Using equity, index and commodity options to obtain forward-looking measures of equity and commodity betas and idiosyncratic variance

Ehud Ronn

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This paper presents a parsimonious and theoretically-sound basis for extracting forward-looking measures of equity and commodity betas, and idiosyncratic variance.
Defining forward-looking betas and idiosyncratic variance as perturbations of historical estimates, the paper utilizes equity and index options under a single-factor model to discern perceptions of oil companies' prospective beta.
The prospective fraction of idiosyncratic variance relative to total variance indicates the onset of crises, when idiosyncratic fades relative to systematic, thus providing a complement to VIX and CBOE implied correlation.
The model is then applied to options on oil futures. This forward-looking oil beta, in conjunction with risk-neutral futures prices, yields a CAPM-based oil-price forecast.
The paper contributes to the literature on the “message from the markets” – that is, what are markets telling us about quantifying future risk at any point in time.

Abstract

We present a parsimonious and theoretically sound basis for extracting forward-looking measures of equity and commodity betas and idiosyncratic variance. Defining forward-looking betas and idiosyncratic variance as perturbations of historical estimates, we use equity and index options under a single-factor model to discern perceptions of oil companies’ prospective beta. The prospective fraction of idiosyncratic variance relative to total variance indicates the onset of crises, when idiosyncratic fades relative to systematic, complementing the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) and CBOE implied correlation. The model is extended to options on equities and oil futures. This forward-looking oil beta, in conjunction with risk-neutral futures prices, yields an oil-price forecast based on the capital asset pricing model.

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