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2018 | Book

Introduction Read chapter Read first chapter

Hands-On Value-at-Risk and Expected Shortfall

A Practical Primer

Author: Dr. Martin Auer

Publisher: Springer International Publishing

Book Series : Management for Professionals

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

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About this book

This book describes a maximally simple market risk model that is still practical and main risk measures like the value-at-risk and the expected shortfall. It outlines the model's (i) underlying math, (ii) daily operation, and (iii) implementation, while stripping away statistical overhead to keep the concepts accessible. The author selects and weighs the various model features, motivating the choices under real-world constraints, and addresses the evermore important handling of regulatory requirements. The book targets not only practitioners new to the field but also experienced market risk operators by suggesting useful data analysis procedures and implementation details. It furthermore addresses market risk consumers such as managers, traders, and compliance officers by making the model behavior intuitively transparent.

Table of Contents

Frontmatter
1. Introduction
Abstract
Financial markets let people trade promises of future payments. These payment promises are called financial assets. Prominent examples are bonds or company stocks. A bond is a way to borrow money, and it promises its buyer a future debt repayment with interest. Stock is used to raise capital and promises its holder future dividend payments. In addition to those, many other types of assets exist, but at their core they all are tradable contractual claims on future cash flows. Supply and demand determine the prices at which to buy or sell them—the prices at which to enter positions.
Martin Auer
2. Motivation
Abstract
For some intuition on market risk, let’s first take a look at a simple asset position. Assume throughout that our domestic currency is the dollar.
Martin Auer

Measures

Frontmatter
3. Basic Terms and Notation
Abstract
In this chapter, we give names to some basic concepts—assets, prices, returns, positions, portfolios, and profit-and-loss—and introduce a few related notational conventions.
Martin Auer
4. Historical Value-at-Risk
Abstract
One main concern of market risk management is to guess the plausible future behavior of a portfolio’s value. There are two main parts to this:
1.
Estimate asset price movements: compute returns and generate scenarios.
 
2.
Determine the impact of those movements on the positions’ values and distill portfolio risk measures: price positions, aggregate results, and summarize.
 
Martin Auer
5. Sensitivities
Abstract
The price of a position depends on the underlying assets or risk factors, and we express this price as the function p(S) of a scenario. A natural question to ask is how this price reacts to specific scenario changes. The particular price change resulting from a small change in only one of the underlying risk factors is called the sensitivity of the position with regard to that risk factor.
Martin Auer
6. Stress Tests
Abstract
The sensitivity measure we encountered in the previous chapter gives us price impacts of individual, small risk factor changes; it mainly provides comparability of exposures across risk factors. To gauge the impact of simultaneous and large changes to several risk factors at once, we reprice our positions under custom-made scenarios—this is called stress testing.
Martin Auer
7. Analytical Value-at-Risk
Abstract
A second approach, already mentioned at the beginning, to calculate the VaR is an analytical one. It is only approximate, as its assumptions don’t always hold in practice, but it involves fewer computational steps because it relies on sensitivities and avoids the 1000 × 106 full position pricings. Often it is very close to the VaR obtained in the historical simulation, which makes it a useful sanity-check. It also clearly exposes the relation between the VaR and the sensitivities, volatilities, and correlations. Even more importantly, it provides some helpful analysis tools in dealing with the questions we’re most interested in: How does the VaR react if we change our positions? What risk factors contribute most to the VaR? What is the reason for a particular VaR change?
Martin Auer
8. Expected Shortfall
Abstract
The VaR ignores quite a bit of seemingly important information—those losses that are even larger than the VaR. To take large losses into account, we could measure, e.g., the average of the 2.5% largest losses. This is called expected shortfall or ES.
Martin Auer
9. Model Choices
Abstract
Without much ado, Chap. 4 outlined a relatively straightforward historical VaR model. In the bank I worked at, such a model proved to work reliably right through the 2008 financial crisis and its aftermath. Many a model aspect, however, could be tuned or tweaked or altered, and this chapter zooms in on some of those model choices. But how to weigh these features, how to choose between model options? Let me give you my personal take on this.
Martin Auer
10. A Monte Carlo Modification
Abstract
Our VaR model typically uses 2 years of data or 500 returns, and it generates, via mirroring, twice that number of scenario returns.
Martin Auer
11. Support Measures
Abstract
We have selectively presented a few risk measures in the preceding chapters that, in our experience, cover many relevant aspects and tasks in a real-world market risk setup. We propose to mainly use the volatility-rescaled historical VaR[Ω] for daily risk management. It is especially well-suited to capturing “tomorrow’s PnL,” as it reacts fast to changes in volatility levels. The concurrent use of the sensitivity-based analytical VaR(s Ω ) serves as a sanity check and provides an additive decomposition to VaR-contributions of the risk factors, which is a handy analysis tool because it appropriately weighs risk factors by both their sensitivity and volatility. Finally, the most helpful measure we take away from the expected shortfall world is the position-wise conditional expected shortfall cES[α|Ω], which provides a useful complementary breakdown of risk to positions.
Martin Auer

