Semi-analytical solutions for dynamic portfolio choice in jump-diffusion models and the optimal bond-stock mix

This paper studies the optimal portfolio selection problem in jump-diffusion models where an investor has a HARA utility function, and there are potentially a large number of assets and state variables. More specifically, we incorporate jumps into both stock returns and state variables, and then derive semi-analytical solutions for the optimal portfolio policy up to solving a set of ordinary differential equations to greatly facilitate economic insights and empirical applications of jump-diffusion models. To examine the effect of jump risk on investors’ behavior, we apply our results to the bond-stock mix problem and particularly revisit the bond/stock ratio puzzle in jump-diffusion models. Our results cast new light on this puzzle that unlike pure-diffusion models, it cannot be rationalized by the hedging demand assumption due to the presence of jumps in stock returns

An Evolutionary Approach to Multistage Portfolio Optimization

Portfolio optimization is an important problem in quantitative finance due to its application in asset management and corporate financial decision making. This involves quantitatively selecting the optimal portfolio for an investor given their asset return distribution assumptions, investment objectives and constraints. Analytical portfolio optimization methods suffer from limitations in terms of the problem specification and modelling assumptions that can be used. Therefore, a heuristic approach is taken where Monte Carlo simulations generate the investment scenarios and' a problem specific evolutionary algorithm is used to find the optimal portfolio asset allocations. Asset allocation is known to be the most important determinant of a portfolio's investment performance and also affects its risk/return characteristics. The inclusion of equity options in an equity portfolio should enable an investor to improve their efficient frontier due to options having a nonlinear payoff. Therefore, a research area of significant importance to equity investors, in which little research has been carried out, is the optimal asset allocation in equity options for an equity investor. A purpose of my thesis is to carry out an original analysis of the impact of allowing the purchase of put options and/or sale of call options for an equity investor. An investigation is also carried out into the effect ofchanging the investor's risk measure on the optimal asset allocation. A dynamic investment strategy obtained through multistage portfolio optimization has the potential to result in a superior investment strategy to that obtained from a single period portfolio optimization. Therefore, a novel analysis of the degree of the benefits of a dynamic investment strategy for an equity portfolio is performed. In particular, the ability of a dynamic investment strategy to mimic the effects ofthe inclusion ofequity options in an equity portfolio is investigated. The portfolio optimization problem is solved using evolutionary algorithms, due to their ability incorporate methods from a wide range of heuristic algorithms. Initially, it is shown how the problem specific parts ofmy evolutionary algorithm have been designed to solve my original portfolio optimization problem. Due to developments in evolutionary algorithms and the variety of design structures possible, a purpose of my thesis is to investigate the suitability of alternative algorithm design structures. A comparison is made of the performance of two existing algorithms, firstly the single objective stepping stone island model, where each island represents a different risk aversion parameter, and secondly the multi-objective Non-Dominated Sorting Genetic Algorithm2. Innovative hybrids of these algorithms which also incorporate features from multi-objective evolutionary algorithms, multiple population models and local search heuristics are then proposed. . A novel way is developed for solving the portfolio optimization by dividing my problem solution into two parts and then applying a multi-objective cooperative coevolution evolutionary algorithm. The first solution part consists of the asset allocation weights within the equity portfolio while the second solution part consists 'ofthe asset allocation weights within the equity options and the asset allocation weights between the different asset classes. An original portfolio optimization multiobjective evolutionary algorithm that uses an island model to represent different risk measures is also proposed.Imperial Users onl

Are fund managers incentivised to ignore stock market jumps?

In this paper, we show that the way in which fund managers are compensated can, under plausible conditions, lead them to act in a way that does not maximise the wellbeing of their clients. Due to performance bonuses in fund managers' rewards, there is a highly non-linear relationship between the wealth of the client and the fees that the manager receives. We demonstrate that jumps in equity returns can lead to a conflict of interest between the investor and the manager in such a setting. Specifically, the managers' option-type payment structure can incentivise them to not account for the downside risk induced by jumps, especially if the fund manager is only in post for a few years; thus managers may pursue a more aggressive asset allocation strategy than their clients desire. Our key policy recommendation is that regulators should consider imposing a negative fund fee in times of very poor absolute fund performance to mitigate against suboptimal fund management asset allocation decisions

