Portfolio size effect in retirement accounts : what does it imply for lifecycle asset allocation funds?

Lifecycle funds offered by retirement plan providers allocate aggressively to risky asset classes when the employee participants are young, gradually switching to more conservative asset classes as they grow older and approach retirement. This approach focuses on maximizing growth of the accumulation fund in the initial years and preserving its value in the later years. The authors simulate terminal wealth outcomes based on conventional lifecycle asset allocation rules as well as on contrarian strategies that reverse the direction of asset switching. The evidence suggests that the growth in portfolio size over time significantly impacts the asset allocation decision. Due to the portfolio size effect that is observed by the authors, the terminal value of accumulation in retirement accounts is influenced more by the asset allocation strategy adopted in later years relative to that adopted in early years. By mechanistically switching to conservative assets in the later years of a plan, lifecycle strategies sacrifice significant growth opportunity and prove counterproductive to the participant's wealth accumulation objective. The authors' conclude that this sacrifice does not seem to be compensated adequately in terms of reducing the risk of potentially adverse outcomes.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Essays in asset price bubbles

This thesis studies the field of asset price bubbles. It is comprised of three independent chapters. Each of these chapters either directly or indirectly analyse the existence or implications of asset price bubbles. The type of bubbles assumed in each of these chapters is consistent with rational expectations. Thus, the kind of price bubbles investigated here are known as rational bubbles in the literature. The following describes the three chapters. Chapter 1: This chapter attempts to explain the recent US housing price bubble by developing a heterogeneous agent endowment economy asset pricing model with risky housing, endogenous collateral and defaults. Investment in housing is subject to an idiosyncratic risk and some mortgages are defaulted in equilibrium. We analytically derive the leverage or the endogenous loan to value ratio. This variable comes from a limited participation constraint in a one period mortgage contract with monitoring costs. Our results show that low values of housing investment risk produces a credit easing effect encouraging excess leverage and generates credit driven rational price bubbles in the housing good. Conversely, high values of housing investment risk produces a credit crunch characterized by tight borrowing constraints, low leverage and low house prices. Furthermore, the leverage ratio was found to be procyclical and the rate of defaults countercyclical consistent with empirical evidence. Chapter 2: It is widely believed that financial assets have considerable persistence and are susceptible to bubbles. However, identification of this persistence and potential bubbles is not straightforward. This chapter tests for price bubbles in the United States housing market accounting for long memory and structural breaks. The intuition is that the presence of long memory negates price bubbles while the presence of breaks could artificially induce bubble behaviour. Hence, we use procedures namely semi-parametric Whittle and parametric ARFIMA procedures that are consistent for a variety of residual biases to estimate the value of the long memory parameter, d, of the log rent-price ratio. We find that the semi-parametric estimation procedures robust to non-normality and heteroskedasticity errors found far more bubble regions than parametric ones. A structural break was identified in the mean and trend of all the series which when accounted for removed bubble behaviour in a number of regions. Importantly, the United States housing market showed evidence for rational bubbles at both the aggregate and regional levels. In the third and final chapter, we attempt to answer the following question: To what extend should individuals participate in the stock market and hold risky assets over their lifecycle? We answer this question by employing a lifecycle consumption-portfolio choice model with housing, labour income and time varying predictable returns where the agents are constrained in the level of their borrowing. We first analytically characterize and then numerically solve for the optimal asset allocation on the risky asset comparing the return predictability case with that of IID returns. We successfully resolve the puzzles and find equity holding and participation rates close to the data. We also find that return predictability substantially alter both the level of risky portfolio allocation and the rate of stock market participation. High factor (dividend-price ratio) realization and high persistence of factor process indicative of stock market bubbles raise the amount of wealth invested in risky assets and the level of stock market participation, respectively. Conversely, rare disasters were found to bring down these rates, the change being severe for investors in the later years of the life-cycle. Furthermore, investors following time varying returns (return predictability) hedged background risks significantly better than the IID ones.

Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

Contagion and regulation in endogenous bank networks

We develop a simple model of endogenous bank networks to study financial contagion and how leverage regulation may affect it. Banks maximize expected profit by choosing the optimal allocation of resources between three different classes of assets. An interbank network arise as result of loans between banks, creating a direct channel of contagion in the financial system. Contagion may occur when the realized return of the risky asset is sufficiently low to make a bank insolvent, subsequently triggering a cascade effect that propagates through default in interbank loans. Contrary to what would be expected, our results show that despite forcing banks to deleverage, increasing minimum capital requirements may lead to a system with higher aggregate levels of default.

