Heteroskedastic

Heteroskedastic

Heteroskedastic refers to a condition in which the variance of the residual term, or error term, in a regression model varies widely. 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. These predictor variables have been added because they explain or account for variance in the dependent variable, portfolio performance, then is explained by CAPM. With this factor now included in the model, the performance anomaly of low volatility stocks was accounted for. Extensions of this model have added other predictor variables such as size, momentum, quality, and style (value vs. growth).

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.

Related terms:

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model is a model that describes the relationship between risk and expected return. read more

Error Term

An error term is a variable in a statistical model when the model doesn't represent the actual relationship between the independent and dependent variables. read more

Factor Investing

Factor investing is looks at statistical similarities among investments to identify common factors to leverage in an investing strategy. read more

Generalized AutoRegressive Conditional Heteroskedasticity (GARCH)

Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) is a statistical model used to estimate the volatility of stock returns.  read more

Heteroskedasticity

In statistics, heteroskedasticity happens when the standard deviations of a variable, monitored over a specific amount of time, are nonconstant. read more

Homoskedastic

Homoskedastic refers to a condition in which the variance of the error term in a regression model is constant.  read more

Multi-Factor Model

A multi-factor model uses many factors in its computations to explain market phenomena and/or equilibrium asset prices.  read more

R-Squared

R-squared is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable.  read more

Regression

Regression is a statistical measurement that attempts to determine the strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing variables (known as independent variables). read more

Residual Sum of Squares (RSS)

The residual sum of squares (RSS) is a statistical technique used to measure the variance in a data set that is not explained by the regression model. read more