Long Term Risk: An Operator Approach / Lars Peter Hansen, Jose Scheinkman.

Format:

Book

Author/Creator:

Hansen, Lars Peter.

Contributor:

National Bureau of Economic Research.

Scheinkman, Jose.

Series:

Working Paper Series (National Bureau of Economic Research) no. w12650.

NBER working paper series no. w12650

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Other Title:

Long Term Risk

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2006.

Summary:

We create an analytical structure that reveals the long run risk-return relationship for nonlinear continuous time Markov environments. We do so by studying an eigenvalue problem associated with a positive eigenfunction for a conveniently chosen family of valuation operators. This family forms a semigroup whose members are indexed by the elapsed time between payoff and valuation dates. We represent the semigroup using a positive process with three components: an exponential term constructed from the eigenvalue, a martingale and a transient eigenfunction term. The eigenvalue encodes the risk adjustment, the martingale alters the probability measure to capture long run approximation, and the eigenfunction gives the long run dependence on the Markov state. We establish existence and uniqueness of the relevant eigenvalue and eigenfunction. By showing how changes in the stochastic growth components of cash flows induce changes in the corresponding eigenvalues and eigenfunctions, we reveal a long-run risk return tradeoff.

Notes:

Print version record

October 2006.