The Return-Volatility Relation in Commodity Futures Markets

By employing a continuous time stochastic volatility model, we analyse the dynamic relation between price returns and volatility changes in the commodity futures markets. We use an extensive daily database of gold and crude oil futures and futures options to estimate the model that is well suited to assess the return–volatility relation for the entire term structure of futures prices. Our empirical results indicate a positive relation in the gold futures market and a negative relation in the crude oil futures market, especially over periods of high volatility principally driven by market-wide shocks. However, the opposite reaction occurs over quiet volatility periods when typically commodity-specific effects dominate. As leverage effect and volatility feedback effect do not adequately explain this reaction especially for the crude oil futures, we propose the convenience yield effect. We demonstrate that commodity futures markets in normal backwardation entail a positive relation, while futures markets in contango entail a negative relation.