Asset pricing with heterogeneous investors and portfolio constraints

We study dynamic general equilibrium in one-tree and two-trees Lucas economies with one consumption good and two CRRA investors with heterogeneous risk aversions and portfolio constraints. We provide a tractable characterization of equilibrium without relying on the assumption of logarithmic constrained investors, popular in the literature, under which wealth-consumption ratios of these investors are unaffected by constraints. In one-tree economy we focus on the impact of limited stock market participation and margin constraints on market prices of risk, interest rates, stock return volatilities and price-dividend ratios. We demonstrate conditions under which constraints increase or decrease these equilibrium processes, and generate dynamic patterns consistent with empirical findings. In a two-trees economy we demonstrate that investor heterogeneity gives rise to large countercyclical excess stock return correlations, but margin constraints significantly reduce them by restricting the leverage in the economy, and give rise to rich saddle-type patterns. We also derive a new closed-form consumption CAPM that captures the impact of constraints on stock risk premia

Dynamic equilibrium with rare events and heterogeneous Epstein-Zin investors

We consider a general equilibrium Lucas (1978) economy with one consumption good and two heterogeneous Epstein-Zin investors. The output is subject to rare large drops or, more generally, can have non-lognormal distribution with higher cumulants. The heterogeneity in preferences generates excess stock return volatilities, procyclical price-dividend ratios and interest rates, and countercyclical market prices of risk when the elasticity of intertemporal substitution (EIS) is greater than one. Moreover, the latter results cannot be jointly replicated in a model where investors have EIS_ 1 or CRRA preferences. We propose new approach for deriving equilibrium, and extend the analysis to the case of heterogeneous beliefs about probabilities of rare events

Collateral constraints and asset prices

We study the effects of collateral constraints in an economy populated by investors with nonpledgeable labor incomes and heterogeneous preferences and beliefs. We show that these constraints inflate stock prices, generate spikes and crashes in price-dividend ratios and volatilities, clustering of volatilities, and leverage cycles. They also lead to substantial decreases in interest rates and increases in Sharpe ratios when investors are anxious about hitting constraints due to production crises in the economy. Furthermore, stock prices have large collateral premiums over nonpledgeable incomes. We derive asset prices and stationary distributions of the investors' consumption shares in closed form

Asset pricing with index investing

We provide a novel theoretical analysis of how index investing affects capital market equilibrium. We consider a dynamic exchange economy with heterogeneous investors and two Lucas trees and find that indexing can either increase or decrease the correlation between stock returns and in general increases (decreases) volatilities and betas of stocks with larger (smaller) market capitalizations. Indexing also decreases market volatility and interest rates, although those effects are weak. The impact of index investing is particularly strong when stocks have heterogeneous fundamentals. Our results highlight that indexing changes not only how investors can trade but also their incentives to trade

Portfolio choice and asset pricing in incomplete markets

This Thesis studies the portfolio choice and asset pricing in economic settings with incomplete markets and is comprised of three chapters. Chapter 1 explores the formation of stock prices in a general equilibrium economy with heterogeneous investors facing portfolio constraints. We compute the equilibrium when both investors have (identical for simplicity) CRRA preferences, one of them is unconstrained while the other faces an upper bound constraint on the proportion of wealth invested in stocks. We demonstrate that under certain parameters the model can generate countercyclical stock return volatilities, procyclical price-dividend ratios, excess volatility and other patterns observed in the data. Our baseline analysis is also extended to models with heterogeneous beliefs. Chapter 2 studies the portfolio choice in economies with incomplete markets with investors guided by mean-variance criteria. Mean-variance criteria remain prevalent in multiperiod problems, and yet not much is known about their dynamically optimal policies. In this chapter we provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the total risky asset demand. Chapter 3 provides a simple solution to the hedging problem in a general incomplete-market economy in which a hedger, guided by the minimum-variance criterion, aims at reducing the risk of a non-tradable asset. We derive fully analytical optimal time-consistent hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks" familiar in risk management applications. We demonstrate that our optimal hedges typically outperform their static and myopic counterparts under plausible economic environments

Collateral constraints and asset prices

We study the effects of collateral constraints in an economy populated by investors with nonpledgeable labor incomes and heterogeneous preferences and beliefs. We show that these constraints inflate stock prices and generate spikes and crashes in price-dividend ratios and volatilities, clustering of volatilities, and leverage cycles. They also lead to substantial decreases in interest rates and increases in Sharpe ratios when investors are anxious about hitting constraints due to production crises in the economy. Furthermore, stock prices have large collateral premiums over nonpledgeable incomes. We derive asset prices and stationary distributions of the investors' consumption shares in closed form

Asset pricing with heterogeneous preferences, beliefs, and portfolio constraints

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

Multi-asset noisy rational expectations equilibrium with contingent claims

We consider a noisy rational expectations equilibrium in a multi-asset economy populated by informed and uninformed investors, and noise traders. Informed investors privately observe an aggregate risk factor affecting the probabilities of different states of the economy. Uninformed investors attempt to extract that information from asset prices, but full revelation is prevented by noise traders. We relax the usual assumption of normally distributed asset payoffs and allow for assets with more general payoff distributions, including contingent claims, such as options and other derivatives. We show that assets reveal information about the risk factor only if they help span the exposure of probabilities of states to the risk factor. When the market is complete, we provide equilibrium asset prices and optimal portfolios of investors in closed form. In incomplete markets, we derive prices and portfolios in terms of easily computable inverse functions

Investor protection and asset prices

Empirical evidence suggests that investor protection has significant effects on ownership concentration and asset prices. We develop a dynamic asset pricing model to address the empirical regularities and uncover the underlying mechanisms at play. Our model features a controlling shareholder who endogenously accumulates control over a firm, and diverts a fraction of its output. In line with empirical evidence, better investor protection decreases stock holdings of controlling shareholders, increases stock mean-returns, and increases stock return volatilities when ownership concentration is sufficiently high. The model also predicts that better protection increases interest rates and decreases leverage

Securitized banking, asymmetric information, and financial crisis: regulating systemic risk away

We develop a model of securitized (Originate, then Distribute) lending, in which both publicly observed aggregate shocks to values of securitized loan portfolios, and later some asymmetrically observed discernment of varying qualities of subsets thereof, play crucial roles. We find that originators and potential buyers of such assets may differ in their preferences over their timing of trades, leading to a reduction in the aggregate surplus accruing from securitization. In addition, heterogeneity in sellers' selected timing of trades - arising from differences in their ex ante beliefs - coupled with initial leverage choices based on pre-shock prices, may lead to financial crises, implying uncoordinated asset liquidations inconsistent with any inter-temporal market equilibrium. We consider and contrast two mitigating regulatory interventions: leverage restrictions, and ex ante specified resale price guarantees on securitized asset portfolios. We show that the latter tool performs strictly better than the former, by ensuring not only bank survival, but also enhanced social surplus arising from securitized lending. It does so by inducing a more coordinated market equilibrium, that does not lead to interim leverage buildup to support a "cherry picking" seller trading strategy