Robust consumption and portfolio choice for time varying investment opportunities

This paper examines a continuous-time intertemporal consumption and portfolio choice problem for an investor with recursive preferences. The investor worries about model misspecification and seeks robust decision rules. The expected excess return of a risky asset follows a mean-reverting process. I find that whether the concern about model misspecification decreases the total demand for equities largely depends on risk aversion and the attitude toward intertemporal substitution. When the elasticity of intertemporal substitution is about 1 and risk aversion is moderate, the aversion to model uncertainty increases the proportion of wealth invested in equities. The calibration analysis based on detection-error probabilities shows that the quantitative effect of robustness is almost negligible.     

Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach

This paper develops a nonparametric approach to examine how portfolio and consumption choice depends on variables that forecast time-varying investment opportunities. I estimate single-period and multiperiod portfolio and consumption rules of an investor with constant relative risk aversion and a one-month to 20-year horizon. The investor allocates wealth to the NYSE index and a 30-day Treasury bill. I find that the portfolio choice varies significantly with the dividend yield, default premium, term premium, and lagged excess return. Furthermore, the optimal decisions depend on the investor's horizon and rebalancing frequency.     

Equilibrium Interest Rates and Multiperiod Bonds in a Partially Observable Economy

This paper analyzes the market for financial assets in a production and exchange economy with several realized outputs and a single unobservable source of nondiversifiable risk. The paper demonstrates that, for a large class of diffusion outputs and preferences, optimizing consumers first estimate the realizations of the unobservable factor and then use these estimates to determine portfolio and consumption rules. Moreover, the explicit consideration of this unobservable productivity factor affects equilibrium demands and prices. The equilibrium spot rate of interest emerges as the “best estimate” of the unobservable factor, and multiperiod default-free bonds arise as the optimal hedge for the unobservable changes of the stochastic investment opportunity set.     

An intemporal model of asset prices in a Markov economy with a limiting stationary distribution

A testable single-beta model of asset prices is presented. Ifstate variables have a long-run stationary joint dysfunction,then the rate return on a very long-term default-free discountbond will be perfectly correlated with the representative investor'smarginal utility of consumption. Thus, the covariance of anasset's return with the return on such a bond will be an appropriatemeasure of the asset's riskiness. The model can be, therefore,applied or tested even though the market portfolio or aggregateconsumption may not be observable. It also is shown that theexpected rate of return on a very long-term bond is equal toits variance. This proposition can be tested to determine whetherstate variables follow stationary processes.     

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.     

Equilibrium asset prices and no-arbitrage with portfolio constraints

We examine intertemporal asset pricing when short sales areconstrained in proportion to the value of an investor's portfolio.All assets' prices exceed every investor's marginal utilityof consumption-based valuation of the associated dividends ifevery investor finds himself constrained in some asset in somestate; we exhibit such an equilibrium. An asset's price decomposesinto three (investor-specific) components: the consumption valueof its dividends, a speculative value premium, and a collateralvalue premium. The validity of the no-arbitrage pricing approachis shown to depend critically on the difference between realsecurities and their synthetic counterparts.     

LONG-TERM AND SHORT-TERM CAUSAL RELATIONS BETWEEN DIVIDENDS AND STOCK PRICES: A TEST OF LINTNER'S DIVIDEND MODEL AND THE PRESENT VALUE MODEL OF STOCK PRICES

In this paper we test the joint implications for the intertemporal behavior of stock prices and dividends expressed in the Lintner dividend model and the present value model of stock prices. We use macro data corresponding to quarterly S&P 500 index prices and dividends for January 1930–December 1990. The methodology used is the error correction model (ECM), which allows testing for long-term and short-term relations between the two variables. Results from the ECM indicate that a long-term equilibrium relation exists between dividends and stock prices, and that an error correction mechanism is at work when a disequilibrium exits between the two variables. Stock prices and dividends also influence each other in the short term. Finally, the results show that dividends and stock prices exhibit a contemporaneous causal relation.     

