16 - Discount Rates, Default Risk and Asset Pricing in a Regime Change Model

Abstract

As Cochrane (2011) has argued recently, discount rates that are used to price assets highly covary with risk premia and are tied to macroeconomic data. We would like to add that risk premia could be regime-dependent. In a regime of high growth rates the risk premia and discount rates are low, and in a regime of low or negative growth the risk premia and discount rates are high. To estimate the interaction of risk premia with growth regimes we employ a Markov regime switching model (MRSM). The MRSM predicts expansions and contractions from which we extract state-dependent risk premia and discount rates, which in turn impact the asset value of firms. Traditionally it is assumed, since Merton (1974) , that the asset value of the firm is exogenously given, e.g. through a Brownian motion, and not affected by leveraging and risk premia. In our model, where a state-dependent risk premium employed as a proxy for the discount rate, we can make sustainable leveraging and asset value of the firm endogenous. We solve the asset value of the firm with leveraging by the use of numerical methods. We can also compute, as the KMV model suggests, sustainable debt and the probability of bankruptcy, which interact with risk premia and discount rates.