# Heteroscedasticity Explained: Definition, Types, and Impact on Finance

![Heteroscedasticity](https://www.investopedia.com/thmb/5OcFKT9DnRGOCnJqhEyvm8Obzlw=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Heteroscedasticity-4195124-3x2-blue-b87819cfe00743baaa78cb9c70a4bc77.jpg)

*— Investopedia / Joules Garcia*

## What Is Heteroskedasticity?

Heteroscedasticity, or heteroskedasticity, emerges in statistics when the standard deviations of a predicted variable vary over time. In finance, this manifests as changing volatility in stock and bond prices, challenging the assumptions in linear regression models. It can affect the precision of econometric and financial analyses, especially those using the Capital Asset Pricing Model (CAPM).

### Key Takeaways

*   Heteroskedasticity occurs in statistics when the standard deviations of a variable, monitored over time, are non-constant.
*   Conditional heteroskedasticity is linked to past periods' volatility, whereas unconditional heteroskedasticity involves structural changes not related to past volatility.
*   In finance, heteroskedastic patterns are observed in stock and bond prices, impacting models like CAPM.
*   While heteroskedasticity doesn't bias coefficient estimates, it reduces their precision, affecting model reliability.
*   Unconditional heteroskedasticity can relate to predictable cyclical variables, unlike conditional heteroskedasticity, which is not predictable.

![Heteroskedasticity](https://www.investopedia.com/thmb/4Sla7gn1oEesGSFp7aopQBrbIy0=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Heteroskedasticity22-ce5acc2acef6494d91935588b0599579.png)

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> **Important**
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> While heteroskedasticity does not cause bias in the coefficient estimates, it does make them less precise; lower precision increases the likelihood that the coefficient estimates are further from the correct population value.

## Understanding the Fundamentals of Heteroskedasticity

In finance, conditional heteroskedasticity is often seen in the prices of stocks and bonds. [The level of volatility](https://www.investopedia.com/articles/active-trading/040515/how-profit-volatility.asp) of these equities cannot be predicted over any period. Unconditional heteroskedasticity can be used when discussing variables that have identifiable seasonal variability, such as electricity usage.

As it relates to statistics, heteroskedasticity (also spelled _heteroscedasticity)_ refers to the error variance, or dependence of scattering, within a minimum of one independent variable within a particular sample. These variations can be used to calculate the margin of error between data sets, such as expected results and actual results, as it provides a measure of the deviation of data points from the mean value.

For a dataset to be considered relevant, the majority of the data points must be within a particular number of standard deviations from the mean as described by Chebyshev’s theorem, also known as Chebyshev’s inequality. This provides guidelines regarding the probability of a random variable differing from the mean.

Based on the number of standard deviations specified, a random variable has a particular probability of existing within those points. For example, it may be required that a range of two standard deviations contain at least 75% of the data points to be considered valid. A common cause of variances outside the minimum requirement is often attributed to issues of data quality.

The opposite of heteroskedastic is [homoskedastic](https://www.investopedia.com/terms/h/homoskedastic.asp). Homoskedasticity refers to a condition in which the variance of the residual term is constant or nearly so. Homoskedasticity is one assumption of linear regression modeling. It is needed to ensure that the estimates are accurate, that the prediction limits for the dependent variable are valid, and that confidence intervals and p-values for the parameters are valid.

## Exploring Different Types of Heteroskedasticity

### Unconditional

Unconditional heteroskedasticity is predictable and often ties to cyclical variables. Examples include increased retail sales during holidays or more air conditioner repairs in warmer months.

Variance changes can link directly to specific events or markers if shifts aren't seasonal. An example is the rise in smartphone sales when a new model launches, showing event-based but not seasonal cycles.

Heteroskedasticity can also occur when data approach a boundary, causing smaller variance due to range restrictions.

### Conditional

Conditional heteroskedasticity is unpredictable. Analysts can't easily foresee when data will scatter more or less. Financial products often exhibit conditional heteroskedasticity since not all changes stem from specific events or seasons.

A common application of conditional heteroskedasticity is to stock markets, where the volatility today is strongly related to volatility yesterday. This model explains periods of persistent high volatility and low volatility.

## Key Considerations for Heteroskedasticity in Financial Models

### Heteroskedasticity and Financial Modeling

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)](https://www.investopedia.com/terms/c/capm.asp), 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 versus growth).

These predictor variables have been added because they explain or account for variance in the dependent variable. Portfolio performance is explained by CAPM. For example, CAPM developers knew their model fell short in explaining why high-quality, less volatile stocks often outperformed what the 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](https://www.investopedia.com/terms/m/multifactor-model.asp), form the basis of factor investing and smart beta.

## The Bottom Line

Heteroskedasticity, a key concept in statistical analysis, occurs when the variance of errors across variables is non-constant. It can undermine the accuracy of regression models like the Capital Asset Pricing Model (CAPM), impacting financial analysts' conclusions and predictions. Recognizing the difference between conditional and unconditional heteroskedasticity—where conditional relates to volatility dependent on prior periods and unconditional is related to structural changes—can lead to better financial modeling and risk assessment. Understanding and managing heteroskedasticity can enhance model reliability and inform more robust economic and financial analyses

> **Article Sources**
>
> 1.  Fidelity. "[Understanding Factor-based Investing](https://www.fidelity.com/learning-center/investment-products/etf/factor-based-investing)."