NBER Reporter: Winter 2000/2001

Asset Pricing

The NBER's Program on Asset Pricing met in Cambridge on November 3. Jacob Boudoukh, NBER and New York University, and Jiang W. Wang, NBER and MIT, organized the program and chose the following papers for discussion:

John Y. Campbell and Luis M. Viceira, NBER and Harvard University, and Lewis Chan, Hong Kong University of Science and Technology, "A Multivariate Model of Strategic Asset Allocation"

Discussant: Anthony Lynch, New York University

Joao F. Gomes, Leonid Kogan, and Lu Zhang, University of Pennsylvania, "Equilibrium Cross Section of Returns"

Discussant: Jonathan Berk, NBER and University of California, Berkeley

Qiang Dai, New York University, "From Equity Premium Puzzle to Expectations Puzzle: A General Equilibrium Production Economy of Stochastic Habit Formation"

Discussant: John H. Cochrane, NBER and University of California, Los Angeles

Nicholas C. Barberis, NBER and University of Chicago, and Ming Huang, Stanford University, "Mental Accounting, Loss Aversion, and Individual Stock Returns"

Discussant: John Heaton, NBER and University of Chicago

Erzo G. J. Luttmer and Thomas Mariotti, London School of Economics, "Subjective Discounting in an Exchange Economy"

Discussant: Stanley Zin, NBER and Carnegie Mellon University

Michael W. Brandt, NBER and University of Pennsylvania, Qi Zeng, University of Pennsylvania, and Lu Zhang, "Equilibrium Stock Return Dynamics under Alternative Rules of Learning about Hidden States"

Discussant: Pietro Veronesi, University of Chicago

Campbell, Chan, and Viceira show how the predictability of asset returns can affect the portfolio choices of long-lived investors who value wealth not for its own sake but for the consumption it can support. The authors develop an approximate solution method for the optimal consumption-and-portfolio-choice problem of an infinitely-lived investor with Epstein-Zin utility who faces a set of asset returns described by a vector autoregression in returns and state variables. Their empirical estimates, based on long-run annual and postwar quarterly U.S. data, suggest that the predictability of stock returns greatly increases the optimal demand for stocks. Nominal bonds have only a small role in optimal long-term portfolios. The authors extend the analysis to consider long-term inflation-indexed bonds and find that extremely conservative investors should hold large positions in these bonds when they are available.

Gomes, Kogan, and Zhang explicitly link expected stock returns to firm characteristics--such as firm size and book-to-market (B/M) ratio--in a dynamic general equilibrium production economy. Although stock returns in the model are characterized by an intertemporal Capital Asset Pricing Model (CAPM) with the market portfolio as the only factor, both size and B/M play separate roles in describing the cross section of returns. These two firm characteristics appear to predict stock returns because they are correlated with the true conditional market beta of returns. These cross-sectional relations can subsist even after controlling for a typical empirical estimate of market beta. This supports the view that the documented ability of size and B/M to explain the cross section of stock returns is not necessarily inconsistent with a single-factor conditional CAPM.

Dai develops a general equilibrium model for a representative agent production economy with stochastic internal habit formation. The model Dai describes has a scale-independent economy with a unique stochastic investment opportunity set. Local correlation between the stochastic interest rate and the time-varying market price of risk can be determined endogenously and leads to correct predictions of the sign and magnitude of several major empirical puzzles in both equity and bond markets. Dai shows that the equity premium puzzle, the risk-free rate puzzle, and the expectations puzzle are completely resolved under reasonable parameter values. Thus, he establishes the inextricable link between the equity and bond markets, both theoretically and empirically.

Barberis and Huang study equilibrium asset prices in a model where investors are loss averse, paying particular attention to what they are loss averse about. The authors consider two possibilities, which correspond to different assumptions about how people do mental accounting or about how they evaluate their investment performance. In one case, investors track their performance stock by stock and are loss averse over individual stock fluctuations. In the other case, they measure their performance at the portfolio level, and are loss averse only over portfolio fluctuations. The authors find that loss aversion over individual stock fluctuations helps to explain a wide range of empirical facts, both in the time series and in the cross section. In simulated data, individual stock returns have a high mean excess volatility, and are slightly predictable in the time series. There are also large "value" and "size" premiums in the cross section. Investor loss aversion over portfolio fluctuations is less successful in explaining the facts: individual returns are insufficiently volatile and excessively correlated, while the premiums for value and size largely disappear.

Luttmer and Mariotti describe the equilibrium of a discrete-time exchange economy in which consumers with arbitrary subjective discount factors and quasi-homothetic period utility functions follow linear Markov consumption and portfolio strategies. The authors provide an analytically convenient continuous-time approximation and show how subjective rates of time preference affect risk-free rates but not instantaneous risk-return trade-offs. They also examine the quantitative effects of hyperbolic discounting in an economy in which log endowments are subject to temporary and permanent shocks that are governed by a Feller (1951) square-root process. They find that hyperbolic and quasi-hyperbolic discount factors can significantly increase the volatility of aggregate wealth and raise the expected excess return on aggregate wealth.

Brandt, Zeng, and Zhang examine the properties of equilibrium stock returns in an incomplete information economy in which the agents need to learn the hidden state of the endowment process. They consider the case of optimal Bayesian learning and suboptimal learning, including near-rational learning, over- or underconfidence, optimism or pessimism, adaptive learning, and limited memory. They find that Bayesian learning can quantitatively explain long-run mean-reversion, predictability, volatility clustering, and leverage effects in stock returns. However, it cannot generate enough short-run momentum because any uncertainty about the state is resolved too quickly (that is, agents learn too fast). Among the suboptimal learning rules, only overconfidence can marginally improve some aspects of the model (that is, introduce short-run momentum) without substantially deteriorating other aspects.

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