Table Of ContentMulti-Asset Risk
Modeling
Multi-Asset Risk
Modeling
Techniques for a Global
Economy in an Electronic and
Algorithmic Trading Era
Morton Glantz
Robert Kissell
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To my wife Maryann,an endless sourceoflove,patience, and inspiration.
To my wife Felise, anendless sourceof love andencouragement.
Preface
Multi-Asset Risk Modeling: Techniques for a Global Economy in an Electronic
and Algorithmic Era is written to assist readers improve their understanding
financial risk and risk management practices in a new and ever volatile environ-
mentandacrossmultiple asset classes.
Thetextfocusesontheapplicationofpropervolatilityandfactormodels,optimi-
zation techniques and provides insight into the evaluation of traditional and non-
traditional sources of risk (for example, extreme value events, and electronic and
algorithmictradingrisk).Readerswilllearnhowtoproperlyevaluatenon-traditional
sourcesofrisk,andmonetizefinancialinvestmentdecisionsinreal-time.
We describe the latest and most advanced risk-modeling techniques for equi-
ties, debt, fixed income, futures and derivatives, commodities, and foreign
exchange, as well as advanced algorithmic and electronic risk management. With
mathematics playing a prominent role, we present standard risk-management and
asset allocation models and more advanced extensions, discuss the laws in stan-
dard models that contributed to the 2008 financial crisis, and talk about current
and future banking regulation. Importantly, we will also explore algorithmic trad-
ing, which currently receives sparse attention in the literature. You will study
extreme value functions, explore Basel III compliance modeling specifically in
areas of specialized lending, develop concepts of sustainability management, and
work with risk-hedging techniques. Emphasis throughout the text will focus on
applying an financial risk management framework and proper utilization of statis-
tical analysisrequired for fiduciary decisionmaking.
Primary readership includes graduate students, industry practitioners, risk
managers, money managers, bankers, regulators, corporate risk officers, accoun-
tants, andCFOs.
In order to address the essential aspects of Multi-Asset Risk Modeling, the
book is arranged in fourteen chapters, each providing a specific focus. A descrip-
tion ofthe chapters inthe book is as follows:
In Chapter 1, Introduction to Multi-Asset Risk Modeling (cid:1) Lessons from the
Debt Crisis, we review how statistical pricing and risk-forecasting models con-
tributed to the debt crisis. For example, many of these models provided improper
insight for risk analysis, and lead to mispriced collateralized debt obligations,
mortgage backed securities andcredit derivatives, aswell as misguidealgorithmic
trading instructions.
The chapter shows how risk managers can incorporate views and information
sets across different asset classes to improve risk forecasts in rapid changing mar-
kets. We present an overview of different types of risk and risk management pro-
ducts. In particular, we discuss details inherent in credit and equity risk: price risk
(volatility), operational risk, country risk, default risk, company specific risk,
liquidity risk, interest rate risk, operational risk, macro-economic factor risk; how
xix
xx Preface
money managers, investors, and risk managers expand their understanding of risk
and infer real-time information from derivatives and options, FX rates, debt mar-
kets, and macro-economic changes. Finally, we discuss components of algorith-
mictrading (cid:1)the industry’s lifeblood.
In Chapter 2, A Primer on Risk Mathematics, we discuss applications of risk
modeling, providing an overview of the mathematics, statistics, and probability
required to measure, analyze, forecast, and measure risk. We discuss probability
theory and statistical analysis, unbiased estimates, time series math, linear regres-
sion, and non-linear estimation techniques including logit and probit models. The
chapteralsoprovides anoverview ofsomeoftheimportantstatisticsused toeval-
uate regression models such as T-test, F-test, and R2 goodness of fit. We provide
an overview of the linear algebra technique used to estimate model parameters
and corresponding parameter errors to develop confidence intervals surrounding
the estimates. The chapter concludes with an in-depth discussion of probability
distribution functions and their use in finance and risk management. This include
continuous distributions, discrete distributions, and extreme value functions such
as Gumbel (type I), Frechet (type II), and Weibul (type III). Extreme value func-
tionshavegainedrecenttractioninthefinancialindustrysincethefinancial crisis,
and have become essential risk-managementtools across all assetclasses.
Chapter 3 preserves the quantitative focus as we learn to develop uncertainty
forecast models. A Primer on Quantitative Risk Analysis provides the fundamen-
tals of quantitative risk analysis that is required knowledge and a prerequisite for
more advanced applications in financial services. The chapter begins with an
interesting historical perspective of risk, followed by discussions of the basic
characteristics of risk and the nature of risk versus returns. It then provides
detailed hands-on applications of running quantitative Monte Carlo risk simula-
tions using Real Options Valuation’s Risk Simulator software. Other topics pre-
sented include correlations and precision control, setting seed values, setting run
preferences (simulation properties), and creating a simulation report and forecast
statistics table. Finally, the chapter wraps up with two hands-on exercises for
using the software on running risk simulations and understanding the diversifica-
tion effects of correlations on risk. Readers are invited to reinforce concepts pre-
sented in Chapter 3 by visiting www.realoptionsvaluation.com for free videos,
case studies, and models,as well asdownloadabletrial versions ofthe software.
