Differences in Opinion and Risk Premium

When people agree to disagree, this paper examines the impact of the disagreement among agents on market equilibrium and equity premium. Within the standard mean variance framework, we consider a market of two risky assets, a riskless asset and two (and then a continuum of) agents who have different preferences and heterogeneous beliefs in the means and variance/covariances of the asset returns. By constructing a consensus belief, we introduce a boundedly rational equilibrium (BRE) to characterize the market equilibrium and derive a CAPM under heterogeneous beliefs. When the differences in opinion are formed as mean-preserving spreads of a benchmark homogeneous belief, we analyz eexplicitly the impact on the market equilibrium and risk premium, showing that the risk tolerance, optimism/pessimism and con?dence/doubt can jointly generate high risk premium and low risk-free rate. JELClassi?cation:.Assetprices;heterogeneousbeliefs;boundedlyrationalequilibriuasset prices; heterogeneous beliefs; boundedly rational equilibrium; zero-beta CAPM; risk premium

Implications of Asymmetry Risk for Portfolio Analysis and Asset Pricing

Asymmetric shocks are common in markets; securities' payoffs are not normally distributed and exhibit skewness. This paper studies the portfolio holdings of heterogeneous agents with preferences over mean, variance and skewness, and derives equilibrium prices. A three funds separation theorem holds, adding a skewness portfolio to the market portfolio; the pricing kernel depends linearly only on the market return and its squared value. Our analysis extends Harvey and Siddique's (2000) conditional mean-variance-skewness asset pricing model to non-vanishing risk-neutral market variance. The empirical relevance of this extension is documented in the context of the asymmetric GARCH-in-mean model of Bekaert and Liu (2004).Financial markets; Market structure and pricing

Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Levy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps, and also different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements, but the maximally allowable premium on downward index movements.dampened power law; alpha-stable distribution; central limit theorem; upside movement; downside movement

Does Lumpy Investment Matter for Business Cycles?

We present an analytically tractable general equilibrium business cycle model that features micro-level investment lumpiness. We prove an exact irrelevance proposition which provides sufficient conditions on preferences, technology, and the fixed cost distribution such that any positive upper support of the fixed cost distribution yields identical equilibrium dynamics of the aggregate quantities normalized by their deterministic steady state values. We also give two conditions for the fixed cost distribution, under which lumpy investment can be important to a first-order approximation: (i) The steady-state elasticity of the adjustment rate is large so that the extensive margin effect is large. (ii) More mass is on low fixed costs so that the general equilibrium price feedback effect is small.generalized (S,s) rule, lumpy investment, general equilibrium, business cycles, marginal Q, exact irrelevance proposition

Heterogeneity, Bounded Rationality and Market Dysfunctionality

As the main building blocks of the modern finance theory, homogeneity and rational expectation have faced difficulty in explaining many market anomalies, stylized factors, and market inefficiency in empirical studies. As a result, heterogeneity and bounded rationality have been used as an alterative paradigm of asset price dynamics and this paradigm has been widely recognized recently in both academic and financial market practitioners. Within the framework of Chiarella, Dieci and He (2006a, 2006b) on mean-variance analysis under heterogeneous beliefs in terms of either the payoffs or returns of the risky assets, this paper examines the effect of the heterogeneity. We first demonstrate that, in market equilibrium, the standard one fund theorem under homogeneous belief does not held under heterogeneous belief in general, however, the optimal portfolios of investors are very close to the market efficient frontier. By imposing certain distribution assumption on the heterogeneous beliefs, we then use Monte Carlo simulations to show that certain heterogeneity among investors can improve the Sharpe and Treynor ratios of the portfolios and investors can benefit from the diversity in investors’ beliefs. We also show that non-normality of market equilibrium return distributions is an outcome of the market aggregation of individual investors who make rational decisions based on their beliefs. Our results explain the empirical funding that that managed funds under-perform the market index on average and show that heterogeneity can improve the market efficiency.heterogeneity; bounded rationality; heterogeneous CAPM; mean-variance efficiency; Sharpe and Treynor ratios

Does Lumy Investment Matter for Business Cycles?

We present an analytically tractable general equilibrium business cycle model that features micro-level investment lumpiness. We prove an exact irrelevance proposition which provides sufficient conditions on preferences, technology, and the fixed cost distribution such that any positive upper support of the fixed cost distribution yields identical equilibrium dynamics of the aggregate quantities normalized by their deterministic steady state values. We also give two conditions for the fixed cost distribution, under which lumpy investment can be important to a first-order approximation: (i) The steady-state elasticity of the adjustment rate is large so that the extensive margin effect is large. (ii) More mass is on low fixed costs so that the general equilibrium price feedback effect is small. Our theoretical results may reconcile some debate and some numerical findings in the literature.generalized (S,s) rule, lumpy investment, general equilibrium, business cycles, marginal Q, exact irrelevance proposition

The Degree of Stability of Price Diffusion

The distributional form of financial asset returns has important implications for the theoretical and empirical analyses in economics and finance. It is now a well-established fact that financial return distributions are empirically nonstationary, both in the weak and the strong sense. One first step to model such nonstationarity is to assume that these return distributions retain their shape, but not their localization (mean ) or size (volatility ) as the classical Gaussian distributions do. In that case, one needs also to pay attention to skewedness and kurtosis, in addition to localization and size. This modeling requires special Zolotarev parametrizations of financial distributions, with a four parameters, one for each relevant distributional moment. Recently popular stable financial distributions are the Paretian scaling distributions, which scale both in time T and frequency . For example, the volatility of the lognormal financial price distribution, derived from the geometric Brownian asset return motion and used to model Black-Scholes (1973) option pricing, scales according to T^{0.5}. More generally, the volatility of the price return distributions of Calvet and Fisher's (2002) Multifractal Model for Asset Returns (MMAR) scales according to T^{(1/(_{Z}))}, where the Zolotarev stability exponent _{Z} measures the degree of the scaling, and thus of the nonstationarity of the financial returns. Keywords: Stable distributions, price diffusion, stability exponent, Zolotarev parametrization, fractional Brownian motion, financial markets.Stable distributions, price diffusion, stability exponent, Zolotarev parametrization, fractional Brownian motion, financial markets

Occupational Choice and the Private Equity Premium Puzzle

This paper suggests a solution to what has become known as the "private equity premium puzzle" (Moskowitz and Vissing-Jorgensen (2002)). We interpret occupational choice as a dynamic portfolio choice problem of a life-cycle investor facing a liquidity constraint and imperfect information about the profitability of potential businesses. In this setting, becoming an entrepreneur is equivalent to investing in non-traded private equity capital subject to transaction costs. We model the return on private equity as the sum of two components, the individual ability of the entrepreneur and idiosyncratic business risk. Information is imperfect, because only entrepreneurs observe their own business risk realizations. Using numerical techniques we find that the model generates the observed return structure for private equity using standard CRRA-preferences and fully rational expectations.Portfolio choice, Life-cycle models, Private equity

Dollarization Persistence and Individual Heterogeneity

The most salient feature of financial dollarization, and the one that causes more concern to policy makers, is its persistence: even after successful macroeconomic stabilizations, dollarization ratios often remain high. In this paper we claim that this persistence is connected to the fact that the participants in the dollar deposit market are fairly heterogenous, and so is the way they form their optimal currency portfolio.We develop as simple model when agents differ in their ability to process information, which turns out to be enough to generate persistence up on aggregation. We find empirical support for this claim with data from three Latin American countries and Poland.Dollarization, individual heterogeneity, persistence, aggregation