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53
Portfolio Choice with Many Risky Assets, Market Clearing and Cash Flow Predictability
, 2000
"... This paper examines portfolio allocations and market clearing prices when the representative agent can allocate across equity portfolios formed on the basis of characteristics like size and booktomarket and portfolio cash flows are predictable. The state space is discrete and priceconsumption rati ..."
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This paper examines portfolio allocations and market clearing prices when the representative agent can allocate across equity portfolios formed on the basis of characteristics like size and booktomarket and portfolio cash flows are predictable. The state space is discrete and priceconsumption ratios are obtained portfolio by portfolio simply by inverting an economywide matrix and multiplying this matrix by a portfoliospecific vector. The economywide matrix has the dimensionality of the state space. The paper calibrates cash flow predictability to the data using the consumptionwealth fraction (cay) of Lettau and Ludvigson (2000a) and dividend yield (div) as state variables. Annual cash flow processes are calibrated for three stock portfolios and for the aggregate consumption stream. The economy’s representative agent possesses a relative risk aversion coefficient of either 5 or 10. When cash flow predictability is calibrated to the data using cay as the predictor and risk aversion
A Dynamic Model of Labor Supply, Consumption/Savings, and Annuity Decisions Under Uncertainty
, 2000
"... This paper presents a dynamic model of labor/leisure, consumption/saving and annuity decisions over the life cycle. Such a dynamic model provides a framework for considering important policy experiments related to the reforms in Social Security. We address the role of labor supply in a life cyle uti ..."
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This paper presents a dynamic model of labor/leisure, consumption/saving and annuity decisions over the life cycle. Such a dynamic model provides a framework for considering important policy experiments related to the reforms in Social Security. We address the role of labor supply in a life cyle utility maximization model, extending the classical optimal lifetime consumption problem under uncertainty first formalized in Phelps (1962) and later in Hakansson (1970). We introduce the labor decision in the finite horizon consumption/saving problem and solve numerically the stochastic dynamic programming utility maximization problem of the individual. Analytical solutions are infeasible when the individual is maximizing utility over consumption and leisure, given nonlinear marginal utility. We illustrate how such a model captures changes in labor supply over the life cycle and show that simulated consumption and wealth accumulation paths are consistent with empirical evidence. We also present a model of endogenously determined annuities for the consumption/saving and labor/leisure framework with capital uncertainty in the presence of bequest motives and Social Security. This provides new insights into the
Introduction to Asset Pricing Theory and Tests
 in The International Library of Critical Writings in Financial Economics
, 2001
"... ..."
Good Times or Bad Times? Investors' Uncertainty and Stock Returns." Working paper  INSEAD
, 2003
"... This paper investigates empirically the dynamics of investors ’ beliefs and Bayesian uncertainty about the state of the economy as state variables that describe the timevariation in investment opportunities. Using measures of uncertainty constructed from the state probabilities estimated from two ..."
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This paper investigates empirically the dynamics of investors ’ beliefs and Bayesian uncertainty about the state of the economy as state variables that describe the timevariation in investment opportunities. Using measures of uncertainty constructed from the state probabilities estimated from twostate regimeswitching models of aggregate market return and of aggregate output, I find a negative relationship between the level of uncertainty and asset valuations. This relationship shows substantial crosssectional variation across portfolios sorted on size, booktomarket, and past returns, especially conditional on the state of the economy. I show that a conditional model with investors ’ beliefs and an uncertainty risk factor is remarkably successful in explaining a large part of the crosssectional variation in average portfolio returns. The uncertainty risk factor retains its incremental explanatory power when compared to other conditional models such as the conditional CAPM. (JEL G12, G14 and D80) Uncertainty is a central tenet of finance. Investors often do not have perfect knowledge of the processes associated with macrolevel variables or stock dividends but instead must make intelligent estimates on key state variables
Mispricing of S&P 500 Index Options
"... We address the implied volatility smile of the S&P 500 index options before and after the October 1987 crash. In a singleperiod model, the cross sections of onemonth calls and puts violate stochastic dominance even with realistic bidask spreads and transaction costs on the options and the ind ..."
