Quantitative Financial Risk Management

Theory and Practice

Constantin Zopounidis, Emilios Galariotis

• Publisher: Wiley
• Year: 2015
• Print ISBN:
  9781118738184
• Edition: 1
• eBook ISBN:
  9781118738221
• Topic: Business
• Subtopic: Finance
• Index: Business

A Comprehensive Guide to Quantitative Financial Risk Management

Written by an international team of experts in the field, Quantitative Financial Risk Management: Theory and Practice provides an invaluable guide to the most recent and innovative research on the topics of financial risk management, portfolio management, credit risk modeling, and worldwide financial markets.

This comprehensive text reviews the tools and concepts of financial management that draw on the practices of economics, accounting, statistics, econometrics, mathematics, stochastic processes, and computer science and technology. Using the information found in Quantitative Financial Risk Management can help professionals to better manage, monitor, and measure risk, especially in today's uncertain world of globalization, market volatility, and geo-political crisis.

Quantitative Financial Risk Management delivers the information, tools, techniques, and most current research in the critical field of risk management. This text offers an essential guide for quantitative analysts, financial professionals, and academic scholars.

Section Three
Portfolio Management

Chapter 7
Portfolio Optimization: Theory and Practice

William T. Ziemba

Alumni Professor of Financial Modeling and Stochastic Optimization (Emeritus), University of British, Columbia

Distinguished Visiting Research Associate, Systemic Risk Center, London School of Economics

Static Portfolio Theory

In the static portfolio theory case, suppose there are n assets,

, with random returns

. The return on asset i, namely

, is the capital appreciation plus dividends in the next investment period such as monthly, quarterly, or yearly or some other time period. The n assets have the distribution

with known mean vector

and known

variance-covariance matrix

with typical covariance

for

and variance

for

. A basic assumption (relaxed in section 6) is that the return distributions are independent of the asset weight choices, so

.

A mean-variance frontier is

where e is a vector of ones,

are the asset weights, K represents other constraints on the x, and w₀ is the investor's initial wealth.

When variance is parameterized with

, it yields a concave curve, as in Figure 7.1(a). This is a Markowitz (1952, 1987, 2006) mean-variance efficient frontier and optimally trades off mean, which is desirable, with variance, which is undesirable. Tobin (1958) extended the Markowitz model to include a risk-free asset with mean

and no variance. Then the efficient frontier concave curve becomes the straight line as shown in Figure 7.1(b). The standard deviation here is plotted rather than the variance to make the line straight. An investor will pick an optimal portfolio in the Markowitz model by using a utility function that trades off mean for variance or, equivalently, standard deviation, as shown in Figure 7.1(a), to yield portfolio A. For the Tobin model, ...

Table of contents

• Cover
• Title Page
• Copyright
• Table of Contents
• Dedication
• Preface
• About the Editors
• Section One: Supervisory Risk Management
• Section Two: Risk Models and Measures
• Section Three: Portfolio Management
• Section Four: Credit Risk Modelling
• Section Five: Financial Markets
• About the Contributors
• Glossary
• Index
• End User License Agreement