pwc-archive/papers-with-abstracts huggingface dataset:
Optimal Tracking Portfolio with A Ratcheting Capital Benchmark
Authors: Lijun Bo, Huafu Liao, Xiang Yu
Date: 2020-06-24 00:00:00
Tasks: Management

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a non-decreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, the problem is further shown to be equivalent to an auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation and some stochastic flow analysis, the existence of the unique classical solution to the HJB equation is established. The verification theorem is carefully proved, which gives the complete characterization of the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.
An elementary approach to the Merton problem
Authors: Martin Herdegen, David Hobson, Joseph Jerome
Date: 2020-06-09 00:00:00

In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black - Scholes - Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down a candidate value function and to use a verification argument to prove that this is the solution to the problem. However, features of the problem take it outside the standard settings of stochastic control, and the existing primal verification proofs rely on parameter restrictions (especially, but not only, R<1), restrictions on the space of admissible strategies, or intricate approximation arguments. The purpose of this paper is to show that these complications can be overcome using a simple and elegant argument involving a stochastic perturbation of the utility function.
Relative utility bounds for empirically optimal portfolios
Authors: Dmitry B. Rokhlin
Date: 2020-06-09 00:00:00

We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns with unknown distribution. Assuming that the utility function is Lipschitz or H\"{o}lder continuous (the concavity is not required), we obtain high probability utility bounds under the sole assumption that the returns are independent and identically distributed. These bounds depend only on the utility function, the number of assets and the number of observations. For concave utilities similar bounds are obtained for the portfolios produced by the exponentiated gradient method. Also we use statistical experiments to study risk and generalization properties of empirically optimal portfolios. Herein we consider a model with one risky asset and a dataset, containing the stock prices from NYSE.
Optimal Control of Investment for an Insurer in Two Currency Markets
Authors: Qianqian Zhou, Junyi Guo
Date: 2020-06-04 00:00:00
Tasks: Vocal Bursts Valence Prediction

In this paper, we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model. Investment in the foreign market is allowed, and therefore, the foreign exchange rate model is considered and incorporated. It is assumed that the instantaneous mean growth rate of foreign exchange rate price follows an Ornstein-Uhlenbeck process. Dynamic programming method is employed to study the problem of maximizing the expected exponential utility of terminal wealth. By soloving the correspoding Hamilton-Jacobi-Bellman equations, the optimal investment strategies and the value functions are obtained. Finally, numerical analysis is presented.
Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time
Authors: Ying Hu, Hanqing Jin, Xun Yu Zhou
Date: 2020-06-02 00:00:00

We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of sophisticated consistent planners who seek (subgame perfect) intra-personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than 1 corresponding to an effective reduction in risk premium due to probability weighting.
A Portfolio Choice Problem Under Risk Capacity Constraint
Authors: Weidong Tian, Zimu Zhu
Date: 2020-05-28 00:00:00

This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the optimal investment strategy under the specific condition on model parameters in terms of second-order ordinary differential equations. We demonstrate an endogenous number that measures the expected value to sustain the spending post-retirement. The optimal portfolio is nearly neutral to the stock market movement if the portfolio's value is higher than this number; but, if the portfolio is not worth enough to sustain the retirement spending, the retiree actively invests in the stock market for the higher expected return. Besides, we solve an optimal portfolio choice problem under a leverage constraint and show that the optimal portfolio would lose significantly in stressed markets. This paper shows that the time-varying risk capacity constraint has important implications for asset allocation in retirement.
RM-CVaR: Regularized Multiple $β$-CVaR Portfolio
Authors: Kei Nakagawa, Shuhei Noma, Masaya Abe
Date: 2020-04-28 00:00:00
Tasks: Portfolio Optimization

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the most fundamental risk measure to be minimized, it has several drawbacks. Conditional Value-at-Risk (CVaR) is a relatively new risk measure that addresses some of the shortcomings of well-known variance-related risk measures, and because of its computational efficiencies, it has gained popularity. CVaR is defined as the expected value of the loss that occurs beyond a certain probability level ($\beta$). However, portfolio optimization problems that use CVaR as a risk measure are formulated with a single $\beta$ and may output significantly different portfolios depending on how the $\beta$ is selected. We confirm even small changes in $\beta$ can result in huge changes in the whole portfolio structure. In order to improve this problem, we propose RM-CVaR: Regularized Multiple $\beta$-CVaR Portfolio. We perform experiments on well-known benchmarks to evaluate the proposed portfolio. Compared with various portfolios, RM-CVaR demonstrates a superior performance of having both higher risk-adjusted returns and lower maximum drawdown.
Portfolio optimization in the case of an exponential utility function and in the presence of an illiquid asset
Authors: Ljudmila A. Bordag
Date: 2019-10-15 00:00:00
Tasks: Portfolio Optimization