Chapter 4 explores, in mathematical and practical terms, Price Volatility.
We open with an overview of price-volatility forecasting models. We describe the
mathematics behind these models and provide an in-depth analysis of scaling
properties. We discuss various techniques employed in the industry to forecast
volatility as well as appropriate methods to calibrate these models. We expand
volatility concepts by providing readers with findings and empirical evidence
across time period and asset classes. We will further develop scaling properties of
volatility over time. This chapter also reiterates and expands on techniques pre-
sented in the Price Volatility Chapter in The Science of Algorithmic Trading and
Portfolio Management (Kissell,2013).
Preface xxi
Chapter 5 concentrates on defining the challenges and use of Factor Models.
Factormodelshavegainedincreasedstatus.Muchofthisisduetocontinuedmar-
ket turmoil and asset price uncertainty. Analysts are now turning to factor risk
models to estimate asset returns and corresponding financial risk rather than rely-
ing on their traditional approaches that all too often have proven unreliable. Our
goal using factor risk models is to determine a set of factors (e.g., explanatory
variables) that explain price movement. Analysts able to successfully forecast
these factors or factor returns will be in a position to successfully forecast asset
returns (the ultimate goal of financial management!). Factor models have also
become increasingly widespread for estimating asset volatility, especially covari-
ance and correlation across asset returns. This chapter also reiterates and expands
on techniques presented in the Price Volatility Chapter in The Science of
Algorithmic Trading andPortfolio Management (Kissell,2013).
Moving on to Chapter 6, Equity Derivatives, we introduce readers to the equi-
ties derivatives market and related financial instruments. We explore options, for-
wards, futures, and swaps. We show how practitioners can infer risk from the
different derivatives via implied volatilities and implied correlations. The chapter
begins with a focus on the various options-pricing models (Black-Scholes, bino-
mial trees, etc.), put-call parity, and pricing call and put options. We introduce
the reader to the different derivative risks: delta, vega, theta, and gamma, as well
as volatility smiles and volatility skew. We then expand on these models and
show how the implied volatility and implied correlation measures derived from
these instrumentscanleadtobetterreal-timeriskmetricsandrisk-monitoringsys-
tems. We provide an in-depth analysis of the financial crisis period of 2008-2009,
and show how these equity derivatives risk metrics provided practitioners with
better metrics and more timely market insight. Readers will gain a thorough
knowledge of the different risks and modeling approaches used in the equity deri-
vatives asset class and proper methods to apply these approaches and build more
efficient risk metrics.
With increased globalization comes an increased need to understand the for-
eign exchange markets. In Chapter 7, we present readers with an overview of the
Foreign Exchange Market and Interest Rates, spot prices, forwards, futures,
cross-currency interest rate swaps, and options. We explore the economics corre-
sponding to exchange rates and international trades, differences between fixed
and variable exchange rates, the gold standard, and provide an overview of the
different currency risk metrics. We apply the mathematical models and
approaches developed in Chapter 2 to develop best-in-class FX volatility and cor-
relation risk models. The chapter concludes with practical examples and
applications.
We study Algorithmic Trading Risk in Chapter 8. Algorithmic trading repre-
sents computerized executions of financial instruments. Currently, algorithms are
being used to trade stocks, bonds, currencies, and a plethora of financial deriva-
tives. The new era of algorithmic trading has provided investors with more effi-
cient strategy implementation and lower transaction costs, resulting in improved
xxii Preface
portfolio performance. In addition to these advantages and savings comes a new
set of algorithmic risks. Here we introduce readers to the algorithmic trading pro-
cess and corresponding uncertainty. We follow the techniques presented in The
Science of Algorithmic Trading and Portfolio Management (Kissell, 2013) and
adapt these techniques for Risk Management. Readers interested in a more thor-
oughexamination ofalgorithms can obtain(Kissell,2013).
In Chapter 9, Risk Hedging Techniques, we provide mathematics behind some
of the more advanced portfolio-hedging techniques. In particular, we discuss deri-
vation of the hedge ratio andits usage in finance todetermine the optimal manner
to hedge a held portfolio. We examine the hedge ratio in terms of various pricing
models, such as CAPM and APT, and discuss the ratio in terms of portfolio dol-
lars and weights. The chapter concludes with a general solution to the optimal
hedging ratio problem thatmovesacrossassetclass and investment instruments.
