target="_blank" rel="nofollow" href="#litres_trial_promo">15.2 Log-normal probability distribution
15.3 American at-the-money call swaption, July 8, 2011
15.4 American at-the-money put swaption, July 8, 2011
15.5 Correlation functions
17.1 Fraction of homes sold per year
17.2 Natural log of mortgage factor due to incentive
18.1 Conventional 30-year mortgage rates
18.2 Calculation error for 30-year conventional mortgages
18.3 Conventional 15-year mortgage rates
20.1 Newton's optimization method
21.1 Propagation from bucket j to bucket k
Abbreviations
Notation
For notational convenience most variable names have been limited to a single character. Subscripts have been used to differentiate related variables. Subscripts i, j, and k have been used exclusively as running integers and are interchangeable. Other subscript letters are used to differentiate closely related names. For example, pm and pc are used for the market price and calculated price of a security, respectively. When these subscripts are mixed with running subscripts, a comma is inserted between them (e.g. pm,i or pc,k).
SUBSCRIPTS
VARIABLE NAMES
Preface
Fixed income management has become significantly more quantitative and competitive over the last 20 years or so, and the days where fund managers could make very large duration bets are mostly over. Most clients prefer portfolios with diversified sources of alpha and duration targets that are comparable to the risk profiles of their liabilities or their intended risk/return expectations. Developments of strategies that are quantifiable and repeatable are essential for the success of fixed income business.
Understanding the factors that contribute to risk and return are essential, in order to structure a sound portfolio. Risk management and return attribution require the quantification of sources of risk and return and thus are math intensive. A portfolio manager who is familiar with linear programming can structure an optimum portfolio based on analysts' recommendations, portfolios policies and guidelines as well as his own views of the markets that is likely to have a superior return than another portfolio of similar weights and risk profiles.
This book provides a comprehensive framework for the management of fixed income, both horizontally and vertically. It covers in detail all sectors of fixed income, including treasuries, mortgages, international bonds, swaps, inflation linked securities, credits and currencies and their respective derivatives. We develop a methodology for decomposing valuation metrics and risks into common components that can easily be understood and managed. Valuation, risk measurement and management, performance attribution, hedging and cheap/rich analysis are the natural byproducts of the framework.
Nearly all the concepts in the book were developed out of necessity over more than 20 years as a fund manager at DuPont Capital Management, Putnam Investments, Banc of America Capital Management and Nuveen Investments. Even though the book is rich in theory and mathematical derivations, the primary focus is alpha generation, understanding valuations and exploiting market opportunities.
The intended audience of the book includes the following:
● Portfolio managers – Throughout the book there are numerous strategies and valuation formulas to help portfolio managers structure optimal portfolios and identify value opportunities without changing their intended risk profile.
● Analysts – Estimation of default probability and recovery value from market prices of securities as well as recovery adjusted yield and duration can help analysts compare securities on a level playing field.
● Traders – Throughout the book there are numerous examples of cheap/rich analysis of securities to help traders identify trading opportunities. Synthetic securities can be constructed when a security that provides the necessary exposure does not exist or is not available for trading.
● Hedge funds – There is coverage for nearly all liquid fixed income derivatives together with methods for the identification of value and hedging the risks of derivatives. Several backtests demonstrate the efficacy of value identification and provide systematic approaches to long/short and leveraged strategies.
● Proprietary trading desks – There is broad coverage of risk decomposition and hedging for all securities and their derivatives, including credit securities and credit default swaps.
● Risk measurement/management – The risks of all securities are decomposed into components that can be separately measured or hedged by both the back office and portfolio managers.
● Performance attribution – Performance attribution and contribution at the security and portfolio levels for all asset classes and derivatives is performed using the same methodology. The performance of a treasury portfolio can be measured to within 1 basis point on an annual basis, with similar accuracy for other sectors.
● Central bankers – The analysis of default probability and recovery for sovereign countries based on the traded price of their securities and precise calculations of the term structure of inflation expectations provide methods for the measurements of systemic risk in global markets.
● Academics – There are a few concepts covered in the book that have not been published elsewhere, including:
● proof that long term yields cannot change;
● structural problems of swaps and why they are subject to arbitrage;
● why corporate bonds violate the efficient market hypothesis;
● real rates cannot have log-normal distribution.
● Finance and financial engineering textbook – This book can serve as an advanced book for graduate students in finance or financial engineering.
Many of the mathematical derivations are followed by practical examples or backtests to show how the analysis can be used to uncover value or measure risks in fixed income portfolios.
This book assumes that the reader is familiar with basic fixed income securities and their analysis. Knowledge of calculus, linear algebra and matrix operations is necessary to follow many of the quantitative aspects of the book. Some of the math concepts that are not covered in calculus can be easily found