We study an optimization problem for a portfolio with a risk-free, a liquid, and an illiquid risky asset. The illiquid risky asset is sold in an exogenous random moment with a prescribed liquidation time distribution. The investor prefers a negative or a positive exponential utility function. We prove that both cases are connected by a one-to-one analytical substitution and are identical from the economic, analytical, or Lie algebraic points of view. It is well known that the exponential utility function is connected with the HARA utility function through a limiting procedure if the parameter of the HARA utility function is going to infinity. We show that the optimization problem with the exponential utility function is not connected to the HARA case by the limiting procedure and we obtain essentially different results. For the main three dimensional PDE with the exponential utility function we obtain the complete set of the nonequivalent Lie group invariant reductions to two dimensional PDEs according to an optimal system of subalgebras of the admitted Lie algebra. We prove that in just one case the invariant reduction is consistent with the boundary condition. This reduction represents a significant simplification of the original problem.
A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models
Authors: Juan Li, Wenqiang Li, Gechun Liang
Date: 2020-05-06 00:00:00

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the homothetic robust forward performance processes in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.
Collectivised Post-Retirement Investment
Authors: John Armstrong, Cristin Buescu
Date: 2019-09-27 00:00:00
Tasks: Management

We quantify the benefit of collectivised investment funds, in which the assets of members who die are shared among the survivors. For our model, with realistic parameter choices, an annuity or individual fund requires approximately 20\% more initial capital to provide as good an outcome as a collectivised investment fund. We demonstrate the importance of the new concept of pension adequacy in defining investor preferences and determining optimal fund management. We show how to manage heterogeneous funds of investors with diverse needs. Our framework can be applied to existing pension products, such as Collective Defined Contribution schemes.
Spanning analysis of stock market anomalies under Prospect Stochastic Dominance
Authors: Stelios Arvanitis, Olivier Scaillet, Nikolas Topaloglou
Date: 2020-04-06 00:00:00

We develop and implement methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for prospect investors. We formulate a new testing procedure for prospect spanning for two nested portfolio sets based on subsampling and Linear Programming. In an application, we use the prospect spanning framework to evaluate whether well-known anomalies are spanned by standard factors. We find that of the strategies considered, many expand the opportunity set of the prospect type investors, thus have real economic value for them. In-sample and out-of-sample results prove remarkably consistent in identifying genuine anomalies for prospect investors.
Asymptotically Optimal Management of Heterogeneous Collectivised Investment Funds
Authors: John Armstrong, Cristin Buescu
Date: 2020-04-02 00:00:00
Tasks: Management

A collectivised fund is a proposed form of pension investment, in which all investors agree that any funds associated with deceased members should be split among survivors. For this to be a viable financial product, it is necessary to know how to manage the fund even when it is heterogeneous: that is when different investors have different preferences, wealth and mortality. There is no obvious way to define a single objective for a heterogeneous fund, so this is not an optimal control problem. In lieu of an objective function, we take an axiomatic approach. Subject to our axioms on the management of the fund, we find an upper bound on the utility that can be achieved for each investor, assuming a complete markets and the absence of systematic longevity risk. We give a strategy for the management of such heterogeneous funds which achieves this bound asymptotically as the number of investors tends to infinity.
Asymptotic distribution of the Markowitz portfolio
Authors: Steven E. Pav
Date: 2013-12-02 00:00:00

The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect, one can estimate the proportion of error in the Markowitz portfolio due to mis-estimation of the covariance matrix. A likelihood ratio test is given which generalizes Dempster's Covariance Selection test to allow inference on linear combinations of the precision matrix and the Markowitz portfolio. Extensions of the main method to deal with hedged portfolios, conditional heteroskedasticity, conditional expectation, and constrained estimation are given. It is shown that the Hotelling-Lawley statistic generalizes the (squared) Sharpe ratio under the conditional expectation model. Asymptotic distributions of all four of the common `MGLH' statistics are found, assuming random covariates. Examples are given demonstrating the possible uses of these results.
Diffusion Approximations for Expert Opinions in a Financial Market with Gaussian Drift
Authors: Jörn Sass, Dorothee Westphal, Ralf Wunderlich
Date: 2018-07-02 00:00:00

This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as an external source of information. For estimating the hidden drift it is crucial to consider the conditional distribution of the drift given the available observations, the so-called filter. For an investor observing both the return process and the discrete-time expert opinions, we investigate in detail the asymptotic behavior of the filter as the frequency of the arrival of expert opinions tends to infinity. In our setting, a higher frequency of expert opinions comes at the cost of accuracy, meaning that as the frequency of expert opinions increases, the variance of expert opinions becomes larger. We consider a model where information dates are deterministic and equidistant and another model where the information dates arrive randomly as the jump times of a Poisson process. In both cases we derive limit theorems stating that the information obtained from observing the discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process which can be interpreted as a continuous-time expert. We use our limit theorems to derive so-called diffusion approximations of the filter for high-frequency discrete-time expert opinions. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.
Diversity and Sparsity: A New Perspective on Index Tracking
Authors: Yu Zheng, Timothy M. Hospedales, Yongxin Yang
Date: 2018-09-06 00:00:00
Tasks: Diversity