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We address the implied volatility smile of the S&P 500 index options before and after the October 1987 crash. In a singleperiod model, the cross sections of onemonth calls and puts violate stochastic dominance even with realistic bidask spreads and transaction costs on the options and the index (SPDRs). The violations are frequent even prior to the crash, in contrast to the extant literature that considers the postcrash pronounced smile to be the primary challenge to economic theory. In a multiperiod model, the restrictions on prices that prevent stochastic dominance are less stringent, yet violations of stochastic dominance persist both before and after the crash.
Discounting Expected Values with Parameter Uncertainty
, 2000
"... In valuing future cash ows standard practice i s to take the current cash ow and then extrapolate at an expected growth rate , which can vary at dierent points in time. This practice stems form the standard way of deal ing with time value of money problems under certainty. However, with uncertai ..."
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In valuing future cash ows standard practice i s to take the current cash ow and then extrapolate at an expected growth rate , which can vary at dierent points in time. This practice stems form the standard way of deal ing with time value of money problems under certainty. However, with uncertain cash ows this practice underestimates the expected cash ows when the growth rates are serial ly correlated. As a result, both va lue and the equity cost, calculated as an internal rate of return, are biased low. Given the prevalence of serial corre lation i n the economy this paper demonstrates how to incorporate the eects of serial correlation i n a simple way and demonstrates by way of a simulation that the eects can be signicant. As a result, it casts doubt on the usefulness of several standard valuation approaches and results.
Digital Portfolio Theory
"... Abstract. The Modern Portfolio Theory of Markowitz maximized portfolio expected return subject to holding total portfolio variance below a selected level. Digital Portfolio Theory is an extension of Modern Portfolio Theory, with the added dimension of memory. Digital Portfolio Theory decomposes the ..."
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Abstract. The Modern Portfolio Theory of Markowitz maximized portfolio expected return subject to holding total portfolio variance below a selected level. Digital Portfolio Theory is an extension of Modern Portfolio Theory, with the added dimension of memory. Digital Portfolio Theory decomposes the portfolio variance into independent components using the signal processing decomposition of variance. The risk or variance of each security’s return process is represented by multiple periodic components. These periodic variance components are further decomposed into systematic and unsystematic parts relative to a reference index. The Digital Portfolio Theory model maximizes portfolio expected return subject to a set of linear constraints that control systematic, unsystematic, calendar and noncalendar variance. The paper formulates a single period, digital signal processing, portfolio selection model using crosscovariance constraints to describe covariance and autocorrelation characteristics. Expected calendar effects can be optimally arbitraged by controlling the memory or autocorrelation characteristics of the efficient portfolios. The Digital Portfolio Theory optimization model is compared to the Modern Portfolio Theory model and is used to find efficient portfolios with zero calendar risk for selected periods. Key words: portfolio optimization, portfolio theory, digital signal processing, calendar anomalies 1.
Asset Pricing with Heterogeneous Preferences ∗
, 2013
"... Finding a stochastic discount factor that is robust to model misspecification is not trivial. I consider a general equilibrium model with many agents who can invest their wealth in many assets. As long as (i) agents have (individual, time, and statedependent) recursive preferences that arehomothe ..."
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Finding a stochastic discount factor that is robust to model misspecification is not trivial. I consider a general equilibrium model with many agents who can invest their wealth in many assets. As long as (i) agents have (individual, time, and statedependent) recursive preferences that arehomotheticincurrentconsumptionandcontinuationvaluewithacommon relativeriskaversioncoefficientγ and(ii)assetreturnsandindividual state variables are conditionally independent (e.g., GARCH processes), I prove that the −γth power of market return is a valid stochastic discount factor. Within this class of models, asset prices are determined by relative risk aversion and technology alone, and “returnsbased asset pricing” is robust to model misspecification as opposed to the consumptionbased approach. Using the historical returns on portfolios of U.S. stocks sorted by size and booktomarket value, I find that a relative risk aversion coefficient of around 2 explains asset returns. The conditional and unconditional moment restrictions are not rejected. I recast the equity premium puzzle as a macroeconomics puzzle, not as a finance puzzle.