Portfolio Allocation Problem Research Articles

What Drives Risky Investments Lower Around Retirement?

I solve the life-cycle portfolio allocation problem of a disappointment averse (DA) agent. DA agents overweight disappointing outcomes. Unlike expected utility investors, DA investors drastically cut their allocation to stocks around retirement due to a distinct effect associated with the drop in income risk. The effect is driven by the changing comovement between returns and the disappointment/elation realization. The allocations are consistent with empirical evidence on portfolio shares and the allocation rules of target-date retirement funds. Sufficiently disappointment-averse agents abstain from investing in stocks after retirement, which is consistent with the observed low rates of stock market participation among retirees.

Life-Cycle Portfolio Allocation for Disappointment Averse Agents

I solve the life-cycle portfolio allocation problem of a disappointment averse (DA) agent with labor income risk. DA preferences overweight disappointing outcomes and are consistent with behavior highlighted by the Allais paradox. I show that unlike constant relative risk aversion (CRRA) investors, DA investors drastically cut their allocation to stocks when they retire. This result is consistent with empirical evidence on portfolio shares and with the allocation rules of target-date retirement funds. I also show that sufficiently disappointment averse agents abstain from stocks after retirement, which is consistent with the observed low rates of stock market participation among retirees. I further show that when crashes are possible, agents with low levels of wealth invest little (or nothing) in the stock market.

Does stock return predictability affect ESO fair value?

Executive Stock Options (ESOs) are modified American options that cannot be valued using standard methods. With a few exceptions, the literature has discussed the ESO fair value by assuming unpredictable stock returns which are not supported by the available empirical evidence. In this paper we obtain the fair value of American ESOs when stock returns are predictable and, specifically, driven by the trending Ornstein–Uhlenbeck process of Lo and Wang (1995). We solve the executive’s portfolio allocation problem for a simple buy-and-hold strategy when his wealth can be distributed between a risk-free asset and a market portfolio. This problem is jointly solved with the executive’s optimal exercise policy. We find that executives tend to wait longer the higher the predictability, independently of the composition of executive’s asset menu. We have also analyzed the implications under the FAS123R proposals for the ESO fair value and found that, even for low autocorrelations, there is a meaningful mispricing when unpredictable returns are erroneously assumed.

Investing in Tough Times: What Investors’ Behavior Across the Business Cycle Tells About the Mutual Fund Market

In academic literature mutual fund investment has been traditionally studied from the perspective of an optimal portfolio allocation problem. An increasing body of empirical and experimental evidence has suggested that the investors’ behavior share remarkable similarities with the behavior of buyers in consumer goods markets. In this study develop and test a number of hypotheses based on empirical evidence in marketing literature. Using data on US mutual funds from 1991 to 2011 I show that investors price awareness (sensitivity of investment flows to expense ratios) increases as the macroeconomic environment worsens. I also show that this effect is due to expectations of future economic hardship rather than to the current situation. These results are robust to alternative explanations based on time-varying risk aversion, informativeness of past performances and competition from low-cost passive funds. Finally, using a new dataset of advertising expenditures I show that advertising becomes more effective in tough times, also due to the fact that, contrary to common beliefs, high advertising budgets are paid through increased volumes rather than higher expense ratios.

Correlation Neglect in Financial Decision-Making

Good decision-making often requires people to perceive and handle a myriad of statistical correlations. Notably, optimal portfolio theory depends upon a sophisticated understanding of the correlation among nancial assets. In this paper, we examine people’s understanding of correlation using a sequence of portfolio-allocation problems and nd it to be strongly imperfect. Our experiment uses pairs of portfolio-choice problems that have the same asset span|identical sets of attainable returns|and dier only in the assets’ correlation. While any outcome-based theory of choice makes the same prediction across paired problems, subjects behave very differently across pairs. We nd evidence for correlation neglect|treating correlated variables as uncorrelated|as well as for a form of \1/n heuristic|investing half of wealth each of the two available assets. (JEL B49)

Asset allocation in the Athens stock exchange: a variance sensitivity analysis

ABSTRACTThis paper provides an analysis of asset allocation using univariate portfolio GARCH models applied on daily data for the period January 1999 to December 2009 on stocks traded in the Athens Stock Exchange, a recently monitored emerging market. Our analysis adopts the variance sensitivity analysis (VSA) methodology due to Manganelli (2004) and we are able to recover from the univariate approach the multivariate dimension of the portfolio allocation problem. The main results of the analysis are: First, we demonstrate that using a two asset portfolio consisting of blue chips traded in the Greek capital market the estimated variance is a parabolic and convex function of the estimated weights providing evidence that diversification produces significant gains in terms of risk reduction. Second, based on the shape of the first and second derivatives the model misspecification due to the fitting univariate GARCH models is insignificant. Third, we compare the performance of VSA against that of three popular multivariate GARCH models and it is shown that the adopted methodology provides more efficient results than the competing models. The gains in efficiency get larger as the size of the portfolio increases. Finally, with the application of the Kupiec's test for out‐of‐sample forecasting performance we demonstrate that the VSA outperforms all three alternative models at both the 95% and 99% confidence interval independently of the trading position. Copyright © 2011 John Wiley & Sons, Ltd.

