Comonotonic Approximations for Optimal Portfolio Selection Problems

We investigate multiperiod portfolio selection problems in a Black and Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of “constant mix” portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari's dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene et al. (2002 a,b) . Our analytical approach avoids simulation, and hence reduces the computing effort drastically.     

Correlation Risk and Optimal Portfolio Choice

We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.     

Flight Capital as a Portfolio Choice

This article sets flight capital in the context of portfoliochoice, focusing on the proportion of private wealth that isheld abroad. There are large regional differences in this proportion,ranging from 5 percent in South Asia to 40 percent in Africa.The authors explain cross-country differences in portfolio choiceusing variables that proxy differences in the risk-adjustedrate of return on capital. They apply the results to three policyissues: how the East Asian crisis affected domestic capitaloutflows; the effect of the International Monetary Fund–WorldBank debt relief initiative for heavily indebted poor countrieson capital repatriation; and why so much of Africa's privatewealth is held outside the continent.     

Optimal Portfolio Choice Under Incomplete Information

Models of asset pricing generally assume that the variables which characterize the state of the economy are observable. However, the distributional properties of asset prices that are relevant for portfolio decisions are in general not observable, and therefore must be estimated. The estimation of expected returns is a particularly difficult problem and estimation errors are likely to be substantial. In this light, it is reasonable to examine whether the assumption of observability of expected returns and other relevant state variables causes significant mis-specification in equilibrium models of asset prices. This paper has three main objectives: first, to derive optimal estimators for the unobservable expected instantaneous returns using observations of past realized returns; second, to establish that estimation and portfolio choice can be solved in two separate steps; third, to analyze the impact of estimation error on investment choices. The estimators of expected returns are in general not consistent, i.e., the estimation error does not tend to disappear asymptotically. The effects of the estimation error, therefore, cannot be ignored even if realized returns are observed continuously over an infinite time period.     

Systemic Risk and International Portfolio Choice

Returns on international equities are characterized by jumps; moreover, these jumps tend to occur at the same time across countries leading to systemic risk. We capture these stylized facts using a multivariate system of jump‐diffusion processes where the arrival of jumps is simultaneous across assets. We then determine an investor's optimal portfolio for this model of returns. Systemic risk has two effects: One, it reduces the gains from diversification and two, it penalizes investors for holding levered positions. We find that the loss resulting from diminished diversification is small, while that from holding very highly levered positions is large.     

Pension Portfolio Choice and Peer Envy

I examine the effect of envy on the portfolio allocation of workers in a defined contribution (DC) pension plan. If a worker’s DC plan performs better than his co‐worker’s, he may gloat; on the other hand, if his DC plan performs worse, he may feel envy. I model anticipated envy when workers make portfolio allocations, and find that in equilibrium, workers will mimic their co‐worker’s allocation to eliminate the disutility from envy. This portfolio allocation is riskier than that of a worker who does not exhibit envy.     

Hedging, Familiarity and Portfolio Choice

We exploit the restrictions of intertemporal portfolio choicein the presence of nonfinancial income risk to test hedgingusing the information contained in the actual portfolio of theinvestor. We use a unique data set of Swedish investors withinformation broken down at the investor level and into variouscomponents of investor wealth, income, and demographic characteristics.Portfolio holdings are identified at the stock level. We showthat investors do not hedge but invest in stocks closely relatedto their nonfinancial income. We explain this with familiarity,that is, the tendency to concentrate holdings in stocks to whichthe investor is geographically or professionally close or thathe has held for a long period. We show that familiarity is nota behavioral bias, but is information driven. Familiarity-basedinvestment allows investors to earn higher returns than theywould have otherwise earned if they had hedged.     

Optimal Portfolio Choice under Heterogeneous Beliefs

This paper analyzes how an investor who is convinced that he can``beat the market' should behave when the equilibrium priceprocess is endogenous. The investor's optimal portfolio is shownto consist of three components: (1) a tangency portfolio, (2) ahedge portfolio against changes in the market's valuation ofsecurities, and (3) a hedging position against changes in thedivergence between the investor's and the market's beliefs. Thesign and magnitude of this third component will depend on investorpreferences and on the divergence in the investor's and themarket's quality of information. A numerical example illustratesthat the effect of heterogeneous beliefs on optimal portfolioallocations can be significant.     

