# What Happens to the R Square When There Is a Decline in Stocks?

by Walter Johnson

Regression analysis is an important tool in the social sciences, especially economics. The r-squared is a measure of “fit” in a regression analysis based upon what you are trying to explain. The idea of a “decline in stock prices,” by itself does not mean anything unless it is a part of a broader research project. Stock prices ad their movements are important questions, the dominant questions among those following the stock market. It, however, must be contextualized to become meaningful.

## Model

A regression model is generally trying to explain the movement of a dependent variable through a group of independent variables. For example, a stock model might be trying to figure out which variables cause price fluctuation in a firm's assets. A researcher might theorize, according to the past literature and studies on the subject, that fuel costs, macroeconomic stability, investor confidence and interest rates are the main, most important, variables explaining movements in stock prices. This is the model at its most basic.

## Capital Asset Pricing Model

Capital asset pricing model (CAPM) is only indirectly a statistical theory. It generally rests on two definitions of risk: that of the market as a whole, and that of the specific firm in which you are invested. These become two independent variables when trying to grasp the causes for investment returns. Hence, when comparing two specific securities, there are two forms of risk that must be carefully analyzed and kept separate from each other. The r-squared in this particular case behaves no differently from any other regression model. It measures the “fit” between the actual return on investment and its connection to its major causal risk factors: market and firm risk. This forms the very basic concept of CAPM.

## Decline in Prices

This same model might be trying, more specifically, to explain how and why stock prices fall. The same variables would prevail, and are the “independent variables” that dictate how and why prices fall. Risk, according to the CAPM, is two-fold, and this model assumes that the decline in stock prices -- presumably causing a loss -- is based on a faulty reading of the market. When prices decline and harm your portfolio, there is no direct relationship between that fact and the statistical model itself. What has occurred is that your reading of the market has been false, and either has misread either the firm and its financial health on the one hand, or, on the other, the state of the market as a whole.

## R-Squared

CAPM is just a very specific and controversial use of regression analysis. It is a single model, while regression analysis itself can use any set of variables to discuss price decline. Such concepts as interest rates, macroeconomic stability and investor confidence themselves are just specific aspects of market risk. While other variables such as management competence are specific to the firm. If you lose money, it is not the fault of the model and the r-squared it as generated. Chances are, it has more to do with the data you have entered and your definition and analysis of the two major risk categories.

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