Nonlinearity and Flight to Safety in the Risk-Return Trade-Off for Stocks and Bonds

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe document a highly significant, strongly nonlinear dependence of stock and bond returns on past equity-market volatility as measured by the VIX. We propose a new estimator for the shape of the nonlinear forecasting relationship that exploits additional variation in the cross section of returns. The nonlinearities are mirror images for stocks and bonds, revealing flight to safety: Expected returns increase for stocks when volatility increases from moderate to high levels, while they decline for Treasuries. We further demonstrate that these findings are evidence of dynamic asset pricing theories where the time variation of the price of risk is a function of the level of the VIX.

Vulnerable Growth

“…Longstaff, Pan, Pedersen, and Singleton (2011) estimate that the price of sovereign risk is strongly correlated with the VIX. Furthermore, Adrian, Crump, and Vogt (2015) show that a nonlinear transformation of the VIX forecasts stock and bond returns, suggesting that the pricing of risk depends on the VIX. In general equilibrium, pricing of risk is associated with GDP growth, and risk to GDP growth.…”

Risk Control: Who Cares?

“…The contrary evidence to this prediction observed in the post‐2006 sample is consistent with the empirical results concerning the break down in the positive and linear risk‐return relationship around the financial crisis documented in Adrian et al . () and Ghysels et al . () and with the argument that this period is characterised by flight to safety behaviour (Baele et al ., ).…”

“…By contrast, the post‐2006 period is characterised by strong performance. This finding is argued to be consistent with the inverse risk‐return relationship and flight to safety behaviour observed in the post‐2006 period (Adrian et al ., ; Baele et al ., ; and Ghysels et al ., ).…”

A forecasting analysis of risk‐neutral equity and Treasury volatilities

“…Given the evidence reported by Adrian, Crump, and Vogt () on the importance of nonlinearities, our analysis of forecasting employs the square of VIX and MOVE rather than the volatilities themselves. The in‐sample relative forecasting ability of VIX 2 and MOVE 2 suggests that VIX 2 tends to dominate MOVE 2 in both real activity and financial returns.…”