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2022 | Book

Introducing Economic Capital Read chapter Read first chapter

Modelling Economic Capital

Practical Credit-Risk Methodologies, Applications, and Implementation Details

Author: David Jamieson Bolder

Publisher: Springer International Publishing

Book Series : Contributions to Finance and Accounting

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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About this book

How might one determine if a financial institution is taking risk in a balanced and productive manner? A powerful tool to address this question is economic capital, which is a model-based measure of the amount of equity that an entity must hold to satisfactorily offset its risk-generating activities. This book, with a particular focus on the credit-risk dimension, pragmatically explores real-world economic-capital methodologies and applications. It begins with the thorny practical issues surrounding the construction of an (industrial-strength) credit-risk economic-capital model, defensibly determining its parameters, and ensuring its efficient implementation. It then broadens its gaze to examine various critical applications and extensions of economic capital; these include loan pricing, the computation of loan impairments, and stress testing. Along the way, typically working from first principles, various possible modelling choices and related concepts are examined. The end result is a useful reference for students and practitioners wishing to learn more about a centrally important financial-management device.

Table of Contents

Frontmatter
Chapter 1. Introducing Economic Capital
Abstract
Absent an appreciation of accounting capital and the central role of capital-adequacy analysis in assessing firm creditworthiness, there is little sense in discussing economic capital. The story thus begins with a critical investigation of some key principles in accounting and corporate finance, which help identify the fundamental need to incorporate a (worst-case) risk perspective into one’s examination of any firm’s assets. Economic-capital is—all technicalities aside—a multifaceted measure of asset riskiness intended to complement the average, or expected, risk perspective found in financial statements. It captures potential demands on a firm’s capital, which, when compared to its capital supply, speaks volumes about corporate risk. Not easy to measure, economic capital requires careful thought about idiosyncratic and systemic risk as well as notions of diversification and concentration. Unsurprisingly, economic-capital measurement necessitates use of complex mathematical models. This chapter provides a comprehensive, but gentle, introduction to the conceptual framework underlying economic capital. In doing so, we lay the foundation for the more technical discussion found in the remainder of this book.
David Bolder

Modelling Credit-Risk Economic Capital

Frontmatter
Chapter 2. Constructing a Practical Model
Abstract
Economic capital is unfortunately—for any dimension of risk—neither easily computed nor uniquely determined. Its measurement necessitates the use of complex mathematical models, which ultimately involve some degree of choice and subjectivity. With our focus on the centrally important credit-risk dimension for financial institutions, we have selected a multivariate t-threshold model with stochastic recovery and credit migration. Quite a mouthful, this credit-risk modelling structure requires context, description, and defence. To this end, this chapter presents a number of challenger models, the fundamental principles of our choice, multiple important derivations, and the mechanics of risk attribution in this setting. Equipped with this background, we can confidently proceed to the difficult questions of parametrization and implementation addressed in the immediately subsequent chapters.
David Bolder
Chapter 3. Finding Model Parameters
Abstract
Irrespective of the elegance or mathematical complexity of one’s modelling framework, it has little practical usefulness without proper parametrization. This observation is particularly pertinent in the credit-risk setting. Transition and default probabilities, factor correlations and loadings, systemic weights, default dependence, recovery dispersion, spread duration, and credit spreads all need to be estimated and specified to produce meaningful economic-capital estimates. This necessarily lengthy and detailed chapter (metaphorically) rolls up its sleeves and sequentially addresses, explains, and motivates our choices with respect to each of these key parameter families. Where possible and relevant, alternatives and implications are presented. Finally, during the discussion, the consequences of the generally accepted and centrally important through-the-cycle perspective are also explored.
David Bolder
Chapter 4. Implementing the Model
Abstract
Implementation questions are rarely discussed in textbooks. The reason is simple: their highly institutional nature makes them notoriously slippery. Our unambiguous consideration of the Nordic Investment Bank changes this calculus. Exploiting this unique situation, this chapter touches upon rarely addressed issues relating to system architecture, whether to build or buy one’s modelling software, the choice of programming language, and how these points relate to staffing policy. It also deals with more mainstream questions such as algorithmic design and the numerous thorny topics surrounding convergence of our simulation-based estimation methods. Although uncommon, the following discussion should have broad-based appeal to practitioners facing similar challenges.
David Bolder

Loan Pricing

Frontmatter
Chapter 5. Approximating Economic Capital
Abstract
Solving complex credit-risk economic capital models requires the use of simulation methods. This powerful technique is nonetheless computationally slow. For certain applications—such as loan pricing and stress testing—it is far too slow to be of practical use. This creates a frustrating conceptual impasse: the only practicable solution method for our model stands in the way of our ability to perform critical applications. This chapter—to resolve this practical problem—constructs a fast, accurate, semi-analytic, instrument-level approximation of both default and migration economic capital. This is accomplished by exploiting our knowledge of the economic-capital model to build a structurally motivated statistical model. Not only does this approach facilitate a number of productive computations, it also provides additional insight into our base credit-risk framework.
David Bolder
Chapter 6. Loan Pricing
Abstract
Loan pricing is a surprisingly multifaceted undertaking touching on asset-pricing theory, accounting principles, corporate finance, and the fundamentals of risk management. Taking a tour of these modern financial concepts, this chapter builds on previously discussed economic-capital ideas to construct a risk-adjusted return on capital. Each loan decision is treated as a separate investment project with these risk-adjusted returns acting as a (fair) enterprise-wide decision criterion; this is accomplished by incorporating cost recovery, firm capital structure, portfolio concentrations, and the risk-return characteristics of the individual loan. The following discussion, quite naturally given our focus, touches solely on the quantitative aspects of loan pricing. Market forces and an institution’s mandate or strategy play an equally important role, but are beyond the scope of this work.
David Bolder