Stock prices,inflation, and the term structure of interest rates

In this article, the quantitative form of capital market equilibrium is derived for a multi-period economy in which (a) there are many consumption goods whose future prices are uncertain, and (b) the investment opportunities available to consumers include both common stocks and default-free bills of many different maturities. Particular emphasis is placed on consumer reaction to uncertainty about shifts in commodity prices and the term structure of interest rates and on the way one should expect to observe this reaction reflected in portfolio choices and equilibrium stock prices.     

Portfolio choice and equilibrium in capital markets with safety-first investors

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.     

The Valuation of Multivariate Contingent Claims in Discrete Time Models

There are several examples in the literature of contingent claims whose payoffs depend on the outcomes of two or more stochastic variables. Familiar cases of such claims include options on a portfolio of options, options whose exercise price is stochastic, and options to exchange one asset for another. This paper derives risk neutral valuation relationships (RNVRs) in a discrete time setting that facilitate the pricing of such complex contingent claims in two specific cases: joint lognormally distributed underlying variables and constant proportional risk aversion on the part of investors, and joint normally distributed underlying variables and constant absolute risk aversion preferences, respectively. This methodology is then applied to the valuation of several interesting complex contingent claims such as multiperiod bonds, multicurrency option bonds, and investment options.     

Precautionary Saving and Consumption Smoothing across Time and Possibilities

This paper examines how aversion to risk and aversion to intertemporal substitution determine the strength of the precautionary saving motive in a two-period model with Selden/Kreps–Porteus preferences. For small risks, we derive a measure of the strength of the precautionary saving motive that generalizes the concept of "prudence" introduced by Kimball (1990b) . For large risks, we show that decreasing absolute risk aversion guarantees that the precautionary saving motive is stronger than risk aversion, regardless of the elasticity of intertemporal substitution. Holding risk preferences fixed, the extent to which the precautionary saving motive is stronger than risk aversion increases with the elasticity of intertemporal substitution. We derive sufficient conditions for a change in risk preferences alone to increase the strength of the precautionary saving motive and for the strength of the precautionary saving motive to decline with wealth. Within the class of constant elasticity of intertemporal substitution, constant-relative risk aversion utility functions, these conditions are also necessary.     

Comments on the valuation of derivative assets

This paper presents an alternative approach to derive the Breeden-Litzenberger valuation formula, which expresses the price of an arbitrary derivative security in terms of call options' prices. This valuation formula follows from the observation that a continuous derivative security can be replicated by a portfolio including a bond and call options with all possible exercise prices. Discrete terms are added to the original Breeden-Litzenberger formula to reflect possible discontinuities of the call option price's derivative with respect to the exercise price. These discontinuities are subsequently shown to correspond to mass points of the probability distribution of the stock price. Several applications of the Breeden-Litzenberger valuation formula are demonstrated.     

Market Created Risk

We develop a multiperiod rational expectations model of securities market equilibrium in which equilibrium prices may move between periods even though it is common knowledge that no new information has arrived about ultimate security payoffs. This happens because investors know they have imperfect information about the endowments of other investors and this knowledge affects their probability beliefs about the prices that will prevail at the intermediate trading date. These beliefs are reflected in the equilibrium at the initial trading date when investors focus on the probabilities of intermediate capital gains and losses, rather than ultimate payoffs.     

A Generalized Earnings‐Based Stock Valuation Model with Learning

We present a stock valuation model in an incomplete‐information environment in which the unobservable mean of earnings growth rate (MEGR) is learned and price is updated continuously. We calibrate our model to a market portfolio to empirically evaluate its performance. Of the 8.84% total risk premium we estimate, the earnings growth premium is 4.57%, the short‐rate risk contributes 3.38%, and the learning‐induced risk premium on the unknown MEGR is 0.89% (a nontrivial 10% of the total risk premium). This result highlights the significant learning effect on valuation, implying an additional risk premium in an incomplete‐information environment.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

What is the impact of wealth shocks on asset allocation?

