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Portfolio Optimization and Performance Analysis

Jean-Luc Prigent
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Chapman & Hall/CRC Financial Mathematics Series 7
[Reviewed by
Ita Cirovic Donev
, on

Interest in modern portfolio theory is constantly growing along with the ever increasing number of new financial products in the market. Such an increase calls for more intense and rigorous analysis behind it. This book answers the call.

The contents of the book are structured as follows:

Part I – Utility theory and risk analysis

The first two chapters provide the reader with the standard results on utility theory and risk measure minimization. These results are necessary for further understanding of portfolio theory and are presented in an elegant way with clear definitions. The author also turns to VaR measure and discusses its structure, use as well as its shortfalls.

Part II – Standard portfolio optimization

The next three chapters deal with standard portfolio optimization. The author discusses both passive and active portfolio optimization. One chapter is wholly devoted to Markowitz analysis of mean-variance. The chapter on portfolio performance states the results in detail, omitting, however, the detailed presentation of examples.

Part III – Dynamic portfolio optimization

Chapters 6, 7 and 8 provide the reader with a detailed overview of the stochastic optimization when applied to finance problems. Trying to avoid too much mathematical rigor the author concentrates on stating the results and proofs as clearly as possible. One does miss, however, a more intuitive discussion or smaller examples. This makes the text a bit terse.

Part IV – Structured portfolio management

In the last section the author presents some applications. The discussion is accompanied by full illustrations along with certain calculations. Overall it should give the reader a good overview of the applied methods.

The writing and mathematical rigor is at the level of graduate studies. However, it is not strictly theorem-proof style. Rather, the author uses many examples and illustrations along with mathematical exposition in discussions. The text is filled with examples which are presented in great detail with plenty of narrative explanations. These should guide the reader through more technical propositions and definitions.

In general, the text is easy to follow. The illustrations provided nicely blend with the theory and discussions.

Given the context and style of writing the book should be very attractive to graduate students with an interest in portfolio theory and researchers in the specified field. The book can be placed somewhere between a reference and a study book. Each chapter is further extended with a section on “further reading”. This provides the reader with additional notes and references, which are quite extensive.

One of the big drawbacks is the lack of exercises. The style of the presentation is such that one would expect exercises and even some applied computer projects. Due to this missing link, the book can probably not be efficiently used for self-study or an applied class course.

Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.

Utility Theory
Preferences under uncertainty
Expected utility
Risk aversion
Stochastic dominance
Alternative expected utility theory

Risk Measures
Coherent and convex risk measures
Standard risk measures

Static Optimization
Mean-variance analysis
Alternative criteria
Further reading

Indexed Funds and Benchmarking
Indexed funds
Benchmark portfolio optimization
Further reading

Portfolio Performance
Standard performance measures
Performance decomposition
Further reading

Dynamic Programming Optimization
Control theory
Lifetime portfolio selection
Further reading

Optimal Payoff Profiles and Long-Term Management
Optimal payoffs as functions of a benchmark
Application to long-term management
Further reading

Optimization within Specific Markets
Optimization in incomplete markets
Optimization with constraints
Optimization with transaction costs
Other frameworks
Further reading

Portfolio Insurance
The option-based portfolio insurance
The constant proportion portfolio insurance
Comparison between OBPI and CPPI
Further reading

Optimal Dynamic Portfolio with Risk Limits
Optimal insured portfolio: discrete-time case
Optimal insured portfolio: the dynamically complete case
Value-at-risk and expected shortfall-based management
Further reading

Hedge Funds
The hedge funds industry
Hedge funds performance
Optimal allocation in hedge funds
Further reading