We move on to Chapter 10, Rating Credit Risk: Current Practices, Model
Design, and Applications. The credit crisis of 2008(cid:1)2009 was in many ways a
credit-rating crisis. The financial crisis might not have happened without credit-
ratings agencies issuing stellar ratings on toxic mortgage securities. Doubts about
credit-rating agencies arose due to alleged conflicts of interest and the alleged
backward-looking nature of the analytical process. Structured finance products,
such as mortgage-backed securities, accounted for over 11 trillion dollars of out-
standing U.S. debt. The lion’s share of these securities was highly rated. For
example,morethanhalfofthestructuredfinancesecuritiesrated byMoody’scar-
ried AAA ratings, the highest credit rating, typically reserved for near-riskless
securities. Important point: Financial institutions should develop industry- and
deal-specific internal risk models. Internal ratings, because they are founded on
“know thy customer,” provide a potent framework for assessing multi-asset port-
folios. The internal risk models discussedunderstand client fundamentals.
We offer specialized lending risk models proposed by the Bank for
International Settlements including project finance, commodity finance, real estate,
and object finance. In addition, the chapter includes an industry-specific, deal-
specific corporate system and the CAMELS rating, the United States supervisory
rating of a bank’soverall condition. Risk rating is developed further in Appendix 1
toChapter10,CorporateRiskRating:ObligorandFacilityGradeRequisites.
Chapter 11, A Basic Credit Default Swap Model, provides readers with an
introduction to credit derivatives. The credit derivative market has emerged as
one of the most dynamic and innovative sectors of the global financial system.
Creditderivativecontractsarefinancial instrumentsthattransferbetweentwopar-
ties the risk and return characteristics of a credit-risky reference asset. As such,
they have become an integral part of the risk management and investment strate-
gies of global investors and intermediaries. We explore the credit derivative mar-
ketplace, examine the instruments from various different angles, including
applications, valuation, and control, and demonstrate how each provides perspec-
tive on the essential elements of the marketplace. Finally, readers review the
“bad” side of these assets, so-called toxic credit derivatives and their role in the
Preface xxiii
recent debt crisis. The term “toxic asset” was coined during the recent financial
crisis to refer to mortgage-backed securities, collateralized debt obligations, and
credit-default swaps, none of which could be sold after they exposed their holders
tomassive losses.
Chapter 12, Multi-Asset Corporate Restructurings and Valuations, discusses
techniques for decision making in the presence of risk, such as valuating corpo-
rate restructuring strategies under uncertainty. In particular, we discuss
asset allocation and restructuring, risk budgeting, and stress testing. We present
techniques based on real-world data to construct multi-asset class portfolios, and
provide techniques to minimize risk, manage factor exposure, and maximize
alpha. This chapter relies heavily on techniques presented above, and incorporates
Monte Carlo simulations and stochastic optimization as a means to uncover
potential extreme movements. An appendix to Chapter 12, A Banker’s Guide:
Valuation Appraisal of Business Clients, was developed for readers who operate
as financial consultants and advisors.
Recent history tells us that it is unwise to discount the possibility of extreme
events. Fat tail risk is real, and the real world does not fit neatly into a bell curve.
Chapter 13, Extreme Value Theory and Application to Market Shocks for Stress
Testing and Extreme Value at Risk, deals with extreme value functions and the
role these functions play in the financial services. If credit portfolio losses were
bell shaped, we could specify the likelihood of large losses by defining portfolio
expected and unexpected loss. The problem is that individual debt assets have
very “skewed” loss probabilities. For instance, AAA debt assets enjoy a near-zero
standard deviation, while a B-rated debt asset may have a five standard deviation
within its distribution. In most cases, the obligor does not default, and the loss is
zero, but when default occurs, the loss is substantial. Given the positive correla-
tion between defaults, this unevenness of loss never fully resolves. There is
always a large probability of relatively small losses, and a small probability of
rather large losses. We explore value at risk and extreme value functions and
show derivations. The chapter concludes with a comprehensive extreme value
modelingcase authored by Dr. JohnathanMun.
Tail risk is the bane of a financial institution’s revenue model, and always has
been. Chapter 14, Ensuring Sustainability of an Institution as a Going Concern:
An Approach to Dealing with Black Swan or Tail Risk by Karamjeet Paul
explains that despite rigorous models and risk management controls, financial
institution exposure from tail risk can accumulate. For highly leveraged financial
institutions, cumulative exposure from tail risk can threaten survival in a stressed
environment. While traditional models normally work well in relation to portfo-
lios, they do not address certain critical issues related to policies, governance,
limits, strategies, and guidelines to manage the total risk of an institution. What
should be the goal of tail risk management? How much tail risk does the institu-
tion have? How do you manage tail risk proactively?
As we begin our journey through the chapters, it might be helpful to remem-
ber that quantitative methods, such as the use of advanced models or the
xxiv Preface
employment of math, do not alarm sharp professionals. Modeling tools that work
are not black boxes that ignore or inhibit wisdom or that mechanize the decision-
making process. The traumatic experience of the debt crisis taught us that finan-
cial institutions require fresh multi-asset risk models controlled by risk managers
with,above all, good common sense.
Morton Glantz
Robert Kissell
