A Joint Affine Model of Commodity Futures and US Treasury Yields

We derive a general joint affine term structure model of US government bond yields and the convenience yields on physical commodities. We apply this framework separately to oil and gold. Our results show clear links between bond and commodity markets, since bond factors play a significant role in the pricing of the convenience yield term structure. Our framework allows us to decompose the term structure of futures prices into expectations of future spot prices and risk premia components. We estimate that the risk premium in oil futures has been negative over the 1980s and 1990s, and turned positive in the mid-2000s, consistent with a declining role for supply shocks in the oil market over this period. In contrast, we estimate that the gold risk premium is mostly positive throughout the sample period