Risk and structural instability in US house prices

This paper employs a Component GARCH in Mean model to show that house prices across a number of major US cities between 1987 and 2009 have displayed asset market properties in terms of both risk-return relationships and asymmetric adjustment to shocks. In addition, tests for structural breaks in the mean and variance indicate structural instability across the data range. Multiple breaks are identified across all cities, particularly for the early 1990s and during the post-2007 financial crisis as housing has become an increasingly risky asset. Estimating the models over the individual sub-samples suggests that over the last 20 years the financial sector has increasingly failed to account for the levels of risk associated with real estate markets. This result has possible implications for the way in which financial institutions should be regulated in the future.

Pure higher-order effects in the portfolio choice model

This paper examines the effects of higher-order risk attitudes and statistical moments on the optimal allocation of risky assets within the standard portfolio choice model. We derive the expressions for the optimal proportion of wealth invested in the risky asset to show they are functions of portfolio returns third- and fourth-order moments as well as on the investor’s risk preferences of prudence and temperance. We illustrate the relative importance that the introduction of those higher-order effects have in the decision of expected utility maximizers using data for the US.

Household portfolio allocation, risk attitudes and credit constraints : evidence from the eurozone

Mestrado em Economia Monetária e Financeira

A data mining driven risk profiling method for road asset management

Road surface skid resistance has been shown to have a strong relationship to road crash risk, however, applying the current method of using investigatory levels to identify crash prone roads is problematic as they may fail in identifying risky roads outside of the norm. The proposed method analyses a complex and formerly impenetrable volume of data from roads and crashes using data mining. This method rapidly identifies roads with elevated crash-rate, potentially due to skid resistance deficit, for investigation. A hypothetical skid resistance/crash risk curve is developed for each road segment, driven by the model deployed in a novel regression tree extrapolation method. The method potentially solves the problem of missing skid resistance values which occurs during network-wide crash analysis, and allows risk assessment of the major proportion of roads without skid resistance values.

Are sustainable companies less risky and more profitable?

The purpose of this study was to determine whether there were significant differences in accounting indicators when comparing sustainable enterprises to other similar companies that are not considered as sustainable. The Corporate Sustainability Index of BM (São Paulo Stock, Commodities and Futures Exchange) was the criterion selected to break down the samples into sustainable and non-sustainable enterprises. The accounting indicators were separated into two kinds: risk (dividend payout, percentage growth of assets, financial leverage, current liquidity, asset size, variability of earnings, and accounting beta) and return (ROA, ROE, asset turnover, and net margin). We individually analyzed the companies in the energy sector, followed by those in the banking sector, as well as the entire ISE portfolio as of 2008/2009, including all the sectors. Mann-Whitney tests were performed in order to verify the difference of the means between the groups (ISE and non-ISE). The results, considering the method chosen and the time span covered by the study, indicate that there are no differences between sustainable companies and the others, when they are assessed by the accounting indicators used here.

On the Efficiency of the Benchmarks Used in the Asset Management

In this work we studied the efficiency of the benchmarks used in the asset management industry. In chapter 2 we analyzed the efficiency of the benchmark used for the government bond markets. We found that for the Emerging Market Bonds an equally weighted index for the country weights is probably the more suited because guarantees maximum diversification of country risk but for the Eurozone government bond market we found a GDP weighted index is better because the most important matter is to avoid a higher weight for highly indebted countries. In chapter 3 we analyzed the efficiency of a Derivatives Index to invest in the European corporate bond market instead of a Cash Index. We can state that the two indexes are similar in terms of returns, but that the Derivatives Index is less risky because it has a lower volatility, has values of skewness and kurtosis closer to those of a normal distribution and is a more liquid instrument, as the autocorrelation is not significant. In chapter 4 it is analyzed the impact of fallen angels on the corporate bond portfolios. Our analysis investigated the impact of the month-end rebalancing of the ML Emu Non Financial Corporate Index for the exit of downgraded bond (the event). We can conclude a flexible approach to the month-end rebalancing is better in order to avoid a loss of valued due to the benchmark construction rules. In chapter 5 we did a comparison between the equally weighted and capitalization weighted method for the European equity market. The benefit which results from reweighting the portfolio into equal weights can be attributed to the fact that EW portfolios implicitly follow a contrarian investment strategy, because they mechanically rebalance away from stocks that increase in price.