A New Framework for Risk Indices in Illiquid Markets

Abstract

Employing a generalized Hamiltonian Monte Carlo Bayesian procedure we develop a new framework to construct risk indices in illiquid markets. We account for two types of risk time series. One is signal, which accounts for the stochastic volatility of residuals not explain by a forecasting model. We thus assume that prices do not follow a random walk but carry some predictable component. We also propose an new risk concept associated with noise in the cross section of real estate prices. While one would not expect this to be a risk factor in stock markets, changes to the noise index over time in real estate markets can be associated with varying degrees of valuation uncertainty.
We show that signal and noise indices at the national level capture well periods of turmoil. We demonstrate that prices and volumes respond significantly to changes in the risk indices. Our risk indices do a better job in explaining real estate those fundamentals than existing volatility indices such as the VIX index. Practitioners can use our risk framework to construct more accurate estimates of risk over time which serves to inform their investment decisions.

Keywords: Uncertainty, Stochastic Volatility, Noise, Valuation Uncertainty, Bayesian Estimation, Repeat Sales Model, Commercial Real Estate, Illiquid Markets

JEL Classification: C11, C33, C81, G11, G14, R30