Abstract
We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S. We also consider a reference growth process G that may represent the growth in the payoff of a single asset or of the macroeconomy. Both S and G are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. We consider the pricing implications of parametrized family of growth processes G ε, with G 0=G, as ε is made small. This parametrization defines a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon, we trace a term structure of risk prices that shows how the valuation of risky cash flows depends on the investment horizon. Using methods of Hansen and Scheinkman (Econometrica 77:177–234, 2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily long.
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This material is based on work supported by the National Science Foundation under award numbers SES-07-18407 and SES-05-19372.
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Hansen, L.P., Scheinkman, J.A. Pricing growth-rate risk. Finance Stoch 16, 1–15 (2012). https://doi.org/10.1007/s00780-010-0141-9
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DOI: https://doi.org/10.1007/s00780-010-0141-9