The palgrave handbook of unconventional risk transfer

Scordis eds., The Palgrave Handbook of Unconventional Risk Transfer, DOI 10.1007/978-3-319-59297-8_2 a theoretical foundation for understanding why risk management can add value to a fi

THE PALGRAVE HANDBOOK

OF UNCONVENTIONAL

RISK TRANSFER Edited by Maurizio Pompella and Nicos A Scordis

Risk Transfer

Maurizio Pompella • Nicos A Scordis

Editors

The Palgrave Handbook of Unconventional Risk Transfer

ISBN 978-3-319-59296-1 ISBN 978-3-319-59297-8 (eBook)

DOI 10.1007/978-3-319-59297-8

Library of Congress Control Number: 2017947702

© The Editor(s) (if applicable) and The Author(s) 2017

This work is subject to copyright All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or informa- tion storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.

The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Cover credit: travellinglight / Alamy Stock Photo

Printed on acid-free paper

This Palgrave Macmillan imprint is published by Springer Nature

The registered company is Springer International Publishing AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

St John’s University New York, New York, USA

There will always be risk It is one of the global economy’s certainties, alongside such self-evident ones as death and taxes For this reason alone, a volume covering any aspect of risk transfer is welcome, but a book that addresses unconventional risk transfer is rarer in the field of economic literature and hence still more welcome.There is much fascinating detail in this book Perhaps a few words of context, within the confines of a foreword, may help set the scene for the reader Risk has always been with us it is true, but equally true is the fact that there are those who wish more, rather than less, of it This makes the market Consider that every time someone deals in an instrument as ubiquitous as the humble Eurodollar contract, that transaction represents the coming together of two parties with diametrically opposing views One person’s risk exposure is another’s risk oppor-tunity Of course the conventional or “vanilla” methods of risk transfer are more than suitable for a majority of the world’s participants in finance, energy, com-modities, weather and other “asset classes” But often large risk exposures that cannot be mitigated using vanilla methods but yet cannot for one reason or another be left unhedged require unconventional methods if they are to be dealt with And if one can find a ready and willing counterparty, it is inevitable in a free market that these methods will be developed and pursued

In 2002, I was working in structured finance at JPMorgan Chase Bank when one of the deals we brought to the market was what we thought the world’s first synthetic Collateralised Debt Obligation (“Robeco CSO”), which utilised credit default swaps to transfer risk via a pooled vehicle; this was an unconventional risk transfer but at the same time an investment product, and the technology became quite commonplace within a year or two One year’s unconventional risk management approach is next year’s routine transaction (In fact I believe a firm called Dolmen Securities beat us to that “world’s first”

Foreword

title with a transaction called “Blue Chip CDO”, but unfortunately that deal

did not feature in Risk magazine like our one did!).

This is a welcome feature of a globalised free market environment, where vation thrives and, once in a while, produces genuine benefits for society There will always be innovation in finance, some of it very useful and some of it merely navel gazing, but in the whole, such practice produces value To use an obscure analogy from the world of military aviation, for every Supermarine Spitfire there was first a Boulton Paul Defiant It is a truism that only very rarely does one arrive

inno-at the quality product without sampling some duds along the way

The asset classes described in this book are many and varied, and often it is the more esoteric products that call for unconventional methods to be applied This

is understandable when one has a paucity of market players This is a specialised business, but often dealing in very important areas Without the unconventional approaches to risk management noted in this book, one would risk inefficiencies

in production and delivery, with consequent knock- on impact on the customer

So it is to be welcomed that innovation in risk transfer is something that, nearly ten years after the global financial crash of 2008, remains to the fore

All good textbooks should present a solution as well as the problem I was particularly impressed to see the dissection of various approaches to structuring risk transfer across different product types, which forms the bulk of the latter parts of the book I am sure this material will be of value to practitioners But irrespective of one’s own background, for all true students of risk management,

be they in the finance, insurance, weather or energy industry or elsewhere, this Handbook is a worthwhile addition to the economics literature The editors are

to be commended for their work in bringing to our attention this collection of leading-edge thinking in the exotic world of unconventional risk transfer