Optimal hedge fund portfolios under liquidation risk

We use an expected utility framework to integrate the liquidation risk of hedge funds into portfolio allocation problems. The introduction of realistic investment constraints complicates the determination of the optimal solution, which is solved using a genetic algorithm that mimics the mechanism of natural evolution. We analyse the impact of the liquidation risk, of the investment constraints and of the agent's degree of risk aversion on the optimal allocation and on the optimal certainty equivalent of hedge fund portfolios. We observe, in particular, that the portfolio weights and their performance are significantly affected by liquidation risk. Finally, tight portfolio constraints can only provide limited protection against liquidation risk. This approach is of special interest to fund of hedge fund managers who wish to include the hedge fund liquidation risk in their portfolio optimization scheme.

Financial market equilibria with cumulative prospect theory

The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a non-negativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents’ demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.

Forcing Multinationals to Play Fair: Proposals for a Rigorous Transfer Pricing Theory

This Article incorporates the principles of modern corporate finance and valuation theory into the transfer pricing rules. In particular, I argue that the problem of allocating income among members of a multinational group should be based on the same principles that underlie portfolio allocation. This leap only requires one to assume that multinational enterprises attempt to maximize profit of the group as a whole, rather than maximizing the profit of each individual member of the group Because the problem of portfolio allocation has been extensively studied, incorporating this body of literature into the analysis of transfer pricing would significantly increase both the sophistication of the analysis and well as the accuracy of the resulting allocations.

Financial Market Equilibria with Cumulative Prospect Theory

The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a nonnegativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents' demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.

Cromwell's Rule and the Role of the Prior in the Economic Metric

We show that using Bayesian decision theory to draw inference about the economic significance of a model requires careful specification of model uncertainty in the prior density. As an example, we use the Bayesian investor's portfolio allocation problem to show that failure to include probability point mass on the null hypothesis that returns are not predictable will overstate the economic significance of the predictive model. The dissonance between the statistical and economic significance of asset return predictability seen in previous research appears to be an artifact of how model uncertainty is treated in the specification of the prior.

Bayesian REIT Volatility Estimation and Institutional Portfolio Allocation

Executive Summary.Volatility estimation is an integral part of institutional finance with applications in risk management and portfolio allocation. Real estate investment trust volatility is examined using a Bayesian asymmetric GARCH model and is found to better estimate the true volatility series than does the traditional maximum likelihood approach. This paper discusses the shortfalls of maximum likelihood (ML) estimation and the advantages of the Bayesian estimation, particularly to real estate. Conditional variance estimation uncertainty is found to increase with volatility. A portfolio allocation problem highlights that the Bayesian approach performed better than the ML method in preserving capital.

Asset Pricing and the Consumption-Investment Allocation under Robustness and Short Sales Constraints, using Martingale Methods

This paper is motivated by the existing controversy in the empirical literature on the asset pricing effect of divergence of opinions and short-sales constraints. On the one hand, the partisans of Miller's (1977) hypothesis argue that divergence of opinion can lead to asset overvaluation and subsequent long-term underperformance, on the other hand, robust decision theorists argue that divergence of opinions is priced negatively, as it proxies for the uncertainty in forming returns expectations. In this paper I argue that the two theories can be nested together in a problem of robust portfolio allocation with short sale constraints. I solve for the optimal portfolio demand of an investor who faces short sales constraints, and show that assets characterized by high uncertainty require higher returns, while assets that are constrained from short-selling require lower returns. The overall effect when the two characteristics overlap is unknown, but it can be decomposed into the pricing effects of each of the two.

Cromwell's Rule and the Role of the Prior in the Economic Metric: An Application to the Portfolio Allocation Problem

I show that using Bayesian decision theory to draw inference about the economic significance of a model requires careful specification of model uncertainty in the prior density. As an example, I use the Bayesian investor's portfolio allocation problem to show that failure to include probability point mass on the null hypothesis that returns are not predictable will overstate the economic significance of the predictive model. The dissonance seen in previous research between the statistical and economic significance of asset return predictability appears to be an artifact of how model uncertainty is treated in the specification of the prior.

Global Asset Allocation in Fixed Income Markets

Many global investors are faced with the problem of choosing an appropriate currency allocation of their assets in the capital markets. This paper addresses the asset allocation problem under the assumption that the investment universe is comprised of unhedged risk-free bonds in different countries. In general, the total return arising from holding an unhedged bond portfolio is comprised of two components. One component of the return arises from the bond price changes resulting from yield curve movements and the other component arises from exchange rate fluctuations. In this paper, bond price changes are assumed to be governed by a one factor interest rate term structure model. The return arising from exchange rate changes is extracted by modelling the evolution of exchange rates as a jump stochastic process. The jump process is assumed to occur in the volatility of exchange rate returns. This model is consistent with the empirical evidence that the volatility of currency returns exhibits GARCH behaviour. Using the models that describe the evolution of interest rates and exchange rates, the optimal portfolio allocation problem is solved in a mean-variance setting by Monte Carlo simulation. The out-of-sample performance of the portfolios selected is also presented and is compared against those obtained using other existing methods.