We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking portfolio must also be diverse in order to minimise risk -- a requirement which has only been dealt with by ad-hoc methods before. We introduce the first index tracking method that explicitly optimises both diversity and sparsity in a single joint framework. Diversity is realised by a regulariser based on pairwise similarity of assets, and we demonstrate that learning similarity from data can outperform some existing heuristics. Finally, we show that the way we model diversity leads to an easy solution for sparsity, allowing both constraints to be optimised easily and efficiently. we run out-of-sample backtesting for a long interval of 15 years (2003 -- 2018), and the results demonstrate the superiority of the proposed algorithm.
A note on the worst case approach for a market with a stochastic interest rate
Authors: Dariusz Zawisza
Date: 2020-01-07 00:00:00

We solve robust optimization problem and show the example of the market model for which the worst case measure is not a martingale measure. In our model the instantaneous interest rate is determined by the Hull-White model and the investor employs the HARA utility to measure his satisfaction.To protect against the model uncertainty he uses the worst case measure approach. The problem is formulated as a stochastic game between the investor and the market from the other side. PDE methods are used to find the saddle point and the precise verification argument is provided.
Leakage of rank-dependent functionally generated trading strategies
Authors: Kangjianan Xie
Date: 2019-12-09 00:00:00

This paper investigates the so-called leakage effect of trading strategies generated functionally from rank-dependent portfolio generating functions. This effect measures the loss in wealth of trading strategies due to renewing the portfolio constituent stocks. Theoretically, the leakage effect of a trading strategy is expressed explicitly by a finite-variation term. The computation of the leakage is different from what previous research has suggested. The method to estimate leakage in discrete time is then introduced with some practical considerations. An empirical example illustrates the leakage of the corresponding trading strategies under different constituent list sizes.
Analysing Global Fixed Income Markets with Tensors
Authors: Bruno Scalzo Dees
Date: 2019-08-06 00:00:00
Tasks: Management

Global fixed income returns span across multiple maturities and economies, that is, they naturally reside on multi-dimensional data structures referred to as tensors. In contrast to standard "flat-view" multivariate models that are agnostic to data structure and only describe linear pairwise relationships, we introduce a tensor-valued approach to model the global risks shared by multiple interest rate curves. In this way, the estimated risk factors can be analytically decomposed into maturity-domain and country-domain constituents, which allows the investor to devise rigorous and tractable global portfolio management and hedging strategies tailored to each risk domain. An empirical analysis confirms the existence of global risk factors shared by eight developed economies, and demonstrates their ability to compactly describe the global macroeconomic environment.
Comparative Companies' Stock Valuation through Financial Metrics and its Social Implications
Authors: Jack Colleran, Harris K. Kim, Benny C. Pickle, John Sun
Date: 2019-09-13 00:00:00
Tasks: Marketing

Out of the companies, Dolby is the company with the best overall financial and operation health. According to the table that accounted its financial statements for the past three years, Dolby has stable profit margins that generates a revenue in the billions, the only company in ten figures. Corporate competition to gain more patents as old ones expire may mean new jobs created, increased funding for schools, investment in technology or engineering education, and further need for purchase of marketing and salespeople.
Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach
Authors: Roberto Baviera, Giulia Bianchi
Date: 2019-02-18 00:00:00

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach. In the minimum-variance case, we prove that the analytical solution is significantly different from the one found numerically by Glasserman and Xu (2014) and that model risk reduces to an estimation risk. A detailed numerical example is provided.
Singular Perturbation Expansion for Utility Maximization with Order-$ε$ Quadratic Transaction Costs
Authors: Andrew Papanicolaou, Shiva Chandra
Date: 2019-10-14 00:00:00
Tasks: Portfolio Optimization

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $\epsilon$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of $\sqrt\epsilon$. In this paper we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.
Optimal Convergence Trading with Unobservable Pricing Errors
Authors: Sühan Altay, Katia Colaneri, Zehra Eksi
Date: 2019-10-03 00:00:00
Tasks: Portfolio Optimization

We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced ones with the expectation that their prices converge in the future. We build on the model of Liu and Timmermann (2013) and extend it by incorporating unobservable Markov-modulated pricing errors into the price dynamics of two co-integrated assets. We characterize the optimal portfolio strategies in full and partial information settings both under the assumption of unrestricted and beta-neutral strategies. By using the innovations approach, we provide the filtering equation that is essential for solving the optimization problem under partial information. Finally, in order to illustrate the model capabilities, we provide an example with a two-state Markov chain.