Essays in Robust and Data-Driven Risk Management

Risk defined as the chance that the outcome of an uncertain event is different than expected. In practice, the risk reveals itself in different ways in various applications such as unexpected stock movements in the area of portfolio management and unforeseen demand in the field of new product development. In this dissertation, we present four essays on data-driven risk management to address the uncertainty in portfolio management and capacity expansion problems via stochastic and robust optimization techniques.The third chapter of the dissertation (Portfolio Management with Quantile Constraints) introduces an iterative, data-driven approximation to a problem where the investor seeks to maximize the expected return of his/her portfolio subject to a quantile constraint, given historical realizations of the stock returns. Our approach involves solving a series of linear programming problems (thus) quickly solves the large scale problems. We compare its performance to that of methods commonly used in finance literature, such as fitting a Gaussian distribution to the returns. We also analyze the resulting efficient frontier and extend our approach to the case where portfolio risk is measured by the inter-quartile range of its return. Furthermore, we extend our modeling framework so that the solution calculates the corresponding conditional value at risk CVaR) value for the given quantile level.The fourth chapter (Portfolio Management with Moment Matching Approach) focuses on the problem where a manager, given a set of stocks to invest in, aims to minimize the probability of his/her portfolio return falling below a threshold while keeping the expected portfolio returnno worse than a target, when the stock returns are assumed to be Log-Normally distributed. This assumption, common in finance literature, creates computational difficulties. Because the portfolio return itself is difficult to estimate precisely. We thus approximate the portfolio re-turn distribution with a single Log-Normal random variable by the Fenton-Wilkinson method and investigate an iterative, data-driven approximation to the problem. We propose a two-stage solution approach, where the first stage requires solving a classic mean-variance optimization model, and the second step involves solving an unconstrained nonlinear problem with a smooth objective function. We test the performance of this approximation method and suggest an iterative calibration method to improve its accuracy. In addition, we compare the performance of the proposed method to that obtained by approximating the tail empirical distribution function to a Generalized Pareto Distribution, and extend our results to the design of basket options.The fifth chapter (New Product Launching Decisions with Robust Optimization) addresses the uncertainty that an innovative firm faces when a set of innovative products are planned to be launched a national market by help of a partner company for each innovative product. Theinnovative company investigates the optimal period to launch each product in the presence of the demand and partner offer response function uncertainties. The demand for the new product is modeled with the Bass Diffusion Model and the partner companies\u27 offer response functions are modeled with the logit choice model. The uncertainty on the parameters of the Bass Diffusion Model and the logic choice model are handled by robust optimization. We provide a tractable robust optimization framework to the problem which includes integer variables. In addition, weprovide an extension of the proposed approach where the innovative company has an option to reduce the size of the contract signed by the innovative firm and the partner firm for each product.In the sixth chapter (Log-Robust Portfolio Management with Factor Model), we investigate robust optimization models that address uncertainty for asset pricing and portfolio management. We use factor model to predict asset returns and treat randomness by a budget of uncertainty. We obtain a tractable robust model to maximize the wealth and gain theoretical insights into the optimal investment strategies

Essays on Dynamic Asset Allocation and Performance Measures

The present thesis examines two central issues in financial theory, optimal portfolio choice and investment performance evaluation, when the restrictive assumptions of the traditional static, mean-variance framework of analysis are relaxed. Chapter 2 presents a series of model specifications for the risky asset's returns and the underlying risk factor and derives the corresponding optimal portfolio choices. It shows how important the modelling assumptions are for the implementation of dynamic asset allocation in practice and it contributes to the literature by examining the impact of horizon effects on portfolio choice in the presence of both predictability and stochastic volatility in asset returns. Moreover, this chapter shows how important is the introduction of an asset that completes the market and allows investors to hedge against the shocks that affect their opportunity set, Chapter 3 examines the bond portfolio choice of a long-term investor, making use of a macro-finance term structure model that allows for time-varying risk premia. This chapter shows how important is the failure of the expectations hypothesis for both myopic and long-term investors, since the time-variation in the bond premia dictates a market timing behaviour for investment as well as for hedging purposes. Incorporating macroeconomic information, that plays a significant role in bond pricing, we examine how this can be used for the formation of optimal portfolios· by long-term investors. Furthermore, this chapter serves as an evaluation of the very recent term structure models from an asset allocation perspective, drawing the attention to the correlation and the covariance structure of the bond returns. ' Chapter 4 employs the Harvey-Siddique asset pricing model and 'evaluates a sample of UK equity unit trusts, proposing the intercept of this model, that is termed as the Harvey-Siddique alpha, as a new performance measure. This asset pricing model adds to the CAPM the returns of a negative coskewness strategy as an extra risk factor. Constructing this factor for the UK stock market, it is shown that negative coskewness bears a high risk premium. This framework allows us to examine how the adoption of specific performance measures generates incentives in fund management. In particular, we provide evidence that fund managers, who are evaluated by mean-variance performance measures, are incentivized to load negative coskewness risk to their portfolios in order to reap the corresponding premium and present it as outperformance. Chapter 5 overviews the contributions of this thesis, discusses the numerous issues that arise from the present results and outlines the following steps in our research agenda

Computational Finance

With the availability of new and more comprehensive financial market data, making headlines of massive public interest due to recent periods of extreme volatility and crashes, the field of computational finance is evolving ever faster thanks to significant advances made theoretically, and to the massive increase in accessible computational resources. This volume includes a wide variety of theoretical and empirical contributions that address a range of issues and topics related to computational finance. It collects contributions on the use of new and innovative techniques for modeling financial asset returns and volatility, on the use of novel computational methods for pricing, hedging, the risk management of financial instruments, and on the use of new high-dimensional or high-frequency data in multivariate applications in today’s complex world. The papers develop new multivariate models for financial returns and novel techniques for pricing derivatives in such flexible models, examine how pricing and hedging techniques can be used to assess the challenges faced by insurance companies, pension plan participants, and market participants in general, by changing the regulatory requirements. Additionally, they consider the issues related to high-frequency trading and statistical arbitrage in particular, and explore the use of such data to asses risk and volatility in financial markets

Structured Life Insurance and Investment Products for Retail Investors

Structured life insurance and investment products combine individual financial instruments such as bonds and stocks with positions in financial derivatives. These products are tailored to give retail investors the opportunity to optimize their investment portfolios by including derivative structures and strategies which are usually not available to retail investors. The first part of this thesis is concerned with structured life insurance products. Here, existing contracts with a terminal wealth guarantee are analyzed with respect to their optimality for a retail investor. Special emphasis is put on innovative riders and stochastic background risk the investor faces additionally. The second part considers the pricing, risk management and optimality of structured investment products. The fifth chapter provides an analysis of a complex newly issued certicate. The final core chapter compares two prominent portfolio insurance strategies under borrowing constraints with respect to their optimality for a retail investor