Predictability of VRP: A Comparison Study

Abstract

The intertemporal CAPM model of Merton (Econometrica, 41:867–887, 1973) demonstrates that the aggregate market risk is determined by the uncertainty of the underlying return, quantified by the return variance. When holding the market portfolio, however, an investor is also bearing the uncertainty of the variance itself. Just like the equity premium demanded by investors is the result of fear to the uncertainty of future returns, a variance risk premium, defined as the difference between risk-neutral and physical expected variances is also required to compensate for the randomness of the unknown variance. Many recent studies document the link between risk preference and variance risk premium. In particular, Bakshi and Madan (Manag Sci, 52:1945–1956, 2006) argue that the variance risk premium is approximately determined by the risk aversion parameter and the higher order moments of underlying returns. In a similar vein, Bollerslev (J Financ Quant Anal, 2013) assume an affine version of the stochastic volatility model as in Heston (Rev Financ Stud, 6:327–343, 1993) and show that the variance risk premium is linearly related to the risk aversion parameter. Other investigations in this area includes Bekaert and Engstrom (Asset return dynamics under bad environment-good environment fundamentals, Working Paper, NBER, 2010), Todorov (Rev Financ Stud, 23:345–383, 2010), and Gabaix (Q J Econ, 127:645–700, 2012).