Book contents
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Symbols and Abbreviations
- Part I The Foundations
- Part II The Building Blocks: A First Look
- Part III The Conditions of No-Arbitrage
- Part IV Solving the Models
- Part V The Value of Convexity
- Part VI Excess Returns
- 23 Excess Returns: Setting the Scene
- 24 Risk Premia, the Market Price of Risk and Expected Excess Returns
- 25 Excess Returns: Empirical Results
- 26 Excess Returns: The Recent Literature – I
- 27 Excess Returns: The Recent Literature – II
- 28 Why Is the Slope a Good Predictor?
- 29 The Spanning Problem Revisited
- Part VII What the Models Tell Us
- References
- Index
29 - The Spanning Problem Revisited
from Part VI - Excess Returns
Published online by Cambridge University Press: 25 May 2018
- Frontmatter
- Dedication
- Contents
- Acknowledgements
- Symbols and Abbreviations
- Part I The Foundations
- Part II The Building Blocks: A First Look
- Part III The Conditions of No-Arbitrage
- Part IV Solving the Models
- Part V The Value of Convexity
- Part VI Excess Returns
- 23 Excess Returns: Setting the Scene
- 24 Risk Premia, the Market Price of Risk and Expected Excess Returns
- 25 Excess Returns: Empirical Results
- 26 Excess Returns: The Recent Literature – I
- 27 Excess Returns: The Recent Literature – II
- 28 Why Is the Slope a Good Predictor?
- 29 The Spanning Problem Revisited
- Part VII What the Models Tell Us
- References
- Index
Summary
THE PURPOSE OF THIS CHAPTER
This is a short but important chapter. It brings together several strands of empirical and theoretical evidence to answer two questions: first, what type of variables are required to predict future yields or excess returns; and, second, whether affine models are in principle up to this predictive task. The first is an empirical/econometric question, the second a theoretical/modelling one.
We bring together evidence and arguments developed in the previous chapters of this part of the book, and broaden considerably the discussion by including several recent contributions to the debate.
WHAT IS THE SPANNING PROBLEM?
This chapter is about the so-called spanning problem. It is therefore important to be clear what we are talking about.
Informally speaking, a set of variables, ﹛x﹜, ‘span’ another set of variables, ﹛y﹜, if the variables in ﹛y﹜ can be fully accounted for (explained, ‘spanned’) by ﹛x﹜. What does this mean?
Suppose that we are interested in explaining the cross-sectional changes in a set of market yields ﹛y﹜. Let's call this our ‘target set’. Let's take a few yields, ﹛x﹜, as our explanatory variables. We want to see whether we can explain the yield changes ﹛y﹜ by means of the few selected yields, ﹛x﹜. So, for instance, we know that to predict excess returns all we have to predict are changes in yields. We also know that the level of the yield curve has hardly any predictive power for yield changes. So, the time series of any one single yield will not even begin to span the observed yield changes.
Suppose then that we take two yields. With these we can already create a yield-curve slope of sorts. As we well know, we can now explain a fair bit of excess return.
We saw in Part VI that the second principal component has a better predicting factor than a simple-minded difference between a long and a short yield. And we also saw that recent research has suggested that other combinations of yields may have even better predicting power. (See Chapters 26 and 27.) Creating these more powerful return-predicting factors requires more ﹛x﹜ variables. So, more yields explain (span) the yield changes better.
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- Bond Pricing and Yield Curve ModelingA Structural Approach, pp. 547 - 556Publisher: Cambridge University PressPrint publication year: 2018