Operations

Frontmatter
12. Properties of VaR
Abstract
The VaR is an altogether relatively intuitive abbreviation of the two-dimensional concept of risk, but one characteristic in particular might not be self-evident at first sight.
Martin Auer
13. Properties of ES
Abstract
The expected shortfall or ES shares the basic properties of the VaR given in the previous chapter: it is negative; it scales for positive multiples of positions; it vanishes for hedges; it is not additive; etc. For normally distributed PnLs, it is again a mere multiple of the standard deviation, and the scaling factor of the 2.5%-ES is, with 2.34.., very close to the 2.33.. of the 1%-VaR.
Martin Auer
14. VaR Noise
Abstract
Having examined the static properties of the VaR, we now look into its dynamic behavior over time. As new positions are entered or old ones closed, and as the volatilities of the assets involved change, the VaR, recalculated every day, will change as well. Often, such VaR changes and their reasons are of more interest in risk management than the level of the VaR itself.
Martin Auer
15. Backtesting
Abstract
The VaR model estimates tomorrow’s PnL behavior by projecting plausible asset returns from these assets’ recent history. The next day, specific assets returns will materialize, as will a corresponding actual PnL. To compute it, we merely have to price our positions under two scenarios—the market scenario used for the VaR calculation and that of the following day.
Martin Auer
16. Distribution Tests
Abstract
We can relate the VaR model’s prediction (tomorrow’s PnL distribution) with actual, later outcomes (the realized and experienced PnL) in a way that is more expressive than the backtesting with its focus on relatively rare VaR violations.
Martin Auer
17. Nine to Five
Abstract
We now try to examine our risk measures and their properties in the practical context of daily risk management. We structure this chapter by the most common questions you might face, in reverse order of urgency.
Martin Auer

Setup

Frontmatter
18. Context
Abstract
Finance is no stranger to grandiose monikers (my personal favorite has to be the financial crisis’s “Master Liquidity Enhancement Conduit”). The same holds true for software engineering and IT, with many a “business service framework” or “disciplined agile delivery” being thrown around. Each IT area continuously breeds forth new languages, customized frameworks, abstraction layers, and paradigms; some are useful, some promising, others opaque, and quite a few short-lived.
Martin Auer
19. Scope and Workflow
Abstract
In a practical market risk system, we need to calculate several risk measures on a daily basis. Let’s briefly describe this target scope first. We, of course, want to determine the VaR for our main portfolios and to provide corresponding backtesting results. As support, we also calculate several partial VaRs (each with their own backtesting). In addition, we calculate the stressed VaR (without backtesting) as well as sensitivities and stress tests.
Martin Auer
20. Implementation
Abstract
With the overall workflow outlined in the previous chapter in mind, we now zoom in to the individual system components. We first cover the involved tools and their implementation and later focus on data sets and their structure.
Martin Auer

Wrap-Up

Frontmatter
21. Conclusion
Abstract
Here are a few of the glorious blunders I committed that will remain on my head. I first thought it wise to output sorted PnL aggregation vectors (like destroying information is a good thing). I also proposed to add an additional column of zero to the PnL results for some “future use” as special indicator flag—a use that never materialized and now requires constant nudging when we have to explain our file formats. I unthinkingly used the VaR prediction date as label for our daily results, which is just plain stupid—everybody will always refer to the previous, close-of-business date. Each email now requires a qualifier, and each new hire will at least once perform an analysis of the wrong data. (The latter two imbecilities are actually still in place, ingrained and phlegmatic like a glacier.) Hopefully, this account helps you avoid similar pitfalls.
Martin Auer
Backmatter
Metadata
Title
Hands-On Value-at-Risk and Expected Shortfall
Author
Dr. Martin Auer
Copyright Year
2018
Electronic ISBN
978-3-319-72320-4
Print ISBN
978-3-319-72319-8
DOI
https://doi.org/10.1007/978-3-319-72320-4