Definition of Heteroskedastic
Let me explain to you what heteroskedastic means. It refers to a situation where the variance of the residual term, or error term, in a regression model varies widely. If this happens, it might vary in a systematic way, and there could be some factor that explains it. In that case, your model is probably poorly defined, and you should modify it by adding one or more predictor variables to account for that systematic variance.
The Opposite: Homoskedastic
The opposite of heteroskedastic is homoskedastic. This is when the variance of the residual term is constant or nearly so. Homoskedasticity—sometimes spelled homoscedasticity—is one of the assumptions in linear regression modeling. If it's present, it suggests your regression model is well-defined, providing a solid explanation for the dependent variable's performance.
Breaking Down Heteroskedastic
Heteroskedasticity is a key concept in regression modeling, and in the investment world, these models explain the performance of securities and portfolios. The most famous one is the Capital Asset Pricing Model (CAPM), which ties a stock's performance to its volatility compared to the overall market. Over time, extensions to this model have included other predictor variables like size, momentum, quality, and style—value versus growth.
These variables were added because they explain variance in the dependent variable, such as portfolio performance, that CAPM alone doesn't cover. For instance, the developers of CAPM knew their model couldn't explain an anomaly: high-quality stocks, which are less volatile than low-quality ones, often performed better than CAPM predicted. CAPM claims higher-risk stocks should outperform lower-risk ones, meaning high-volatility stocks should beat low-volatility stocks. But in reality, those high-quality, less volatile stocks did better than expected.
Later researchers built on CAPM—which had already been extended with factors like size, style, and momentum—by adding quality as another predictor variable, or 'factor.' Once this was included, the anomaly of low-volatility stocks was explained. These enhanced models, called multi-factor models, are the foundation of factor investing and smart beta.
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