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.
Acknowledgement
You might think that following some of the seven hundred or so formulas in the book is not a trivial task, let alone deriving them. Kris Kowal, Managing Director and Chief Investment Officer of DuPont Capital Management, Fixed Income Division, offered to review the manuscript and re-derive nearly all the formulas in the book. Kris provided numerous helpful suggestions and comments that were instrumental in reshaping the book into its present form. In many cases, following Kris's recommendations additional steps were added to the derivations to make it easier for the reader to follow. Thanks Kris.
Foreword
In 1998, shortly after arriving at Putnam Investments, Saied Simozar began work on a model for the term structure of interest rates that was to become a cornerstone of an entire complex of portfolio management tools and infrastructure. It was fortuitous timing because that rate model had the dual benefits of being derived through current market pricing structure (rather than historical regressions) and the flexibility to quickly incorporate new security types.
The late 1990s marked something of a sea change in the fixed income markets. The years leading up to that period had been defined by big global themes and trends like receding global inflation rates and the development of out of benchmark sectors like high yield corporate bonds and emerging market debt, as well as global interest rate convergence under the nascent stages of European Monetary Union. Under these broad trends, return opportunities, portfolio positioning, and risk could easily be characterized in terms of duration and sector allocation percentages.
Much of that changed in 1998 when the combination of increasingly complex security types, rapid globalization of financial markets, and large mobile pools of capital set the stage for a series of rolling financial crises that rocked global financial markets and eventually led to the collapse of one of the most sophisticated hedge funds of that era – Long Term Capital Management. In the aftermath, it became clear that traditional methods of monitoring portfolio positioning and risk were insufficient to manage all the moving parts in modern fixed income portfolios.
Fortuitously, that term model (and the portfolio management tools built around it) allowed Putnam to effectively navigate through that financial storm. Perhaps more importantly, it provided the basis for an infrastructure that could easily adapt and change with the ever evolving fixed income landscape. Today, while many of the original components of that infrastructure have been augmented and updated, the basic tenants of the philosophical approach remains in place.
In his book, Saied lays out a blueprint for a set of integrated tools that can be used in all aspects of fixed income portfolio management from term structure positioning, analysis of spread product, security valuation, risk measurement, and performance attribution. While the work is firmly grounded in mathematical theory, it is conceptually intuitive and imminently practical to implement. Whether you are currently involved in the management of fixed income
