Measuring Aggregate Volatility with VIX Changes
Summary
The document explains aggregate volatility as an estimated quantity used in studying whether marketwide volatility is priced in stock returns. In the cited research, changes in the VIX serve as a proxy for innovations in aggregate volatility. This is a practical operational choice, not a direct observation of the underlying quantity.
The answer emphasizes that volatility cannot be read directly from returns and must be estimated from price data. Estimates depend on choices such as sampling frequency and return construction; intraday and overnight variation, for example, capture different components. It also points to historical volatility methods and the use of proxies in evaluating forecasts. The discussion does not provide a full calculation procedure or establish that aggregate volatility is a systematic risk factor. Readers would need the referenced paper and its footnote for the specific definition, alternatives, and supporting analysis.
Key ideas
- Aggregate volatility is not directly observable and must be represented by an estimate or proxy.
- The cited paper uses changes in the VIX to proxy innovations in aggregate volatility.
- Volatility estimates depend on choices about return construction and sampling frequency.
- The document raises, but does not resolve, whether aggregate volatility is a priced systematic risk factor.
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# What is the definition of aggregate volatility, and how to compute it? # What is the definition of aggregate volatility, and how to compute it? I am quoting the following sentence from Andrew Ang's paper "The Cross-Section of Volatility and Expected Returns". Can someone explain how aggregate volatility is defined and how to compute it? It looks like the author is trying to use it as a systematic factor in risk-return regression models (The way market return is used in the CAPM model). I am interested in knowing if aggregate volatility is also a systematic risk factor. > we examine how aggregate volatility is priced in the cross-section of stock returns. ## Answer by AKdemy (score 3) https://quant.stackexchange.com/a/76708 As mentioned in the comments, the paper defines how they compute it: > "to proxy innovations on aggregate volatility, (vt+1−γv,t), we use changes in the VIX index from the Chicago Board Options Exchange (CBOE).". The associated footnote shows alternatives and papers they considered. You need to estimate (historical) vol because it is inherently unknown and not directly observable from the return data. For example, there is intraday volatility (not part of the most common measure of volatility because you only use one observation a trading day) and overnight volatility, defined as the variation between trading days. See for example Ruey Tsay, Analysis of Financial Time Series (P.110 3rd edition) To compute vol from historical data, you rely on derived returns data (based on assumptions like using log differences of close to close mid quotes from bod ask spreads). For vol itself, you use some statistics of your choice to derive a volatility estimate (it's in fact called an estimate in the literature for the very reason that vol itself is unobservable, also visible in any proper documentation of computer code that computes volatility, see for example R.). A well cited paper from Andersen, Diebold et al. can be found here. It was published in December 2006 in the Handbook of Economic Forecasting 1:777-878. I'll copy paste a section so you don't need to read the entire piece: > "As discussed at some length in Sections 1 and 5, the “true” variance, or volatility, is inherently unobservable, and we are faced with the challenge of having to rely on a proxy in order to assess the forecast". P.s. I think it is good practice to at least read the entire paper first before posting a question.
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