245, which is not good performance, but
look at this cell here, Merck lost 26% in one month alone. Identifying
outliers like this can help with your analysis skills.
Second, for beta, use the same procedures and ranges of data except
use the function called
Third is the standard error, which is helpful for finding specific risk
of the stock Merck, and for that we'll use the function
Fourth we'll use the function
and the same procedures for correlation, which is the interpretable
measure with a scale of -1 to +1.
And finally, R-squared or correlation squared for a range of 0 to 1.
Now copy that row of regression statistics down and you've done it. Review these with line or bar charts and your portfolio analysis and model building skills are sure to improve.
Click box for answer.
Time Value of Money
Still unclear on rolling regression? Leave a question in the comments section on YouTube or check out the Quant 101 series with 27 free Excel tutorials.
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