Modelling Expected Credit Loss

Frontmatter
Chapter 7. Default-Probability Fundamentals
Abstract
The through-the-cycle perspective, fundamental to the computation of economic capital, takes a long-term, unconditional viewpoint. This is based on a sensible desire to avoid pro-cyclical economic-capital estimates. Some applications—such as loan impairments and stress-testing—nevertheless require conditionality. Instead of averaging across time, conditional analysis explicitly takes into account current or forecasted events leading naturally to the so-called point-in-time perspective. Grappling with this new viewpoint requires additional concepts and machinery; it also necessitates a firm grasp on our base through-the-cycle starting point. This chapter undertakes the unexciting, but crucial, job of preparing the way for the proper construction of the point-in-time stress scenarios so central to our forthcoming applications.
David Bolder
Chapter 8. Building Stress Scenarios
Abstract
This chapter steps definitively into the world of conditionality by examining alternative approaches for linking macro-financial variables to general credit conditions. These latter quantities—operationalized as default and transition probabilities—serve as critical inputs into loan-impairment and stress-testing applications addressed in subsequent chapters. Essentially an exercise in time-series statistical analysis, our progress is hindered by the inherent rarity of default at the higher end of the credit spectrum. The proposed solution is a collection of transformations, approximations, and possible statistical descriptions permitting a manageable degree of model robustness and pragmatism. While the resulting structure is both reasonable and defensible, every reader needs to be keenly aware of the fundamental issues of data sparsity, representativeness, and dimensionality. Such truth in advertising will ensure appropriate use and interpretation of the ensuing results.
David Bolder
Chapter 9. Computing Loan Impairments
Abstract
Loan impairments or expected credit losses—an accounting quantity—are not typically included in one’s economic-capital framework. This is somewhat short-sighted. Expected credit losses are naturally linked to the credit-loss distribution underlying our economic-capital estimation. This chapter thus reviews modern loan-impairment computations with a firm eye pointed towards the intersection with our economic-capital efforts. Current accounting standards also require incorporation of forward-looking macro-financial scenarios, which further overlaps with our point-in-time stress-testing work. A final important connection—arising in the context of concentrated portfolios—stems from possible downward bias associated with sole focus on the central moment of the credit-loss distribution. An imperfect, quantile-based, economic-capital-related correction is proposed to increase the realism and conservatism of one’s loan-impairment estimates in such cases.
David Bolder

Other Practical Topics

Frontmatter
Chapter 10. Measuring Derivative Exposure
Abstract
By virtue of their complexity and propensity for getting incautious users into trouble, financial derivatives have a somewhat tarnished reputation. Much of this is unwarranted; it would be difficult, and probably impossible, to run a modern financial institution without recourse to derivative contracts. Their complexity, however, is difficult to deny. For quantitative analysts working with economic capital, many of the more challenging tasks—legal contracts, valuation, and collateral management—can be blissfully assigned to someone else. There is one important exception: exposure estimation. The possibility of both positive and negative valuations, netting arrangements, and significant future uncertainty have given rise to an entire risk-management sub-field: counterparty credit risk. This chapter introduces the key principles required for our economic-capital purposes and reviews a popular, pragmatic, but necessarily complicated regulatory solution.
David Bolder
Chapter 11. Seeking External Comparison
Abstract
The essence of scientific thought revolves around the centrality of empirical evidence, logical reasoning, and a healthy dose of scepticism. While computation of economic capital and its associated applications can hardly be viewed as a purely scientific endeavour, these fundamental principles still apply. Having taken great pains to build a sensible model, we need to be simultaneously sceptical of it. It is thus essential to gather concrete empirical evidence to either support or reject its reasonableness. A natural avenue to achieve this objective involves considering results stemming from other actors who assess a firm’s capital adequacy. This lengthy chapter, therefore, turns to the regulatory and external rating agency communities for practical points of comparison. Regular computation and interpretation of such alternative estimates goes a long way to adopting a reasonable, and scientific, approach to the measurement of credit-risk economic capital.
David Bolder
Chapter 12. Thoughts on Stress Testing
Abstract
It would be folly to try to write a chapter that captures all of the possible elements of stress-testing. It is too broadly defined and multi-dimensional to permit such a description. Instead, this chapter offers some thoughts on the topic. Pulling together many of the elements introduced and discussed in previous chapters, various top-down and bottom-up stress-testing strategies are explored in the context of a fictitious, but nonetheless interesting and representative example. The central objective is to provide practical guidance on this increasingly important area of economic-capital analysis. In doing so, we wrestle with the inherent tension between the through-the-cycle and point-in-time perspectives as well as the important challenges associated with selecting defensible and meaningful stress scenarios. Not only can these ideas help deepen understanding of one’s portfolio, but they also quite naturally unite the various concepts addressed in this book.
David Bolder
Backmatter
Metadata
Title
Modelling Economic Capital
Author
David Jamieson Bolder
Copyright Year
2022
Electronic ISBN
978-3-030-95096-5
Print ISBN
978-3-030-95095-8
DOI
https://doi.org/10.1007/978-3-030-95096-5