A Stochastic Gordon-Shapiro Formula with Excess Volatility

20 Pages Posted: 18 Feb 2021 Last revised: 31 May 2023

See all articles by Lutz Kruschwitz

Lutz Kruschwitz

Free University of Berlin (FUB) - Department of Business and Economics

Andreas Loeffler

Freie Universität Berlin

Date Written: January 8, 2021

Abstract

Share prices fluctuate far more than dividends. In contemporary literature, this excess volatility is usually discussed involving the Camp\-bell-Shiller present value identity. In our view, it is more appropriate to model future dividends and prices explicitly as random variables. We refer to excess volatility if the coefficient of dispersion for share prices is higher than for dividends.

It is often presumed that excess volatility could be properly explicated by time-varying discount factors. However, we will show that this idea is logically inconsistent as long as one uses deterministic discount factors. This even holds if one assumes more complex stochastic structures of the dividends, such as AR(2) processes.

We therefore propose stochastic discount factors and show that our model is free of arbitrage, the transversality condition is met and prices are unique.

Finally, we try to consolidate our approach with the Lucas Model. Here, it is shown on the one hand that in this model the cost of capital cannot be stochastic. Moreover, the equity premium puzzle can no longer be replicated, but rather a realistic value for risk aversion is obtained.

A newer and revised version of this paper can be found on https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4459364

Keywords: excess volatility, Gordon Shapiro, valuation, transversality, equity premium puzzle

JEL Classification: G12, G30

Suggested Citation

Kruschwitz, Lutz and Loeffler, Andreas, A Stochastic Gordon-Shapiro Formula with Excess Volatility (January 8, 2021). Available at SSRN: https://ssrn.com/abstract=3761127 or http://dx.doi.org/10.2139/ssrn.3761127

Lutz Kruschwitz

Free University of Berlin (FUB) - Department of Business and Economics ( email )

Boltzmannstrasse 20
D-14195 Berlin, 14195
Germany

Andreas Loeffler (Contact Author)

Freie Universität Berlin ( email )

Thielallee 73
Berlin, 14195
Germany

HOME PAGE: http://www.andreasloeffler.de

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