A Forward-Solving Numerical Technique for Dynamic Consumption and Portfolio Allocation Problems

This paper develops a simple approach to solving multi-period consumption and investment problems. All numerical methods in use for these types of problems work by solving the problem backward, i.e., solving the consumption and investment decision at the end of the investment horizon and working backward. For certain problems, such as economies with capital gains taxes, a backward approach is extremely unwieldy. For this reason, this paper develops a forward-solving approach that is based on Monte Carlo simulations. We demonstrate that the methodology in this paper is extremely effective at solving the tax problem and other unwieldy problems. In addition, the methodology works perfectly well with problems that have traditionally used a backward-solving approach.

Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks and State-Dependent Transaction Costs

The seminal work of Constantinides (1986) documents how, when the risky return is calibrated to the U.S. market return, the impact of transaction costs on per-annum liquidity premia is an order of magnitude smaller than the cost rate itself. A number of recent papers have formed portfolios sorted on liquidity measures and found a spread in expected per-annum return that is definitely not an order of magnitude smaller than the transaction cost spread: the expected per-annum return spread is found to be around 6-7% per annum. Our paper bridges the gap between Constantinides' theoretical result and the empirical magnitude of the liquidity premium by examining dynamic portfolio choice with transaction costs in a variety of more elaborate settings that move the problem closer to the one solved by real-world investors. In particular, we allow returns to be predictable and transaction costs to be stochastic, and we introduce wealth shocks, both stationary multiplicative and labor income. With predictable returns, we also allow the wealth shocks and transaction costs to be state dependent. We find that adding these real world complications to the canonical problem can cause transactions costs to produce per-annum liquidity premia that are no longer an order of magnitude smaller than the rate, but are instead the same order of magnitude. For example, predictable returns and i.i.d. labor income growth causes the liquidity premium for an agent with a wealth to monthly labor income ratio of 0 or 10 to be 1.68\% and 1.20\% respectively; these are 21-fold and 15-fold increases, respectively, relative to that in the standard i.i.d. return case. We conclude that the effect of proportional transaction costs on the standard consumption and portfolio allocation problem with i.i.d. returns can be materially altered by reasonable perturbations that bring the problem closer to the one investors are actually solving.

Asset Allocation by Variance Sensitivity Analysis

This article provides a solution to the curse of dimensionality associated to multivariate generalized autoregressive conditionally heteroskedastic (GARCH) estimation. We work with univariate portfolio GARCH models and show how the multivariate dimension of the portfolio allocation problem may be recovered from the univariate approach. The main tool we use is ‘‘variance sensitivity analysis,’’ the change in the portfolio variance induced by an infinitesimal change in the portfolio allocation. We suggest a computationally feasible method to find minimum variance portfolios and estimate full variance-covariance matrices. An application to real data portfolios implements our methodology and compares its performance against that of selected popular alternatives.

On the Malliavin approach to Monte Carlo approximation of conditional expectations

Given a multi-dimensional Markov diffusion X, the Malliavin integration by parts formula provides a family of representations of the conditional expectation E[g(X 2)|X1]. The different representations are determined by some localizing functions. We discuss the problem of variance reduction within this family. We characterize an exponential function as the unique integrated mean-square-error minimizer among the class of separable localizing functions. For general localizing functions, we prove existence and uniqueness of the optimal localizing function in a suitable Sobolev space. We also provide a PDE characterization of the optimal solution which allows to draw the following observation : the separable exponential function does not minimize the integrated mean square error, except for the trivial one-dimensional case. We provide an application to a portfolio allocation problem, by use of the dynamic programming principle.

Alocação de Carteiras Sujeitas a Risco de Crédito

Risco de crédito representa uma dimensão importante de risco a ser considerada por bancos quando realizam empréstimos. Em particular, em mercados emergentes as taxas de inadimplência em produtos de empréstimos bancários são muito altas, demandando maior cuidado com relação ao gerenciamento deste risco. Usualmente o risco de crédito de carteiras que envolvem empréstimos é obtido a partir de simulações de Monte Carlo de alto custo computacional que consideram diferentes fatores estocásticos relacionados a incerteza dos pagamentos dos passivos associados aos devedores. Neste trabalho, sob determinadas hipóteses, nós derivamos fórmulas fechadas para as distribuições de probabilidades das taxas de inadimplência de produtos bancários envolvendo um número grande de clientes. O conhecimento de tais distribuições nos permite calcular com facilidade o risco de crédito associado a cada produto oferecido pelo banco. Adicionalmente, a partir destas distribuições, utilizando Retorno Total como medida de retorno, e Perda Máxima como medida de risco, resolvemos o problema de obtenção de carteiras ótimas envolvendo risco de crédito.