Improving Volatility Forecasts Using Market‐Elicited Ambiguity Aversion Information

Abstract

Distinguishing between risk and uncertainty, this paper proposes a volatility forecasting framework that incorporates asymmetric ambiguity shocks in the (exponential) generalized autoregressive conditional heteroskedasticity‐in‐mean conditional volatility process. Spanning 25 years of daily data and considering the differential role of investors' ambiguity attitudes in the gain and loss domains, our models capture a rich set of information and provide more accurate volatility forecasts both in‐sample and out‐of‐sample when compared to ambiguity‐free or risk‐based counterparts. Ambiguity‐based volatility‐timing trading strategies confirm the economic significance of our proposed framework and indicate that an annualized excess return of 3.2% over the benchmark could be earned from 1995 to 2014.

Ambiguity, Managerial Ability, and Growth Options

“…Analogous to Merton (1977), we view equity as an option that shareholders hold on the firm's assets but adjust value drivers for ambiguity by accounting for model uncertainty in the growth rate (drift) and variance (diffusion) of firm value returns (see e.g. So and Driouchi, 2018 for how ambiguity affects the Brownian motion driving underlying asset and option values): $$\begin{equation}{\rm{E}} = {\rm{V}}{{\rm{e}}^{ - {{{\delta}}^{\rm{^{\prime}}}}{\rm{T}}}}{\rm{N}}\left( {{\rm{d}}{{\rm{^{\prime}}}_1}} \right) - {\rm{B}}{{\rm{e}}^{ - {{\rm{r}}^{\rm{^{\prime}}}}{\rm{T}}}}{\rm{N}}\left( {{\rm{d}}{{\rm{^{\prime}}}_2}} \right){\rm{\ }}\left( {\forall {\rm{c}} \in {\rm{\ }}\left] {0,1} \right[} \right)\end{equation}$$where $$\begin{eqnarray*} \ \mathrm{d}^{\prime}_{1}=\frac{\ln \left(\mathrm{V}/\mathrm{B}\right)+\left({\mathrm{r}}^{\prime}-{\delta}^{\prime}+ \frac{1}{2}{\left(\mathrm{s}\sigma \right)}^{2}\right)\mathrm{T}}{\mathrm{s}\sigma \sqrt{\mathrm{T}}}, \mathrm{d}^{\prime}_{2}=\mathrm{d}^{\prime}_{1}-\mathrm{s}\sigma \sqrt{\mathrm{T}} \end{eqnarray*}$$…”

“…Analogous to Merton (1977), we view equity as an option that shareholders hold on the firm's assets but adjust value drivers for ambiguity by accounting for model uncertainty in the growth rate (drift) and variance (diffusion) of firm value returns (see e.g. So and Driouchi, 2018 for how ambiguity affects the Brownian motion driving underlying asset and option values):…”