Frontmatter Page xiv Monday, March 8, 2004 10:06 AM
Preface
Since the pioneering work of Harry Markowitz in the 1950s, sophisti-
cated statistical and mathematical techniques have increasingly made
their way into finance and investment management. One might question
whether all this mathematics is justified, given the present state of eco-
nomics as a science. However, a number of laws of economics and finance
theory with a bearing on investment management can be considered
empirically well established and scientifically sound. This knowledge can
be expressed only in the language of statistics and mathematics. As a
result, practitioners must now be familiar with a vast body of statistical
and mathematical techniques.
Different areas of finance call for different mathematics. Investment
management is primarily concerned with understanding hard facts about
financial processes. Ultimately the performance of investment manage-
ment is linked to an understanding of risk and return. This implies the
ability to extract information from time series that are highly noisy and
appear nearly random. Mathematical models must be simple, but with a
deep economic meaning.
In other areas, the complexity of instruments is the key driver behind
the growing use of sophisticated mathematics in finance. There is the need
to understand how relatively simple assumptions on the probabilistic behav-
ior of basic quantities translate into the potentially very complex probabilis-
tic behavior of financial products. Derivatives are the typical example.
This book is designed to be a working tool for the investment man-
agement practitioner, student, and researcher. We cover the process of
financial decision-making and its economic foundations. We present
financial models and theories, including CAPM, APT, factor models,
models of the term structure of interest rates, and optimization method-
ologies. Special emphasis is put on the new mathematical tools that
allow a deeper understanding of financial econometrics and financial
economics. For example, tools for estimating and representing the tails
of the distributions, the analysis of correlation phenomena, and dimen-
sionality reduction through factor analysis and cointegration are recent
advances in financial economics that we discuss in depth.xiv