Book Review: Bond Prices and Yield Curve Modeling

Bond Price and Yield Curve Modeling: A Structural Approach. 2018. Riccardo Rebonato. Cambridge University Press.

On Bond Price and Yield Curve Modeling: A Structural Approach, Riccardo Rebonato, a finance professor at EDHEC Business School and the EDHEC-Risk Institute, combines theory with current empirical evidence to build a solid understanding of what drives the government bond market. The book provides the theoretical foundations (non-arbitrage, convexity, expectations and related models) for a treatment of government bond markets, presents and analyzes the large number of empirical findings that have appeared in the financial literature in the last 10 years, and introduces the “structural” models used by central banks, institutional investors, academics and professionals to, among other things, model the yield curve, answer policy questions, measure market expectations and evaluate investment opportunities.

The book is organized in seven parts. Part I presents the fundamentals of the book, including a reasonable taxonomy that describes four different types of models. Two are statistical and structural models without arbitration that Rebonato explores extensively. Statistical models aim to describe how the yield curve moves. They fit well with observed market yield curves and have good predictive power, but lack a solid theoretical basis, because they cannot guarantee the absence of arbitrage between expected returns. No arbitrage structural models make assumptions about how a handful of important drivers behave, ensure that the no arbitrage condition is met, and derive how the three components that drive the yield curve (expectations, risk premiums, and convexity) should affect the shape of the yield curve. The non-arbitrage conditions ensure that the price derived from the bonds does not translate into a free lunch. One of the underlying themes developed by the author is the attempt to combine the predictive and fit virtues of statistical models with the theoretical robustness of models without arbitration.

Part II is dedicated to presenting two of the three building blocks of the temporal structure: expectations and convexity. Part III presents the glue that holds the three building blocks together, that is, the no-arbitration conditions. With the three building blocks and arbitration conditions fully explained, the author focuses on the Vasicek model in Part IV, providing a simple derivation of its salient results, along with a more in-depth discussion of its strengths and weaknesses. The Vasicek model explains the evolution of interest rates. A one-way short rate model describes interest rate movements as driven by a single source of market risk. Part V returns to the topic of convexity, and Part VI deals with excess returns by presenting the bridge between the real world and the risk-neutral description. Finally, in Part VII, the author discusses a series of models that attempt to overcome the limitations of the simple Vasicek-like models that are discussed in Parts I to VI.

The author analyzes the modeling of affine yield curves from a structural perspective and begins by using a simple Vasicek model to build his intuition about the operation of more complex affine models. Despite the elegance and beauty of the Vasicek model, Rebonato includes a substantial extension of it based on recent empirical data on excess returns and term premiums. He argues that for a model to be predictive, it must have a non-constant market risk price that is state dependent and must capture the dependence of expected excess returns on the slope of the yield curve. The author analyzes new models that he has built that incorporate this key information and compares his predictions about term premiums and rate expectations with what has been found empirically in the last decade.

Rebonate finds that after a considerable investment of time and energy, the more complex structural models predict risk premiums and expectations very similar to those produced by purely statistical models. Despite these comparable results, the author explores five reasons why structural models can be useful and why relying solely on statistical information is unsatisfactory. One reason is that models impose parsimony: they are useful because they tell us not only on what the phenomenon in question depends, but also on which variables it does not depend. In the absence of a model, the econometrician is faced with a large number of state variables, as well as their lags, as potentially “significant regressors.” A model, with its simplified description of how the economy works, can reinforce drastic and principled pruning. One of the virtues of a structural model is the ability it provides to reduce the number of parameters that require estimation and to constrain the relative signs and magnitudes of the parameters that remain.

Structural models also enforce cross-sectional constraints, reveal forward-looking and integrative information. The view of models as statistical regularizers can be seen as a special case of statistical contraction in a direction that reflects previous views. The models that fit the current yield curve and the current covariance matrix account for the forward-looking information incorporated in the prices of the relevant instruments. The models provide relevant integrated information because prices are expectations of exponential functions of the path of state variables, while returns are obtained immediately from prices.

However, the author makes the strongest argument for why structural models are necessary when he explains that they are “enhancers of understanding.” Structural models make it possible to understand what drives the yield curve that is difficult to provide for purely statistical analysis. Since statistical information is associative, it does not lend itself to a causal interpretation. The human mind functions causally, but often fails when presented with information based on associations. The main virtue of models is the power they confer on their users to participate in a critical analysis of what may be missing from the model and how it should be improved.

On Bond Price and Yield Curve Modeling: A Structural ApproachRebonate takes readers on an exhilarating journey that will elevate their thinking about term structure modeling. On this journey, they are likely to become more and more comfortable with some simple math techniques that are new to them.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of the CFA Institute or the author’s employer.

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Mark K. Bhasin, CFA

Mark K. Bhasin, CFA, FDP, is Senior Vice President of Basis Investment Group, LLC and Adjunct Associate Professor of Finance at NYU Stern School of Business in New York City.

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