02104cam a22002537 4500001000700000003000500007005001700012008004100029100002400070245010400094260006600198490004200264500001800306520103900324530006101363538007201424538003601496690011201532700002201644710004201666830007701708856003801785856002701823w12650NBER20140711144104.0140711s2006 mau||||fs|||| 000 0 eng d1 aHansen, Lars Peter.10aLong Term Riskh[electronic resource]:bAn Operator Approach /cLars Peter Hansen, Jose Scheinkman. aCambridge, Mass.bNational Bureau of Economic Researchc2006.1 aNBER working paper seriesvno. w12650 aOctober 2006.3 aWe 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aG12 - Asset Pricing • Trading Volume • Bond Interest Rates2Journal of Economic Literature class.1 aScheinkman, Jose.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w12650.4 uhttp://www.nber.org/papers/w12650 uurn:doi:10.3386/w12650