Читать книгу The Advanced Fixed Income and Derivatives Management Guide - Saied Simozar - Страница 6

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 in online sources such as Wikipedia, including Chebyshev polynomials, the gamma function, principal components analysis, and eigenvalues and eigenvectors.

Most of the derivations in the book are original and therefore only a few external references have been mentioned. For some areas that have been extensively studied in the market, we provide comprehensive coverage within our framework, including:

● Mortgage valuations – We provide very detailed measurements of sensitivity to the term structure of volatility and rates by matching volatility across its surface precisely and using a method similar to a closed form solution. We show that hedging the volatility of mortgages requires multiple swaptions.

● Corporate bonds – We estimate the recovery value from the market price of securities and calculate the recovery adjusted spread and credit and interest rate durations. We show that option adjusted spread is not the best measure of value for corporate bonds.

● Bond futures – A self-consistent probability weighted method for the valuation and risk measurement is developed. The valuation result is used in backtests for long/short strategies that produce very respectable information ratios.

● Inflation linked – The decomposition of risks of inflation linked bonds and inflation swaps into the respective components of real and nominal along with seasonal adjustments provides very accurate hedging and valuations.

● Bond options – It is argued that Black-76 model is not arbitrage-free for bond options and we develop a model for pricing American bond options with the accuracy of a closed form solution, if one existed. In the options chapter we show that the most widely used platform to value American bond options is sometimes off by a factor of more than 2 at the time of this analysis.

The backbone of our framework is the term structure of rates, including interest rates, real rates, swap rates (Libor), credit rates and volatility. Through principal components analysis we show that the market's own modes of fluctuations of interest rates are nearly identical to the components of our term structure of interest rates. Essentially, our term structure model speaks the language of the markets. Thus, the model requires the minimum number of components to explain all changes in interest rates. Five components can price all zero coupon treasuries within 2 basis points (bps) of market rates. More importantly, a different number of components can be used for risk management than for valuation without loss of generality. Exact pricing of all interest rate swaps that is provided by our methodology can be used for valuation of swap transactions.

The components of the term structure model represent weakly correlated sectors of the yield curve and can be used for structuring and risk measurement of portfolios. The first component, level, is associated with the duration of the portfolio. The second component, slope, is associated with the flattening/steepening structure and can be used to structure a barbell trade. The third component, bend, represents the exposure of a portfolio at the long and short ends relative to the middle of the curve and is used to structure a butterfly trade.

Valuation metrics along with the term structure durations for the identification of sources of alpha and risk are provided for all asset classes. We introduce the concept of partial yields as a way to decompose the contribution of different sectors to the yield of a portfolio. It is not reasonable to aggregate the yield of a security that has a high probability of default in a portfolio, since the resulting portfolio yield is not likely to be realized. Partial yield addresses this issue, by calculating the default probability and decomposing the yield into components that can be used to aggregate a portfolio's yield.

The valuation metrics and term structure durations along with linear programming provide tools for portfolio construction at the security level. This is also known as the bottom-up approach to portfolio construction and is useful for daily maintenance of a portfolio. Sector allocations and analysis of the portfolio's mix of assets and durations and correlation among different asset classes are the subject of the top-down method of portfolio construction in fixed income. The two methods are complementary to each other; however, top-down is usually analyzed on a monthly or quarterly basis.

There is a step-by-step outline of building a spreadsheet based tool for designing new products or maintaining an existing portfolio. This tool provides the tracking error, marginal contribution to risk, and can be used for what-if analysis or to see how the portfolio would have performed during prior financial crises or how additions of new asset classes or sectors alter the risk profile of the portfolio. There is also a method to identify the structure of the competitive universe and design a product that could compete in that space.

We have provided detailed steps and formulation for the implementation of the framework that is outlined in the book. Many of the components can be built in spreadsheets; however, reliable and efficient analytics require the development of the necessary tools as separate programs. The benefits of such a framework and the potential performance improvements significantly outweigh its development costs.