On trees and logs

In this paper we contrast the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), to a benchmark model in financial equilibrium theory, the real assets model (RA-Model). It is commonly believed that the two models entail similar conclusions since the LT-Model is a special case of the RA-Model. But this is simply wrong: implications of these models can be strikingly at odds. Indeed, under the widely used log-linear specification of households’ preferences, we show that for a large set of initial endowments the LT-Model—even with potentially complete financial markets—admits only peculiar financial equilibria in which the stock market is completely degenerate, in that all stocks offer the same investment opportunity—and yet, allocation is Pareto optimal. We investigate why the LT-Model is so much at variance with the RA-Model, and uncover new results on uniqueness of financial equilibria and introduction of portfolio constraints obtaining in the LT-Model, but not in the RA-Model.     

Lifetime consumption and investment: Retirement and constrained borrowing

Retirement flexibility and inability to borrow against future labor income can significantly affect optimal consumption and investment. With voluntary retirement, there exists an optimal wealth-to-wage ratio threshold for retirement and human capital correlates negatively with the stock market even when wages have zero or slightly positive market risk exposure. Consequently, investors optimally invest more in the stock market than without retirement flexibility. Both consumption and portfolio choice jump at the endogenous retirement date. The inability to borrow limits hedging and reduces the value of labor income, the wealth-to-wage ratio threshold for retirement, and the stock investment.     

Portfolio choice with internal habit formation: a life-cycle model with uninsurable labor income risk

Motivated by the success of internal habit formation preferences in explaining asset pricing puzzles, we introduce these preferences in a life-cycle model of consumption and portfolio choice with liquidity constraints, undiversifiable labor income risk and stock-market participation costs. In contrast to the initial motivation, we find that the model is not able to simultaneously match two very important stylized facts: a low stock market participation rate, and moderate equity holdings for those households that do invest in stocks. Habit formation increases wealth accumulation because the intertemporal consumption smoothing motive is stronger. As a result, households start participating in the stock market very early in life, and invest their portfolios almost fully in stocks. Therefore, we conclude that, with respect to its ability to match the empirical evidence on asset allocation behavior, the internal habit formation model is dominated by its time-separable utility counterpart.     

Dynamic asset allocation with ambiguous return predictability

We study an investor's optimal consumption and portfolio choice problem when he is confronted with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investor's aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. Unlike in the Bayesian framework, the hedging demand against model uncertainty may cause the investor's stock allocation to decrease sharply given a small doubt of return predictability, even though the expected return according to the VAR model is large. Over much of the parameter space, the robust strategy is very close to the Bayesian strategy with Epstein–Zin preferences and risk aversion chosen to match the same average portfolio holdings. This is true in particular when the IID model is unlikely and the dividend yield is low, as in recent years. However, differences in strategies can be substantial if the IID model is unlikely and the dividend yield is high.     

State-uncertainty preferences and the risk premium in the exchange rate market

This paper shows that state-uncertainty preferences help to explain the observed exchange rate risk premium. In the framework of Lucas (1982) economy, state-uncertainty preferences amount to assuming that a given level of consumption will yield a higher level of utility the lower is the level of uncertainty perceived by consumers. Under these preferences we can distinguish between two factors driving the exchange rate risk premium: “macroeconomic risk” and “the risk associated with variation in the private agents' perception on the level of uncertainty”. Empirical evidence from three main European economies in the transition period to the euro provides empirical support for the model. The model is more successful in accounting for the observed currency risk premium than models with more standard preferences, and the general perception of risk by private agents is shown to be a more important determinant of risk premium than macroeconomic uncertainty.     

When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?

In a standard incomplete markets model with a continuum of households that have constant relative risk aversion (CRRA) preferences, the absence of insurance markets for idiosyncratic labor income risk has no effect on the premium for aggregate risk if the distribution of idiosyncratic risk is independent of aggregate shocks and aggregate consumption growth is independent over time. In equilibrium, households only use the stock market to smooth consumption; the bond market is inoperative. Furthermore, the cross-sectional distributions of wealth and consumption are not affected by aggregate shocks. These results hold regardless of the persistence of idiosyncratic shocks, even when households face tight solvency constraints. A weaker irrelevance result survives when we allow for predictability in aggregate consumption growth.     

