The financial economics literature on risk-return trade-off and risk compensation is voluminous and growing. Most of the theoretical developments in this area focus on short or even instantaneous time frames. Very little is known about risk and its compensation for agents who invest over a long time span. The main interest of this paper is the premium on the dividend flows with an infinite horizon. In numerous attempts to resolve conflicts between theory and empirics, asset pricing models have been extended to include a variety of different preference structures. As Hansen (2008) shows many of these utilities have only transient implications and make no difference in pricing assets with long maturity.
the valuation of consumption and dividend cash flows with short and long maturities that generalizes the model of Mehra and Prescott (1985). I use the methodology of semigroup asset pricing theory (Hansen and Scheinkman, 2009) in order to construct transition matrices of stochastic discounting and pricing. I consider three utility functions: expected utility (EU), Epstein and Zin (1989) (EZ), and generalized disappointment aversion (GDA) proposed by Routledge and Zin (2004).
The main result of the paper is that the GDA utility function amplifies risk premia at all investment horizons in comparison to expected utility function. Instead, EZ utility delivers very similar long-term premia, but different short-term premia compared to EU. Hence, we say that GDA is a permanent transformation of EU, while EZ is a transient transformation of EU. The main feature of the GDA utility that produces substantially different risk premia for any horizon is its asymmetric response to different economic outcomes through the implied skewed risk-neutral probabilities.
Long-term returns are also an integral part of short-term returns. Their difference may be interpreted as a term premium. If a short-term risk premium is smaller than its long-term counterpart, then the term premium is positive. This means that an investor is rewarded for holding an asset for a long period of time. The long-term return does not depend on the current state of the economy and hence is a constant. So all the short-term variations in the returns are due to fluctuations in term premia. In this paper I show that a consumption-based model can generate a positive term premium for any holding period and any dividend stream. Moreover, this suggests that in order to understand short-term asset pricing phenomena one should not overlook the long-term component of the model.
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Risk Premia: Short And Long-Term
