This paper analyzes the effects of portfolio constraints on asset returns and volatility. Portfolio constraints may arise due to minimum capital requirement regulations, margin requirements or leverage constraints on portfolio managers. We analyze how cross-sectional heterogeneity in preferences affect the equilibrium stock price, returns and volatility in the presence of portfolio constraints. We show that portfolio constraints can simultaneously produce high equity Sharpe ratio and low interest rates in equilibrium. Moreover, the stock returns volatility decreases when the constraint binds. The negative effect of the constraint on stock returns volatility is most pronounced when the constraint binds in the bad state of the economy and the unconstrained investor is poorer than the constrained investor. In our model the constraint binds more frequently in the bad states of the economy. Given the empirical evidence in support of the stylized fact that stock returns volatility is counter-cyclical, our findings therefore suggest that margin requirements are indeed effective in mitigating the wild fluctuations in the stock market volatility when prices go low. We also perform a welfare analysis and show that the unconstrained investor is made better off while the constrained is worse off when the constraint binds.

Portfolio constraints are widespread and have significant effects on asset prices. This paper studies the effects of constraints in a dynamic economy populated by investors with different risk aversions and beliefs about the rate of economic growth. The paper provides a comparison of various constraints and conditions under which these constraints help match certain empirical facts about asset prices. Under these conditions, borrowing and short-sale constraints decrease stock return volatilities, whereas limited stock market participation constraints amplify them. Moreover, borrowing constraints generate spikes in interest rates and volatilities and have stronger effects on asset prices than short-sale constraints.

While mainstream financial theories and applications assume that asset returns are normally distributed and individual preferences are quadratic, the overwhelming empirical evidence shows otherwise. Indeed, most of the asset returns exhibit “fat-tails” distributions and investors exhibit asymmetric preferences. These empirical findings lead to the development of a new area of research dedicated to the introduction of higher order moments in portfolio theory and asset pricing models. Multi-moment asset pricing is a revolutionary new way of modeling time series in finance which allows various degrees of long-term memory to be generated. It allows risk and prices of risk to vary through time enabling the accurate valuation of long-lived assets. This book presents the state-of-the art in multi-moment asset allocation and pricing models and provides many new developments in a single volume, collecting in a unified framework theoretical results and applications previously scattered throughout the financial literature. The topics covered in this comprehensive volume include: four-moment individual risk preferences, mathematics of the multi-moment efficient frontier, coherent asymmetric risks measures, hedge funds asset allocation under higher moments, time-varying specifications of (co)moments and multi-moment asset pricing models with homogeneous and heterogeneous agents. Written by leading academics, Multi-moment Asset Allocation and Pricing Models offers a unique opportunity to explore the latest findings in this new field of research.

In Asset Pricing and Portfolio Choice Theory, Kerry E. Back at last offers what is at once a welcoming introduction to and a comprehensive overview of asset pricing. Useful as a textbook for graduate students in finance, with extensive exercises and a solutions manual available for professors, the book will also serve as an essential reference for scholars and professionals, as it includes detailed proofs and calculations as section appendices. Topics covered include the classical results on single-period, discrete-time, and continuous-time models, as well as various proposed explanations for the equity premium and risk-free rate puzzles and chapters on heterogeneous beliefs, asymmetric information, non-expected utility preferences, and production models. The book includes numerous exercises designed to provide practice with the concepts and to introduce additional results. Each chapter concludes with a notes and references section that supplies pathways to additional developments in the field.

We analyze the joint effect of borrowing and short-sale constraints in a dynamic economy populated by two constrained investors with heterogeneous risk aversions and beliefs. We find that equilibrium prices adjust in such a way that the constraints never simultaneously bind. When the constraints are tight, we observe a regime switch behavior (discontinuities) in the risk-free rate and market price of risk at a critical state, where two equilibria exist, i.e., either constraint can be binding. Stock return volatility is the lowest at the critical state. Imposing a ban on short-sales at the same time when access to credit is restrictive or tightening borrowing during a short-sale ban can potentially move the equilibrium away from the critical state, thus increase stock return volatility rather than reducing it.