The possibility of informationally efficient markets

A rational expectations equilibrium with positive demand for financial information does exist under fully revealing asset price—contrary to a wide-held conjecture. Whereas a continuum of investors is inconsistent with fully revealing equilibrium, finitely many investors with average portfolios demand information in equilibrium if they can adjust portfolio size in an additive signal-return model. More information diminishes the expected excess return of a risky asset so that investors who only have a choice of portfolio composition or whose asset endowments strongly differ from the average portfolio are worse off. Under fully revealing price, information market equilibria both with and without information acquisition are Pareto efficient.     

Investment horizon effect on asset allocation between value and growth strategies

How does the optimal risk exposure of assets change as their investment horizons increase? Does this impact investment portfolio decision-making, in particular, optimal asset allocation between value and growth strategies over various investment horizons? This paper adopts a new approach to address these questions by examining portfolio allocation between value and growth stocks over various investment horizons. This new approach is based on wavelet analysis, which decomposes the returns of a particular investment strategy across multiple investment horizons. The key empirical results show that the success of pursuing the value strategy (short-selling growth stocks and going long on value stocks) is impacted by the approach used to classify value and growth stock returns. We explore two common alternatives: Fama-French versus Standard & Poor's (S&P) 500/Barra portfolios. The results using Fama-French portfolios show that as the investment horizon increases, the optimal mean allocation of investors tilts heavily away from growth stocks, particularly for lower and moderate levels of risk aversion. Interestingly, for S&P 500/Barra portfolios the allocation weights between value and growth do not vary much.     

Risk aversion and allocation to long-term bonds

As risk aversion approaches infinity, the portfolio of an investor with utility over consumption at time T is shown to converge to the portfolio consisting entirely of a bond maturing at time T. Previous work on bond allocation requires a specific model for equities, the term structure, and the investor's utility function. In contrast, the only substantive assumption required for the analysis in this paper is that markets are complete. The result, which holds regardless of the underlying investment opportunities and the utility function, formalizes the “preferred habitat” intuition of Modigliani and Sutch (Amer. Econom. Rev. 56 (1966) 178).     

Portfolio Choice and Liquidity Constraints*

We study the infinite‐horizon model of household portfolio choice under liquidity constraints and revisit the portfolio specialization puzzle. We show why the puzzle is robust to several model variations, and argue that positive correlation between earnings shocks and stock returns is unlikely to provide an empirically plausible resolution. We find that relatively small fixed costs for stock market entry are sufficient to deter stockholding because, for a plausible range of parameter values, households can achieve desired consumption smoothing with small or zero holdings of stocks. Such costs could arise from informational considerations, sign‐up fees, and investor inertia.     

Linear and non-linear price decentralization

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consumption sets are the positive cone of arbitrary ordered Fréchet spaces—dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prices and for ω-proper economies they are both sufficient and necessary.     

流动性、生命周期与投资组合相异性——中国投资者行为调查实证分析

本文采用Probit和Tobit模型对中国居民的股票市场参与和投资组合的影响因素进行了分析,主要有以下的实证发现:首先,不流动性资产特别是房地产的投资显著影响了投资者的股票市场参与和投资组合,而且影响以“替代”效应或者说“挤出”效应为主。其次,投资者在进行投资组合时极少利用股票市场对其未来现金流所承担的风险进行对冲,也就是说,中国居民投资的“生命周期效应”不明显;第三,中国居民投资的“财富效应”非常显著。财富的增加既增加了居民参与股票市场的概率,也增加了居民参与股票市场的深度。     

Designing social security - a portfolio choice approach

Public social security systems may provide diversification of risks to individuals’ life-time income. Capturing that a pay-as-you-go system (paygo) may be considered as a “quasi-asset”, we study the optimal size of the paygo system as well as the optimal split between funded and unfunded pension saving by means of a theoretical portfolio choice framework. A low-yielding paygo system can benefit individuals if it contributes to hedge other risks to their lifetime resources. Numerical calculations indicate that optimal social security systems should be at least partly paygo financed in many economies. The optimal magnitude of the paygo system depends on the specified risk concept as well as the stochastic properties of stock market returns and implicit paygo-returns.     

