Is It Expected Volatility or Expected Precision?

28 Pages Posted: 14 Sep 2020 Last revised: 29 Oct 2020

See all articles by Maria T. Gonzalez-Perez

Maria T. Gonzalez-Perez

Bank of Spain

David E. Guerrero

Universidad Complutense de Madrid (UCM) - Colegio Universitario de Estudios Financieros (CUNEF)

Date Written: October 16, 2020

Abstract


There is little evidence in support of a normal distribution for most financial assets, including the VIX. This paper concludes that the lambda parameter, in the one-parameter Box & Cox (1964) family, appropriate for VIX to be normal, is minus one (expected precision), which is very far from values of one (no transformation) and zero (logarithm), typically assumed by the financial literature. We provide an economic meaning to the Gaussian transformation of VIX and call this variable "expected precision'' (EP). The EP measures the level of consensus of expectations in the market about future returns, regardless of the expectations accuracy. We show the pdf/acf for VIX from the EP statistical moments and report evidence in favor of a higher leverage effect when the EP is low (less consensus of expectations). From comparing realized and expected precisions, we define the "precision risk premium" (PRP) that informs about the premium the investors are willing to pay to avoid the uncertainty related to the lack of consensus of expectations, regardless of their level of accuracy. The PRP is Gaussian and relates to the VRP and market returns dynamics. Our result suggests that not only the accuracy but the precision of expectations (more or less consensus) of future returns affect the process of price formation in the market.

Keywords: volatility index, time series analysis, forecasting, leverage effect, expected precision, risk premium

JEL Classification: C32, G13, G15

Suggested Citation

Gonzalez-Perez, Maria T. and Guerrero, David E., Is It Expected Volatility or Expected Precision? (October 16, 2020). Available at SSRN: https://ssrn.com/abstract=3685299 or http://dx.doi.org/10.2139/ssrn.3685299

Maria T. Gonzalez-Perez (Contact Author)

Bank of Spain ( email )

Calle Alcala, 48
Madrid, 28014
Spain
+34 913388587 (Phone)

David E. Guerrero

Universidad Complutense de Madrid (UCM) - Colegio Universitario de Estudios Financieros (CUNEF) ( email )

Serrano Anguita 9
Madrid, Madrid 28004
Spain

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
26
Abstract Views
358
PlumX Metrics