## DEFINITION of Heteroskedastic

Heteroskedastic refers to a condition in which the variance of the residual term, or error term, in a regression model varies widely. If this is true, it may vary in a systematic way, and there may be some factor that can explain this. If so, then the model may be poorly defined and should be modified so that this systematic variance is explained by one or more additional predictor variables.

The opposite of heteroskedastic is homoskedastic. Homoskedasticity refers to a condition in which the variance of the residual term is constant or nearly so. Homoskedasticity (also spelled "homoscedasticity") is one assumption of linear regression modeling. Homoskedasticity suggests that the regression model may be well-defined, meaning that it provides a good explanation of the performance of the dependent variable.

## BREAKING DOWN Heteroskedastic

Heteroskedasticity is an important concept in regression modeling, and in the investment world, regression models are used to explain the performance of securities and investment portfolios. The most well-known of these is the Capital Asset Pricing Model (CAPM), which explains the performance of a stock in terms of its volatility relative to the market as a whole. Extensions of this model have added other predictor variables such as size, momentum, quality, and style (value vs. growth).

These predictor variables have been added because they explain or account for variance in the dependent variable, portfolio performance, then is explained by CAPM. For example, developers of the CAPM model were aware that their model failed to explain an interesting anomaly: high-quality stocks, which were less volatile than low-quality stocks, tended to perform better than the CAPM model predicted. CAPM says that higher-risk stocks should outperform lower-risk stocks. In other words, high-volatility stocks should beat lower-volatility stocks. But high-quality stocks, which are less volatile, tended to perform better than predicted by CAPM.

Later, other researchers extended the CAPM model (which had already been extended to include other predictor variables such as size, style, and momentum) to include quality as an additional predictor variable, also known as a "factor." With this factor now included in the model, the performance anomaly of low volatility stocks was accounted for. These models, known as multi-factor models, form the basis of factor investing and smart beta.