Multi-Period Trading Via Convex Optimization

Multi-Period Trading Via Convex Optimization
Author: Stephen Boyd
Publisher:
Total Pages: 92
Release: 2017-07-28
Genre: Mathematics
ISBN: 9781680833287

This monograph collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework.

Multi-period Trading Via Convex Optimization

Multi-period Trading Via Convex Optimization
Author: Stephen P. Boyd
Publisher:
Total Pages: 76
Release: 2017
Genre: Electronic books
ISBN: 9781680833294

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper, we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.

Portfolio Decision Analysis

Portfolio Decision Analysis
Author: Ahti Salo
Publisher: Springer Science & Business Media
Total Pages: 410
Release: 2011-08-12
Genre: Business & Economics
ISBN: 1441999434

Portfolio Decision Analysis: Improved Methods for Resource Allocation provides an extensive, up-to-date coverage of decision analytic methods which help firms and public organizations allocate resources to 'lumpy' investment opportunities while explicitly recognizing relevant financial and non-financial evaluation criteria and the presence of alternative investment opportunities. In particular, it discusses the evolution of these methods, presents new methodological advances and illustrates their use across several application domains. The book offers a many-faceted treatment of portfolio decision analysis (PDA). Among other things, it (i) synthesizes the state-of-play in PDA, (ii) describes novel methodologies, (iii) fosters the deployment of these methodologies, and (iv) contributes to the strengthening of research on PDA. Portfolio problems are widely regarded as the single most important application context of decision analysis, and, with its extensive and unique coverage of these problems, this book is a much-needed addition to the literature. The book also presents innovative treatments of new methodological approaches and their uses in applications. The intended audience consists of practitioners and researchers who wish to gain a good understanding of portfolio decision analysis and insights into how PDA methods can be leveraged in different application contexts. The book can also be employed in courses at the post-graduate level.

Uncertain Portfolio Optimization

Uncertain Portfolio Optimization
Author: Zhongfeng Qin
Publisher: Springer
Total Pages: 200
Release: 2016-09-16
Genre: Business & Economics
ISBN: 9811018103

This book provides a new modeling approach for portfolio optimization problems involving a lack of sufficient historical data. The content mainly reflects the author’s extensive work on uncertainty portfolio optimization in recent years. Considering security returns as different variables, the book presents a series of portfolio optimization models in the framework of credibility theory, uncertainty theory and chance theory, respectively. As such, it offers readers a comprehensive and up-to-date guide to uncertain portfolio optimization models.

Multi-period Portfolio Optimization with Investor Views Under Regime Switching

Multi-period Portfolio Optimization with Investor Views Under Regime Switching
Author: Razvan Gabriel Oprisor
Publisher:
Total Pages: 0
Release: 2021
Genre:
ISBN:

We propose a novel multi-period trading model that allows portfolio managers to perform optimal portfolio allocation while incorporating their interpretable investment views. This model's significant advantage is its incorporation of the latest asset return regimes to quantitatively solve managers' question: how certain should one be that a given investment view is occurring? First, we describe a framework for multi-period portfolio allocation formulated as a convex optimization problem that trades off expected return, risk and transaction costs. Second, we use the Black-Litterman model to combine investment views specified in a simple linear combination based format with the market portfolio. A data-driven method to adjust the confidence in the manager's views by comparing them to dynamically updated regime-switching forecasts is proposed. Our contribution is to incorporate both multi-period trading and interpretable investment views into one efficient framework and offer a novel method of using regime-switching to determine each view's confidence.

Convex Optimization

Convex Optimization
Author: Stephen P. Boyd
Publisher: Cambridge University Press
Total Pages: 744
Release: 2004-03-08
Genre: Business & Economics
ISBN: 9780521833783

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Multi-Period Portfolio Optimization Model with Cone Constraints and Discrete Decisions

Multi-Period Portfolio Optimization Model with Cone Constraints and Discrete Decisions
Author: Ümit Saglam
Publisher:
Total Pages: 28
Release: 2019
Genre:
ISBN:

In this study, we consider multi-period portfolio optimization model that is formulated as a mixed-integer second-order cone programming problems (MISOCPs). The Markowitz (1952) mean/variance framework has been extended by including transaction costs, conditional value-at-risk (CVaR), diversification-by-sector and buy-in thresholds constraints. The model is obtained using a binary scenario tree that is constructed with monthly returns of the stocks from the S&P 500. We solve these models with a MATLAB based Mixed Integer Linear and Nonlinear Optimizer (MILANO). Numerical results show that we can solve small to medium-sized instances successfully, and we provide a substantial improvement in runtimes using warmstarts in outer approximation algorithm.

Single- and Multi-Period Portfolio Optimization with Cone Constraints and Discrete Decisions

Single- and Multi-Period Portfolio Optimization with Cone Constraints and Discrete Decisions
Author: Ümit Saglam
Publisher:
Total Pages: 20
Release: 2019
Genre:
ISBN:

Portfolio optimization literature has come quite far in the decades since the first publication, and many modern models are formulated using second-order cone constraints and take discrete decisions into consideration. In this study, we consider both single-period and multi-period portfolio optimization problems based on the Markowitz (1952) mean/variance framework, where there is a trade-off between expected return and the risk that the investor may be willing to take on. Our model is aggregated from current literature. In this model, we have included transaction costs, conditional value-at-risk (CVaR) constraints, diversification-by-sector constraints, and buy-in-thresholds. Our numerical experiments are conducted on portfolios drawn from 20 to 400 different stocks available from the S&P 500 for the single period-model. The multi-period portfolio optimization model is obtained using a binary scenario tree that is constructed with monthly returns of the closing price of the stocks from the S&P 500. We solve these models with a MATLAB based Mixed Integer Linear and Nonlinear Optimizer (MILANO). We provide a substantial improvement in runtimes using warmstarts in both branch-and-bound and outer approximation algorithms.