Stochastic Discount Factor Models and the Equity Premium Puzzle

One view of the equity premium puzzle is that in the standard asset-pricing model with time-separable preferences, the volatility of the stochastic discount factor, for plausible values of risk aversion, is too low to be consistent with consumption and asset return data. We adopt this characterization of the puzzle, due to Hansen and Jagannathan (1991), and establish two results: (i) resolutions of the puzzle based on complete frictionless markets and non-separabilities in preferences are very sensitive to small changes in the consumption data, and (ii) models with frictions avoid this sensitivity problem. Using quarterly data from 1947-97, we calibrate a state non-separable model and a time non-separable model to satisfy the Hansen-Jagannathan volatility bound and show that the two resolutions are not robust. We support our argument via a bootstrap experiment where the models almost always violate the bound. These violations are primarily due to the fact that small changes in consumption growth moments imply changes in the mean of the stochastic discount factor, which render the volatility of the stochastic discount factor to be too low relative to the bound. Asset-pricing models with frictions, however, are much more successful in the bootstrap experiment relative to the case without frictions.Stochastic Discount Factor; Hansen-Jagannathan Bound; Equity Premium;

Evaluating Asset-Pricing Models Using The Hansen-Jagannathan Bound: A Monte Carlo Investigation

We conduct Monte Carlo experiments to examine whether the bound proposed by Hansen and Jagannathan (1991) is a useful device for evaluating asset pricing models. Specifically, we use recently developed statistical tests, which are based on a 'distance' between the model and the Hansen-Jagannathan bound, to compute the rejection rates of true models. We provide finite-sample critical values for asset pricing models with time separable preferences, and show how they depend upon nuisance parameters—risk aversion and the rate of time preference. Further, we show that the finite-sample distribution of the test statistic associated with the risk-neutral case is extreme, in the sense that critical values based on this distribution will deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. Extending the analysis to accommodate other preferences, we show that in the state non-separable case, the small-sample distributions of the test statistics are influenced significantly by the degree of intertemporal substitution, but not by attitudes toward risk. For habit formation preferences, the small-sample distributions are strongly influenced by the habit parameter. However, the maximal-size critical values for time-separable preferences are appropriate for habit formation as well as state non-separable preferences. We conclude that with these critical values the HJ bound is indeed a useful evaluation device. We then use the critical values to evaluate three asset pricing models using U.S. data. We find evidence against the time-separable model and mixed evidence on the remaining two models.

Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions.Asymmetric Information, Blaschke Factors

Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions

Components of infrared net radiation in a mountain valley

Includes bibliographical references (page 67).October 1977.The infrared components of the surface radiation budget in a mountain valley have been investigated theoretically. Calculations were based on a set of winter and summer atmospheric soundings specifying temperature and moisture content and for two valley models including a linear valley model and a circularly symmetric valley model. Radiance and irradiance calculations are compared with similar calculations for flat terrain. Downward irradiances at the valley center were shown to be higher than for flat terrain and were due to radiation from the valley sidewalls. The largest effect was obtained for a dry winter atmosphere with the sidewalls warmer than the valley bottom. Downward irradiance was increased by 16% over the flat terrain case and the net irradiance at the valley center was decreased by 24% which would lead to a decreased surface cooling. Calculations were made for five spectral intervals including the 6.5 micron water band (4.4 - 7 .8μ), the water vapor continuum or atmospheric window (7. 8 - 13. 4μ), the 15 micron carbon dioxide band (13. 4 - 16. 3μ), a small window (16. 3 - 20. 2μ), and the rotational water bands (20. 2 - 48. 8μ). Only the two bands described as windows contribute significantly to the changes in downward irradiance. The remaining three spectral intervals are nearly opaque to transmission of radiation from the valley sidewalls to the valley center.Sponsored by Cooperative Agreement with the U.S. Forest Service, Rocky Mountain Forest and Range Experiment Station - 16-629-CA

Late Wisconsin glaciation of Hadwen and Summer islands, Tuktoyaktuk Coastlands, NWT, Canada

