Aggregating Daily Volatility-Mimicking Returns into Monthly Factors

Summary

The document asks how to convert Ang et al.’s daily volatility-mimicking factor, FVIX, into a monthly measure. The factor is constructed by regressing daily changes in the VIX on returns of five portfolios sorted by their sensitivity to those changes, then using the fitted portfolio-return combination as the daily factor.

The cited paper describes monthly aggregate volatility risk as the cumulative daily returns on the underlying portfolios used to build the factor. The questioner reports trying both compounding those portfolio returns and compounding daily FVIX directly, but neither matches the reported value in the paper’s table. No resolution or calculation details are provided, so the document does not establish which aggregation procedure is correct. Replicators would need to consult the paper’s precise factor construction and monthly portfolio methodology before treating either attempt as definitive.

Key ideas

• FVIX is formed as a linear combination of returns on portfolios sorted by sensitivity to daily VIX changes.
• The paper describes monthly volatility risk using daily returns on the factor’s underlying portfolios.
• The document raises, but does not resolve, whether monthly aggregation should compound the underlying portfolios or daily FVIX.
• The reported table discrepancy means the aggregation procedure requires verification against the paper’s methodology.

Tags

# How does Ang et al. (2006) aggregate daily‐frequency FVIX returns into a monthly FVIX factor?


# How does Ang et al. (2006) aggregate daily‐frequency FVIX returns into a monthly FVIX factor?












I’m trying to replicate Ang et al. (2006) “The Cross‐Section of Volatility and Expected Returns” where they construct a daily‐frequency volatility‐mimicking factor FVIX via

$\Delta VIX_t = c + b'X_t +u_t$

and define the daily FVIX return as $FVIX = b'X_t$ where $X_t$ is the return of the base assets ($X_t = [Q_1, Q_2, Q_3, Q_4, Q_5]$, $Q_i$ is the value-weigted return for quintile porfolios sorted by sensitivity to $\Delta VIX_t$).

They then say (pp. 18–19) that “we proxy aggregate volatility risk at the monthly frequency by simply cumulating daily returns over the month on the underlying base assets used to construct the mimicking factor.”.

What isn't clear to me is how do they aggregate the FVIX to monthly returns? I've tried to compound both the underlying portfolios returns and the FVIX directly, however neither yields similar results to the last column in Table II.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.