Browsing by Subject "Portfolio management"
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Item Essays on pricing and portfolio choice in incomplete markets(2008-12) Zhou, Ti, 1981-; Zariphopoulou, Thaleia, 1962-This dissertation is a contribution to the pricing and portfolio choice theory in incomplete markets. It consists of three self-contained but interlinked essays. In the first essay, we present a utility-based methodology for the valuation and the risk management of mortgage-backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded pre-payment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools. In the second essay, using forward optimality criteria, we analyze a portfolio choice problem when the local risk tolerance is time-dependent and asymptotically linear in wealth. This class corresponds to a dynamic extension of the traditional (static) risk tolerances associated with the power, logarithmic and exponential utilities. We provide explicit solutions for the optimal investment strategies and wealth processes in an incomplete non-Markovian market with asset prices modelled as Ito processes. The methodology allows for measuring the investment performance in terms of a benchmark and alter-native market views. In the last essay, we extend the forward investment performance approach to study the optimal portfolio choice problem in an incomplete market driven by jump processes. The asset price is modelled by a one-dimensional Lévy-Itô process. We prove the existence of a forward performance process by restricting the local risk tolerance functions to be time-independent and linear in wealth. This yields only three types of performance measurement criteria, namely, exponential, power and logarithmic. The optimal portfolios are constructed via stochastic feedback controls under these criteria.Item Evaluation and comparison of management strategies by Data Envelopment Analysis with an application to mutual funds(2006) Wilson, Chester L.; Cooper, William W.; Ruefli, Timothy W.A new categorical schema for strategic management is developed; a methodology for its implementation is elaborated; an application to mutual funds based on microeconomic theory is demonstrated; and results which establish quantitative measures for evaluating strategies, improve measures of managerial performance, and establish a new viii method of evaluating portfolio performance with guidance for potential mutual fund shareholders is presented. The evaluation of strategies themselves depends fundamentally on distinguishing them from their execution, from their realization in practice. The accounting definition of strategy, “a plan of action used to guide or control other plans of action” finds an observable, indeed measurable, example in the strategic choices of mutual funds, which are required by law to declare and conform to the general strategy by which they conduct investment management. The methodology to exploit the declared strategies and performance data of mutual funds is Data Envelopment Analysis (DEA), a nonparametric linear programming method of analysis for use with empirical data. By producing a piecewise linear frontier based on the Pareto-Koopmans efficient performers, DEA provides a basis for measuring performances and facilitates sensitivity analysis. Data Envelopment Analysis measures assume no prior, underlying functional form (such as regression equations or production functions) to relate input to output or to other variables. An evaluation of a selected group of mutual funds illustrates the general DEA method and evaluates the actual performance of the funds. Then a new application involving an extended, three-stage Data Envelopment Analysis separates the performance of the investment strategies from the effects of managerial shortcomings and abilities to implement the strategies. This makes it possible to separately identify and evaluate what a strategy can accomplish. It also makes it possible to evaluate separately short-run from ix long-run performance. Finally, DEA identifies benchmarking possibilities for removing these short-run deficiencies. This new method for evaluating strategies and shortcomings in performance is demonstrated by application to mutual funds, which display striking contrasts in managerial performance and strategic potential. Although demonstrated with mutual funds, this method is not restricted to such applications. Indeed, the methods in this thesis provide a new way of evaluating investment potentials by distinguishing between actual short-run performance and long-run potentials.Item Forward optimization and real-time model adaptation with applications to portfolio management, indifference valuation and optimal liquidation(2018-12) Wang, Haoran, Ph. D.; Zariphopoulou, Thaleia, 1962-; Sirbu, Mihai; Zitkovic, Gordan; Muthuraman, KumarThe goal of this thesis is to introduce a new, alternative approach to deal with model uncertainty and “real-time” model revisions and, in turn, develop a comparative study with existing approaches in the context of various applications in financial mathematics. This new approach is based on the forward performance criteria which adapt in a time-consistent way to “real-time” model revisions. The novelty is that these revisions are genuinely “model-free” in that they occur in “real-time”, without any modeling pre-commitment. For example, in the context of optimal liquidation (see Chapter 3 and Chapter 4), there is no a priori model for the evolution of the market impact parameter λ. It is rather assumed that this parameter switches at predictable times, to values only observable at the switching times. As such, the model revisions capture the evolving reality and allow for considerable flexibility. This forward approach thus incorporates “real-time” model revisions and is, therefore, close to adaptive optimization. On the other hand, it produces, by construction, time-consistent policies and is, thus, close to the classical optimization with model(s) pre-commitment. In other words, it can be thought as a hybrid approach that accommodates dynamic model changes while preserving time-consistency. We apply the forward approach with “real-time” model revisions in four distinct problems: portfolio management in discrete and continuous settings (binomial and lognormal, respectively), indifference valuation in lognormal models and optimal liquidation in the continuous time Almgren-Chriss model. We produce closed form solutions and characterize the optimal policies and optimal criteria. As the analysis shows, one needs to solve various