The exact timing of the last major advance of the Laurentide Ice Sheet onto the Beaufort Sea coastlands of western Arctic Canada is unclear but significant to our understanding of landscape change and palaeo-ice stream chronology. Optical stimulated luminescence dating of preglacial and postglacial aeolian sand from Hadwen and Summer islands, in the Tuktoyaktuk Coastlands, indicates that glaciation took place between about 17.5 and 15 ka, and most likely between 16.6 and 15.9 ka, coinciding with Heinrich event 1. At this time the Mackenzie Trough palaeo-ice stream advanced into a cold-climate sandy desert, interrupting aeolian activity

A Research-Based Model for Digital Mapping and Art History: Notes from the Field

Most digital mapping in art history today divides the research process from the visualization aspects of the project. This problem became the focus of a summer institute that Paul Jaskot and Anne Kelly Knowles ran at Middlebury College with the support of the Samuel H. Kress Foundation. Our article both reports on the institute and suggests how research questions can complement digital mapping methods. We conclude with three case studies of spatial questions in art history and discuss the Fellows’ use of GIS to explore examples from Qing Dynasty China, medieval Gotland, and contemporary New York City

Stochastic Discount Factor Models and the Equity Premium Puzzle

One view of the equity premium puzzle is that in the standard asset-pricing model with time-separable preferences, the volatility of the stochastic discount factor, for plausible values of risk aversion, is too low to be consistent with consumption and asset return data. We adopt this characterization of the puzzle, due to Hansen and Jagannathan (1991), and establish two results: (i) resolutions of the puzzle based on complete frictionless markets and non-separabilities in preferences are very sensitive to small changes in the consumption data, and (ii) models with frictions avoid this sensitivity problem. Using quarterly data from 1947-97, we calibrate a state non-separable model and a time non-separable model to satisfy the Hansen-Jagannathan volatility bound and show that the two resolutions are not robust. We support our argument via a bootstrap experiment where the models almost always violate the bound. These violations are primarily due to the fact that small changes in consumption growth moments imply changes in the mean of the stochastic discount factor, which render the volatility of the stochastic discount factor to be too low relative to the bound. Asset-pricing models with frictions, however, are much more successful in the bootstrap experiment relative to the case without frictions

Stochastic Discount Factor Models and the Equity Premium Puzzle

One view of the equity premium puzzle is that in the standard asset-pricing model with time-separable preferences, the volatility of the stochastic discount factor, for plausible values of risk aversion, is too low to be consistent with consumption and asset return data. We adopt this characterization of the puzzle, due to Hansen and Jagannathan (1991), and establish two results: (i) resolutions of the puzzle based on complete frictionless markets and non-separabilities in preferences are very sensitive to small changes in the consumption data, and (ii) models with frictions avoid this sensitivity problem. Using quarterly data from 1947-97, we calibrate a state non-separable model and a time non-separable model to satisfy the Hansen-Jagannathan volatility bound and show that the two resolutions are not robust. We support our argument via a bootstrap experiment where the models almost always violate the bound. These violations are primarily due to the fact that small changes in consumption growth moments imply changes in the mean of the stochastic discount factor, which render the volatility of the stochastic discount factor to be too low relative to the bound. Asset-pricing models with frictions, however, are much more successful in the bootstrap experiment relative to the case without frictions

Energy Down Conversion between Classical Electromagnetic Fields via a Quantum Mechanical SQUID Ring

We consider the interaction of a quantum mechanical SQUID ring with a classical resonator (a parallel $LC$ tank circuit). In our model we assume that the evolution of the ring maintains its quantum mechanical nature, even though the circuit to which it is coupled is treated classically. We show that when the SQUID ring is driven by a classical monochromatic microwave source, energy can be transferred between this input and the tank circuit, even when the frequency ratio between them is very large. Essentially, these calculations deal with the coupling between a single macroscopic quantum object (the SQUID ring) and a classical circuit measurement device where due account is taken of the non-perturbative behaviour of the ring and the concomitant non-linear interaction of the ring with this device.Comment: 7 pages, 6 figure