Return Volatility Estimates: A Review and Practical Analysis

Abstract

This paper focuses on the estimation of return volatility and addresses challenges that arise where the frequency of available data is shorter than the desired return horizon. A range of estimators are described and evaluated. The evaluation employs both synthetic data, generated to mimic specific data-generating processes, and real-world data from equities. The synthetic data analysis reveals that the log return method, when returns are independent and identically distributed (IID), provides an unbiased estimator with lower variance than other methods. However, in the presence of serial correlation and momentum, the log return method is biased, requiring correction for autocorrelation. Simpler approaches, such as resampling to a yearly frequency or using rolling annual returns, perform well across various scenarios and do not require assumptions on how returns are generated, making them more robust estimators.

Keywords: volatility, variance, finance, quantitative finance, estimation