Long Run Forward Rates and Long Yields of Bonds and Options in Heterogeneous Equilibria

We prove that, in a heterogeneous economy with scale-invariant utilities, the yield of a long term bond is determined by the agent with maximal expected marginal utility. We also prove that the same result holds for the long term forward rates. Furthermore, we apply Cramér’s large deviations theorem to calculate the yield of a long term European call option. It turns out that there is a threshold risk aversion such that the option yield is independent of the risk aversion when the latter is above the threshold. Surprisingly, the long term option yield is always greater than or equal to the corresponding equity return. That is, in the long run, it is more profitable to buy a long maturity call option on equity than the equity itself.