http://dklevine.com/archive/refs41401.pdf

THE EQUITY PREMIUM A Puzzle

We present a simple overlapping generations model of an asset market in which irrational noise traders with erroneous stochastic beliefs both affect prices and earn higher expected returns. The unpredictability of noise traders' beliefs creates a risk in the price of the asset that deters rational arbitrageurs from aggressively betting against them. As a result, prices can diverge significantly from fundamental values even in the absence of fundamental risk. Moreover, bearing a disproportionate amount of risk that they themselves create enables noise traders to earn a higher expected return than rational investors do. The model sheds light on a number of financial anomalies, including the excess volatility of asset prices, the mean reversion of stock returns, the underpricing of closed-end mutual funds, and the Mehra-Prescott equity premium puzzle.

https://ms.mcmaster.ca/~grasselli/DeLongShleiferSummersWaldmann90.pdf

Noise Trader Risk in Financial Markets

THE SPHERE of model financial economics encompasses finance, micro investment theory and much of the economics of uncertainty. As is evident from its influence on other branches of economics including public finance, industrial organization and monetary theory, the boundaries of this sphere are both permeable and flexible. The complex interactions of time and uncertainty guarantee intellectual challenge and intrinsic excitement to the study of financial economics. Indeed, the mathematics of the subject contain some of the most interesting applications of probability and optimization theory. But for all its mathematical refinement, the research has nevertheless had a direct and significant influence on practice. ’ It was not always thus. Thirty years ago, finance theory was little more than a collection of anecdotes, rules of thumb, and manipulations of accounting data with an almost exclusive focus on corporate financial management. There is no need in this meeting of the guild to recount the subsequent evolution from this conceptual potpourri to a rigorous economic theory subjected to systematic empirical examination? Nor is there a need on this occasion to document the wide-ranging impact of the research on finance practice.2 I simply note that the conjoining of intrinsic intellectual interest with extrinsic application is a prevailing theme of research in financial economics. The later stages of this successful evolution have however been marked by a substantial accumulation of empirical anomalies; discoveries of theoretical inconsistencies; and a well-founded concern about the statistical power of many of the test methodologies.3 Finance thus finds itself today in the seemingly-paradoxical position of having more questions and empirical puzzles than at the start of its

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.1987.tb04565.x

A Simple Model of Capital Market Equilibrium with Incomplete Information

SEQUELS ARE RARELY AS good as the originals, so I approach this review of the market efficiency literature with trepidation. The task is thornier than it was 20 years ago, when work on efficiency was rather new. The literature is now so large that a full review is impossible, and is not attempted here. Instead, I discuss the work that I find most interesting, and I offer my views on what we have learned from the research on market efficiency.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.1991.tb04636.x

Efficient Capital Markets: II

This paper develops a class of recursive, but not necessarily expected utility, preferences over intertemporal consumption lotteries An important feature of these general preferences is that they permit risk attitudes to be disentangled from the degree of intertemporal substitutability Moreover, in an infinite horizon, representative agent context these preference specifications lead to a model of asset returns in which appropriate versions of both the atemporal CAPM and the intertemporal consumption-CAPM are nested as special cases In our general model, systematic risk of an asset is determined by covariance with both the return to the market portfolio and consumption growth, while in each of the existing models only one of these factors plays a role This result is achieved despite the homotheticity of preferences and the separability of consumption and portfolio decisions Two other auxiliary analytical contributions which are of independent interest are the proofs of (i) the existence of recursive intertemporal utility functions, and (ii) the existence of optima to corresponding optimization problems In proving (i), it is necessary to define a suitable domain for utility functions This is achieved by extending the formulation of the space of temporal lotteries in Kreps and Porteus (1978) to an infinite horizon framework A final contribution is the integration into a temporal setting of a broad class of atemporal non-expected utility theories For homogeneous members of the class due to Chew (1985) and Dekel (1986), the corresponding intertemporal asset pricing model is derived

Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework

the average real return to stocks in the United States has been about six percent per year higher than that on Treasury bills. At the same time, the average real return on Treasury bills has been about one percent per year. In this paper, I discuss and assess various theoretical attempts to explain these two different empirical phenomena: the large "equity premium" and the low "risk free rate." I show that while there are several plausible explanations for the low level of Treasury returns, the large equity premium is still largely a mystery to economists. In order to understand why the sample means of the equity premium and the risk free rate represent "puzzles," it is useful to review the basics of modern asset pricing theory. It is well known that the real returns paid by different financial securities may differ considerably, even when averaged over long periods of time. Financial economists typically explain these differences in average returns by attributing them to differences in the degree to which a security's return covaries with the typical investor's consumption. If this covariance is high, selling off the security would greatly reduce the variance of the typical investor's consumption stream; in equilibrium, the investor must be deterred from reducing his risk in this fashion by the security's paying a high average return. There is a crucial problem in making this qualitative explanation of cross-sectional differences in asset returns operational: what exactly is "the typical investor's consumption"? The famous Capital Asset Pricing Model represents one answer to this question: it assumes that the typical investor's consumption stream is perfectly correlated with the return to the stock market. This allows financial analysts to measure the risk of a financial security by its covariance with the return to the stock market (that is, a scaled version of its "beta"). More recently, Douglas Breeden (1979) and Robert Lucas (1978) described so-called "representative" agent models of asset returns in which per capita consumption is perfectly correlated with the consumption stream of the typical investor. (See also

/pdf/the-equity-premium-it-s-still-a-puzzle-2ms6nm9jlw.pdf

The Equity Premium: It's Still a Puzzle

Restrictions that a class of general equilibrium models place upon the average returns of equity and Treasury bills are found to be strongly violated by the U.S. data in the 1889–1978 period. This result is robust to model specification and measurement problems. We conclude that, most likely, an equilibrium model which is not an Arrow-Debreu economy will be the one that simultaneously rationalizes both historically observed large average equity return and the small average risk-free return.

The equity premium: a puzzle

Ongoing questions on the historical mean and standard deviation of the return on equities and bonds and on the equilibrium demand for these securities are addressed in the context of a stationary, overlapping-generations economy in which consumers are subject to a borrowing constraint. The key feature captured by the OLG economy is that the bulk of the future income of the young consumers is derived from their wages forthcoming in their middle age, while the bulk of the future income of the middle-aged consumers is derived from their savings in equity and bonds. The young would like to borrow and invest in equity but the borrowing constraint prevents them from doing so. The middle-aged choose to

/pdf/junior-can-t-borrow-a-new-perspective-on-the-equity-premium-2qt5s0hrsu.pdf

Junior Can't Borrow: A New Perspective on the Equity Premium Puzzle

This paper is a critical review of the literature on the "equity premium puzzle[equal, rising dots]. The puzzle, as originally articulated more than fifteen years ago, underscored the inability of the standard paradigm of Economics and Finance to explain the magnitude of the risk premium, that is, the return earned by a risky asset in excess of the return to a relatively riskless asset such as a U.S. government bond. The paper summarizes the historical experience for the USA and other industrialized countries and details the intuition behind the discrepancy between model prediction and empirical data. Various research approaches that have been proposed to enhance the model's realism are detailed and, as such, the paper reviews the major directions of theoretical financial research over the past ten years. The author argues that the majority of the proposed resolutions fail along crucial dimensions and proposes a promising direction for future research.

/pdf/the-equity-premium-in-retrospect-1jrvu3xtm6.pdf

Rajnish Mehra

Papers

THE EQUITY PREMIUM A Puzzle

The Equity Premium: It's Still a Puzzle

The equity premium: a puzzle

Junior Can't Borrow: A New Perspective on the Equity Premium Puzzle

The equity premium in retrospect