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The authors would like to thank participants at the “New Normality, New Risks” 2020 Conference hosted by Institut Louis Bachelier, Paris; the 4th International Workshop on Financial Markets and Nonlinear Dynamics; the 15th Annual Conference of Macroeconomists from Liberal Arts Colleges; the lOth RCEA Macro-Mo ney-Finance Conference; and the Bates College Casey Lecture Fund in Economies Seminar Series for helpful comments and suggestions. The paper also benefitted from comments from IMF staff in RES and Ricardo Sousa’s insightful discussion.
In particular, popular models used by Central Banks to understand the effects of monetary policy on the economy such as FRB/US (Brayton et al., 2014) at https://www.federalreserve.gov/econresdata/frbus/us-models-about.htm and Euro (Smets and Wouters, 2003, 2007; Christoffel et al., 2008), have this limitation in ternis of refiecting financial market participants’ attitudes towards risk.
See Campbell (2014) for a discussion of the contributions of Eugene Fama, Lars Peter Hansen, and Robert Shiller to this Une of research, which is the basis for their 2013 Nobel Memorial Prize in Economie Sciences.
For example, Cochrane (2011) found substantial time variation in the discount rate or expected SDF across many financial assets including the expected excess return on longer-term bonds.
If the investors also have distinct investment horizon, then the hedging demand strategy will depend on different mean and variance-covariances according to the investor’s horizon.
From Beare and Schmidt (2016), given a pricing kernel, π, (i) the SDF is a random variable at a luture time t + 1; (ii) the current price of a financial instrument Yt is given by 𝔼t [SDF St+1]; (iii) M* = 𝔼t [SDF St+1], where St+i is the price of the market portfolio at time t+1; and (iv) the pricing kernel is defined such that
Following Beare and Schmidt (2016) as in footnote 5, suppose Yt+1 = ft(St+1) is the price at time t + 1 of a market portfolio for some payoff function ft on a contingent security. Thus,
This demand is based on a comparison of the current factors with the expected utility desired by each investor; which is scaled by the variance-covariance matrix for the investor’s expected utility and multiplied by the beta from regressing the return on Treasury securities on the risk factors.
By limiting the utility function to a constant relative risk aversion coefficient we know that the non-linearity of the expected SDF arises from the hedging behavior of investors.
The gross rate of growth for investors’ wealth has conditional mean —0.0640 and standard deviation 0.1065 for the more risk averse group; and conditional mean —0.0366 and standard deviation 0.0798 for the less risk averse group.
Changing the discount rate has a small impact on the portfolio decision of the investor. For example, a discount rate of 10% instead of 5%, leads to a 48–52% allocation, compared to 46–54%.