I test the assumption of constant relative risk aversion using U.S. macroeconomic data and analyse the role of wealth shocks in generating transitory changes in asset portfolio composition. I show that the risky asset share exhibits cyclical behavior and it is significantly (and positively) affected by unexpected variation in wealth. Therefore, the empirical evidence suggests that risk aversion is counter-cyclical. I also find that the portfolio share of housing wealth falls when the agent is faced with a positive wealth shock, i.e. housing is a hedge against unfavorable wealth fluctuations. Finally, considering a variety of wealth definitions, the results show that: (i) wealth effects are stronger for direct holdings of risky assets than for indirect holdings, which highlights that investors do not typically trade some assets such as pension or mutual funds; (ii) although significant, wealth effects on asset allocation are mainly temporary as agents quickly rebalance the asset portfolio composition (i.e. there is weak evidence of inertia or slow adjustment in asset allocation); and (iii) changes in expected returns partially explain the variation in risky asset allocation.     

Tests of the multiperiod two-parameter model

Although investors face multiperiod decision problems, there are conditions under which the results of the one-period two-parameter model apply period by period. In addition to the assumptions made in the development of the two-parameter model itself (a perfect capital market, investor risk aversion, and normal distributions of one-period portfolio returns), the critical assumption in a multiperiod context is that, for any t, returns on portfolio assets from t?1 to t are independent of stochastic elements of the state-of-the-world at time t that affect investor tastes for given levels of wealth to be obtained at t.One such element of the state-of-the-world is the nature of investment opportunities to be available at t. For example, if the level of expected returns on investment portfolios to be available at time t is uncertain at time t?1, and if the returns from t?1 to t on some investment assets are more strongly related to the level of expected returns at t than returns on other assets, then the former assets are better vehicles for hedging against the level of expected returns at t. This can affect the demands for assets and their prices in such a way that the simple results of the one-period two-parameter model do not hold.The empirical tests of this paper reveal no evidence of measurable relationships between the returns on portfolio assets from t?1 to t and the level of expected returns to be available at t. Indeed, in our opinion there is no reliable evidence that the level of expected returns changed during the 1953–1972 period.     

The impact of keeping up with the Joneses behavior on asset prices and portfolio choice

This paper studies the asset pricing and portfolio choice implications of keeping up with the Joneses preferences. In terms of portfolio choice, we provide sufficient conditions on the utility function under which no portfolio bias can arise across agents in equilibrium. Regarding asset prices, we find that under Joneses behavior asset prices are a function of the economy's aggregate consumption, the agents preference parameters, the wealth endowment distribution and the weighting across agents in the Joneses definition. We present necessary and sufficient conditions such that equilibrium prices are only a function of aggregate wealth. Non-financial, non-diversifiable income is introduced in the model. In the presence of Joneses behavior, an under-diversified equilibrium emerges where investors will bias their portfolios towards the financial assets that better hedge their exposure to the non-financial income risk.     

A test of the stability of exchange rate risk: Evidence from the Australian equities market

This paper investigates the sensitivity of equity returns on Australian industry portfolios to an exchange rate factor for the period 1988–1998. Specifically, using daily data, we (1) analyse the exchange rate exposure of the Australian equities market by implementing a basic augmented market model using relevant bilateral exchange rates, (2) investigate the intertemporal stability of the exchange rate exposure by using a dummy variable specification, and (3) attempt to establish the determinants of the exchange rate exposure of Australian industries by undertaking a cross-sectional analysis. A further empirical issue addressed by our study is that of whether the sensitivity is contemporaneous or lagged. We find (a) some evidence of exchange rate exposure, (b) some evidence of intertemporal sensitivity, and (c) a greater sensitivity to movements in the Australian dollar/US dollar exchange rate factor than to movements in the Australian dollar/Japanese yen. Further, we observe a significant lagged effect when employing the basic augmented model. This difference in the response of the industry portfolio returns is not observed, however, in our intertemporal stability investigation. Finally, we do not find significant evidence in terms of the cross-sectional determinants of foreign exchange exposure.     

Housing Collateral, Consumption Insurance, and Risk Premia: An Empirical Perspective

In a model with housing collateral, the ratio of housing wealth to human wealth shifts the conditional distribution of asset prices and consumption growth. A decrease in house prices reduces the collateral value of housing, increases household exposure to idiosyncratic risk, and increases the conditional market price of risk. Using aggregate data for the United States, we find that a decrease in the ratio of housing wealth to human wealth predicts higher returns on stocks. Conditional on this ratio, the covariance of returns with aggregate risk factors explains 80% of the cross‐sectional variation in annual size and book‐to‐market portfolio returns.