Nominal bonds, real bonds, and equity

We decompose the term structure of expected equity returns into (1) the real short rate, (2) a premium for holding real long-term bonds, or the real duration premium, the excess returns of nominal long-term bonds over real bonds which reflects (3) expected inflation and (4) inflation risk, and (5) a real cashflow risk premium, which is the excess return of equity over nominal bonds. All of these risk premiums vary over time. The shape of the unconditional nominal and real bond yield curves are upward sloping due to increasing duration and inflation risk premiums. The average term structures of expected equity returns and equity risk premiums, in contrast, are downward sloping due to the decreasing effect of short-term expected inflation, or trend inflation, across horizons. Around 70 % of the variation of expected equity returns at the 10-year horizon is due to variation in the output gap and trend inflation.