Rational Inattention and Portfolio Selection

Costly information acquisition makes it rational for investors to obtain important economic news with only limited frequency or limited accuracy. We show that this rational inattention to important news may make investors over‐ or underinvest. In addition, the optimal trading strategy is “myopic” with respect to future news frequency and accuracy. We find that the optimal news frequency is nonmonotonic in news accuracy and investment horizon. Furthermore, when both news frequency and news accuracy are endogenized, an investor with a higher risk aversion or a longer investment horizon chooses less frequent but more accurate periodic news updates.     

Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choiceproblems, up to the solution of an ordinary differential equation(ODE), when the asset returns are quadratic and the agent hasa constant relative risk aversion (CRRA) coefficient. My solutionincludes as special cases many existing explicit solutions ofdynamic portfolio choice problems. I also present three applicationsthat are not in the literature. Application 1 is the bond portfolioselection problem when bond returns are described by "quadraticterm structure models." Application 2 is the stock portfolioselection problem when stock return volatility is stochasticas in Heston model. Application 3 is a bond and stock portfolioselection problem when the interest rate is stochastic and stockreturns display stochastic volatility. (JEL G11)     

A Simple Algorithm for the Portfolio Selection Problem

The author presents a rapidly convergent algorithm to solve the general portfolio problem of maximizing concave utility functions subject to linear constraints. The algorithm is based on an iterative use of the Markowitz critical line method for solving quadratic programs. A simple example, taken from the theory of state-contingent claims, is worked out in detail. For technical convergence results, the reader is referred to the appropriate mathematical programming literature.     

Optimal Portfolio Choice for Long-Horizon Investors with Nontradable Labor Income

This paper examines how risky labor income and retirement affect optimal portfolio choice. With idiosyncratic labor income risk, the optimal allocation to stocks is unambiguously larger for employed investors than for retired investors, consistent with the typical recommendations of investment advisors. Increasing idiosyncratic labor income risk raises investors' willingness to save and reduces their stock portfolio allocation towards the level of retired investors. Positive correlation between labor income and stock returns has a further negative effect and can actually reduce stockholdings below the level of retired investors.     

Portfolio Choice in the Presence of Housing

I show that investment in housing plays a crucial role in explainingthe patterns of cross-sectional variation in the compositionof wealth and the level of stockholdings observed in portfoliocomposition data. Due to investment in housing, younger andpoorer investors have limited financial wealth to invest instocks, which reduces the benefits of equity market participation.House price risk crowds out stockholdings, and this crowdingout effect is larger for low financial net-worth. In the modelas in the data leverage is positively correlated with stockholdings.     

The Effect of Housing on Portfolio Choice

We show that characterizing the effects of housing on portfolios requires distinguishing between the effects of home equity and mortgage debt. We isolate exogenous variation in home equity and mortgages by using differences across housing markets in house prices and housing supply elasticities as instruments. Increases in property value (holding home equity constant) reduce stockholdings, while increases in home equity wealth (holding property value constant) raise stockholdings. The stock share of liquid wealth would rise by 1 percentage point—6% of the mean stock share—if a household were to spend 10% less on its house, holding fixed wealth.     

Portfolio Selection with Quadratic Utility Revisited

Considering a simple portfolio selection problem by agents with quadratic utility, an apparently counterintuitive outcome results. When such a choice is over two assets that can be ordered in terms of riskiness, an agent that is more risk averse may optimally invest a larger portion of wealth in the riskier asset. It is shown that such an outcome is not counterintuitive, since for the portfolios from which agents optimally choose, a larger proportion of investment in the riskier asset leads to a less risky portfolio.     

Portfolio Selection and Asset Pricing Models

Finance theory can be used to form informative prior beliefs in financial decision making. This paper approaches portfolio selection in a Bayesian framework that incorporates a prior degree of belief in an asset pricing model. Sample evidence on home bias and value and size effects is evaluated from an asset-allocation perspective. U.S. investors' belief in the domestic CAPM must be very strong to justify the home bias observed in their equity holdings. The same strong prior belief results in large and stable optimal positions in the Fama–French book-to-market portfolio in combination with the market since the 1940s.