sequential “inverse” optimal investment problems with random coefficients, corresponding to model revisions in real-time. We develop a comparative study with the classical settings. A main novelty is the introduction of two performance metrics which measure the discrepancies between the actual performance, and the projected or the true optimal performances under the various criteria and behavior. We study these metrics for various scenaria, related to favorable and non-favorable market changes, and compare their performance. These metrics resemble the notion of “regret”, which is now considered in a more dynamic and “real-time” manner. Among others, we show that the regret of the forward decision maker is always zero, independently of the upcoming model changes. In what follows, we describe each application separately. For each application, we introduce the model, the forward and classical criteria, construct the corresponding solutions and policies, and compare them in detailItem Investment diversification in natural resources(1999) Ramsey, Terry L., 1940-; Van Rensburg, W. C. J.Investment diversification is a process of evaluating and selecting an investment portfolio to maximize returns and minimize volatility of returns. The objective of this study is to provide a robust model of investment diversification and to demonstrate how each company may uniquely achieve its optimum diversification. All theoretical solutions and examples are provided in a Mathematica format so that the reader may duplicate all results in detail. This research integrates the widely applicable gamma probability density distribution with exponential utility to quantify the transformation of the underlying prospect value distribution to a risk adjusted value distribution (RAV). The development of an RAV distribution provides a theoretical basis for the benefits of management financial cutoffs for improvement in return on investment and for the reduction in volatility of those returns. These theoretical developments are the essential elements of diversification which consists of transforming a distribution and truncating a distribution in a repetitive process until the portfolio yields and variance meet management goals. This research uses minimizing volatility and maximizing risk adjusted value per dollar (RAVPD) to derive a new concept of investment efficiency, the MaxRAVPD. The MaxRAVPD is the maximum return on investment that can be achieved with the underlying distribution of value. As fewer projects are considered to increase portfolio returns, the sample variance increases, resulting in a cost (computed as expectation of RAVPD) which establishes when the portfolio return cannot be increased further, defining the MaxRAVPD. The analysis of each investment involves each investor's unique risk preferences represented by exponential utility. Application of exponential utility is accompanied by analytical developments which clarify and extend the existing literature. A set of 375 exploration prospects are subject to a RAVPD cutoff resulting in 50 acceptable prospects evaluated in three portfolios. Portfolio I is the base case: ranking the prospects by return on investment and buying down the list by investing 25 percent in each prospect. Portfolio II illustrates that Portfolio I results can be improved by 17 percent by evaluating the underlying prospects in terms of risk adjusted values. Portfolio III, by maximizing risk adjusted return on investment by using a target RAVPD, improves Portfolio I results by 57 percent. These results confirm the theoretical developments that management should use an initial RAVPD cutoff, and target RAVPD to maximize any portfolio's RAVPD. Engineering deals with the producing results with available resources. Engineering of diversification requires consideration of constraints on budgets, manpower, costs and management policy to define an optimum business structure. Engineering of diversification is formulated as a linear programming model to maximize portfolio returnsItem Residential housing, household portfolio, and intertemporal elasticity of substitution(2005) Hasanov, Fuad; Dacy, Douglas C.In this dissertation, I investigate whether the return on a household portfolio and the inclusion of residential housing in a portfolio are important to the household’s intertemporal consumption choice. In particular, my first essay investigates whether the rate of interest such as the Treasury bill rate or the rate of return such as the return on a household portfolio is more relevant to the household’s intertemporal decision making. In the current era, households hold portfolios of assets, which earn composite returns accounting for capital gains, taxes, and inflation. In addition to stocks and bonds, I incorporate residential housing into a household portfolio. The computed total composite return, a weighted average return on the aggregate household portfolio, is then use v estimating the intertemporal elasticity of substitution (IES), a parameter measuring the response of household’s consumption growth to a change in a rate of return. The estimates obtained using the real after-tax composite return with aggregate consumption are about 0.15-0.3 and are more robust to linear and nonlinear estimations, different consumption measures, and various time periods than those obtained by using individual asset returns such as the Treasury bill rate. My second essay is devoted to measuring and analyzing the return on aggregate residential housing. This essay further investigates a major component of the composite return that is not as straightforwardly computed as financial asset returns. In constructing real after-tax total return on housing, I account for rental income, capital gain, and subsidies due to the tax provisions for homeowners. This is a more comprehensive measure of return than that found in the literature. I find that residential housing provides high average return and low volatility, has low correlation with other assets such as stocks and bonds, exhibits high positive correlation with inflation, and should be a major part of the household portfolio. Lastly, the third essay of the dissertation explores the impact of the inclusion of housing in a household portfolio on the IES using household-level data from the Consumer Expenditure Survey. Moreover, utilizing a household level data set, I estimate IES parameters for different groups of assetholders. My results indicate that housing return positively affects consumption growth, and that housing is an important asset in the household portfolio.