Explicit characterizations of financial prices with history-dependent utility

2011

We study a competitive equilibrium in a production economy, i.e., a system of prices at which firms' profit maximizing production decisions and individuals' preferred affordable consumption choices equate supply and demand in every market. We derive the equilibrium price of the firm and the equilibrium short term interest rate, the optimal consumption in society, as well as the risk premium on equity. Both a linear, and a nonlinear production technology are considered. For the linear one applied to the Standard and Poor's composite stock price index for the last century, a risk premium of 0.062 corresponds to a relative risk aversion of 2.27. The model provides a riskfree interest rate for the period of 0.8%. The nonlinear model, however, highlights a hedging demand for the investors related to the real economy, which would, if taken into account, make the stock market of the last century less risky than it was perceived to be.

Section: A Numerical Calibration Exercisementioning

confidence: 82%

“…Constantinides (1990) introduced habit persistence in the preferences of the agents. Also Campbell and Cochrane (1999) and Haug (2001) used habit formation. These articles manage to explain high risk premiums and a low real interest rate.…”

Section: Introductionmentioning

confidence: 99%

The Equity Premium and the Risk Free Rate in a Production Economy: A New Perspective

2011

“…The variance per time unit of the consumption process is given by (22) and the corresponding variance of any risky asset is…”

Section: The Equity Premium and The Short Rate With Pure Jumpsmentioning

confidence: 99%

“…See also the papers by Haug (2001), Constantinides (1990), Detemple and Zapatero (1991), Sundaresan (1989), and Kocherlacota (1990). Also recursive utility of the Epstein-Zin (1989-91) type (discrete time) and Duffie and Epstein (1991) (continuous time) is analyzed in the literature by many.…”

Section: Introductionmentioning

confidence: 99%

Beyond the Local Mean-Variance Analysis in Continuous Time: The Problem of Non-Normality

Lillestøl

2015

The paper investigates the effects of deviations from normality on the estimates of risk premiums and the real equilibrium, short-term interest rate in the conventional rational expectations equilibrium model of Lucas (1978). We consider a time-continuous approach, where both the aggregate consumption process as well as cumulative dividends from risky assets are assumed to be jump-diffusion processes. This approach allows for random jumps in the fundamental underlying processes at random time points. Preferences are time separable and additive. We derive testable expressions for these quantities, and confront these with 20. century sample estimates. Since there are non-linear components in the formulas for the risk premiums and the interest rate, we can readily explore what effect deviation from normality has on these quantities. Our results test the boundaries of the conventional model.

The Equity Premium in a Production Economy; A New Perspective Involving Recursive Utility

2015

We study a rational expectations' competitive equilibrium in a production economy, i.e., a system of prices at which firms' profit maximizing production decisions and individuals' preferred affordable consumption choices equate supply and demand in every market. We derive the equilibrium price of the firm and the equilibrium short term interest rate, the optimal per capita consumption in society, as well as the risk premium on equity. First a simple linear production technology with constant coefficients is studied, then a more general technology, and finally a general production economy with recursive utility is analyzed by the use of the stochastic maximum principle. While the two first models can not explain the empirics well using conventional preferences, the latter model is found to be much more promising in this regard. Wa also demonstrate a simple proof for the ICAPM.