Moving costs, nondurable consumption and portfolio choice

The substantial adjustment cost for housing affects nondurable consumption and portfolio allocations, as well as the frequency of housing transactions. A simple theoretical model, roughly calibrated, is used to assess the quantitative impact of adjustment costs on those decisions. The impact on portfolios is found to be significant, suggesting that housing wealth should be useful in empirical studies of portfolio choice. The welfare loss from the transaction cost is also substantial. The effect on nondurable consumption is small, however, so adjustment costs can explain only a small part of the equity premium puzzle.     

The Saving Behaviour of a Two-person Household

The facts that wives are typically younger than their husbands and that women typically live longer than men imply that wives may have more incentive to save for old age than do husbands. A theoretical model of the determination of household saving and portfolio choice is introduced which takes into account differences in preferences for saving. The most important result is that the level and the composition (portfolio) of saving and the time path of consumption are dependent on the distribution of income within the household.
JEL classification: D 1; D 7     

Portfolio choice with high frequency data: CRRA preferences and the liquidity effect

This paper suggests a new approach for portfolio choice. In this framework, the investor, with CRRA preferences, has two objectives: the maximization of the expected utility and the minimization of the portfolio expected illiquidity. The CRRA utility is measured using the portfolio realized volatility, realized skewness and realized kurtosis, while the portfolio illiquidity is measured using the well-known Amihud illiquidity ratio. Therefore, the investor is able to make her choices directly in the expected utility/liquidity (EU/L) bi-dimensional space. We conduct an empirical analysis in a set of fourteen stocks of the CAC 40 stock market index, using high frequency data for the time span from January 1999 to December 2005 (seven years). The robustness of the proposed model is checked according to the out-of-sample performance of different EU/L portfolios relative to the minimum variance and equally weighted portfolios. For different risk aversion levels, the EU/L portfolios are quite competitive and in several cases consistently outperform those benchmarks, in terms of utility, liquidity and certainty equivalent.     

Subjective probabilities on “small” domains

The Savagian choice-theoretic construction of subjective probability does not apply to preferences, like those in the Ellsberg Paradox, that reflect a distinction between risk and ambiguity. We formulate two representation results—one for expected utility, the other for probabilistic sophistication—that derive subjective probabilities but only on a “small” domain of risky events. Risky events can be either specified exogenously or in terms of choice behavior; in the latter case, both the values and the domain of probability are subjective. The analysis identifies a mathematical structure—called a mosaic—that is intuitive for both exogenous and behavioral specifications of risky events. This structure is weaker than an algebra or even a λ-system.     

Integrated Risk Management with a Filtered Bootstrap Approach

We present a multi-period risk model to measure portfolio risk that integrates market risk, credit risk and, in a simplified way, liquidity risk. Thus, it overcomes the major limitation currently shared by many risk models that are unable to give a complete picture of all portfolio risks according to a single, coherent framework. The model is based on the Filtered Bootstrap approach; hence, it captures conditional heteroskedasticity, serial correlation and non-normality in the risk factors, that is, most of the features of observed financial time series. Being a simulation risk model, it copes in a natural way with derivatives as it allows the full valuation of the probability density function of the contracts. In addition, it is a suitable and flexible way to generate future scenarios on medium‐term horizons, so this model is particularly appropriate for asset management companies.     

Corporate liquidity and risk management with time-inconsistent preferences

This paper extends the model of corporate liquidity and risk management with limited commitment by incorporating time-inconsistent preferences. With respect to the firm's liquidity w = W∕K, it predicts that in the presence of time-inconsistency, the entrepreneur optimally responds by lowering the maximal debt capacity, over-consuming, under-investing and reducing both the idiosyncratic and systematic volatility of w. When disentangling the entrepreneur's belief with regard to future selves' time-inconsistent behavior, as a result of sophistication effect, the sophisticated entrepreneur reduces the endogenous debt capacity, invests less, decreases consumption, engages less in financial hedging and allocates even smaller liquid assets in the market portfolio than naive entrepreneur.     

Portfolio choice,consumption and welfare when rates of return are related to prices of consumer goods

This paper generalizes the two period model of portfolio selection under uncertainty by decomposing the aggregate consumption in each period into several goods, the prices of some of which are positively related to rates of return on some assets. The effect of these relations on the choice of portfolio is analyzed. The effects on the chosen portfolio of a lateral translation and of a mean preserving increase in the risk of the distributions of the random variables are analyzed. A generalization of the Hicks compensation to the case where the prices of consumer goods are positively related to rates of return on assets is offered and welfare implications are drawn.