Papers

I explore the equilibrium value implications of economic models that incorporate responses to a stochastic environment with growth. I propose dynamic valuation decompositions (DVD’s) designed to distinguish components of an underlying economic model that influence values over long investment horizons from components that impact only the short run. A DVD represents the values of stochastically growing claims to consumption payoffs or cash flows using a stochastic discount process that both discounts the future and adjusts for risk. It is enabled by constructing operators indexed by the elapsed time between the trading date and the date of the future realization of the payoff. Thus formulated, methods from applied mathematics permit me to characterize valuation behavior and the term structure of risk prices in a revealing manner. I apply this approach to investigate how investor beliefs and the associated uncertainty are reflected in current-period values and risk-price elasticities.

@article{hansen:2012dynamic,
  title={Dynamic Valuation Decomposition Within Stochastic Economies},
  author={Hansen, Lars Peter},
  journal={Econometrica},
  volume={80},
  number={3},
  pages={911--967},
  year={2012},
  publisher={Wiley Online Library}
}

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 , with G0 = G, as 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.

@article{hansenscheinkman:2012pricing,
  title={Pricing Growth-Rate Risk},
  author={Hansen, Lars Peter and Scheinkman, Jos{'e} A},
  journal={Finance and Stochastics},
  volume={16},
  number={1},
  pages={1--15},
  year={2012},
  publisher={Springer}
}

We present a novel approach to depicting asset-pricing dynamics by characterizing shock exposures and prices for alternative investment horizons. We quantify the shock exposures in terms of elasticities that measure the impact of a current shock on future cash flow growth. The elasticities are designed to accommodate nonlinearities in the stochastic evolution modeled as a Markov process. Stochastic growth in the underlying macroeconomy and stochastic discounting in the representation of asset values are central ingredients in our investigation. We provide elasticity calculations in a series of examples featuring consumption externalities, recursive utility, and jump risk.

This paper was originally presented as the Journal of Financial Econometrics Lecture at the June 2009 SoFiE conference.

@article{bhhs:2011,
  title={Risk-Price Dynamics},
  author={Borovi{v{c}}ka, Jaroslav and Hansen, Lars Peter and Hendricks, Mark and Scheinkman, Jos{'e} A},
  journal={Journal of Financial Econometrics},
  volume={9},
  number={1},
  pages={3--65},
  year={2011},
  publisher={Oxford Univ Press}
}