Canterbury, UK

30 January 2017

Moorad Choudhry is the former CEO of Habib Bank AG Zurich and was previously the Treasurer of Royal Bank of Scotland (RBS) Corporate Banking, Europe Arab Bank and KBC Financial Products He has over 30 years’ experi-ence in the city and began his career at the London Stock Exchange Choudhry

is a visiting professor at the University of Kent Business School, where he teaches

on the MSc Finance programme He is a fellow of the Chartered Institute of Securities & Investment and of the London Institute of Banking and Finance

He obtained his MBA at Henley Business School and his PhD from Birkbeck,

University of London He is the author of The Principles of Banking (2012).

Maurizio Pompella and Nicos A Scordis

Richard Friberg

3 A Practical Perspective on Corporate Risk Management 35

Nicos A Scordis and Annette Hofmann

4 Reinsurance, Insurability and the New Paradigms

6 Credit Risk Transfer with Single-Name Credit Default

Erzsébet Kovács and Péter Vékás

10 Country Risk: Case Study on Crises Examples and 

Vasily Solodkov and Yana Tsyganova

Part IV Vulnerability, Market Solutions and Societal

Joern Birkmann, Linda Sorg, and Torsten Welle

12 Insurance-Linked Securities: Structured and Market

Annette Hofmann and David Pooser

Douglas Anderson and Steven Baxter

Part V Risk Modelling and Stress Testing 435

17 Stress Testing with Bayesian Nets and Related Techniques:

Riccardo Rebonato

Fig 4.10 Population pyramids (males and females), low- and high-income

Fig 4.15 Enterprise value with and without risk 92

List of Figures

Fig 4.16 (a) Pooling and exposure limits (b) Franchise deductible

westward travelling cyclone in the northern hemisphere

responds to rainfall Note the shape of the hydrograph depends

both sexes; data source: World Development Indicators,

approach and the place of biometric risks in life and pension

Lee–Carter model along with their 95% confidence band

Fig 9.5 Age-specific sensitivities in the Lee–Carter model (England and

Fig 10.1 Thailand macroeconomic overview before and after the

crisis of 1997 Source: World Bank, database: World

Fig 10.2 USD/THB official exchange rate, inflation and interest rate

Fig 10.3 Impact of currency board on Argentina’s economy

Fig 10.4 Argentina’s Macroeconomic Statistics: 1991–2002 Source: IMF

Fig 10.5 The dynamics of USD/RUB exchange rate and oil prices

during 1998–2009 Source: Bank of Russia web page,

Fig 10.6 EU budget expenditures and contributions by member

Fig 10.7 EU budget expenditures and contributions by member

Fig 11.2 The progression of vulnerability (based on Wisner et al

Fig 11.3 Vulnerability within the hazard, exposure, capacities and

Fig 11.5 IPCC framework for systematising hazard, exposure,

Fig 11.6 Structure and indicators of the Urban Risk Index (based on

Fig 11.7 Nexus—urban vulnerability, level of urbanisation and urban

Fig 12.3 Basis risk, credit risk, and moral hazard of catastrophe

Fig 13.1 Profile of deaths by age for UK men and women aged

Fig 13.2 Lifetimes for UK men and women aged 65 in 2014

Fig 13.3 Cashflows from an illustrative annuitant portfolio

Fig 13.4 Smoking rates for UK adult men by socio-economic

Fig 13.5 Illustration of range of mark-to-model views (Hymans

Fig 13.9 A social history of longevity (Hymans Robertson analysis,

Fig 13.11 Conceptual grouping of longevity trend models (Hymans

Fig 13.13 Convergence of life expectancy outcomes between

Fig 13.14 Longevity-related transactions originating from large

corporate pension funds in the UK (Hymans Robertson (2016);

Fig 13.15 (a) Capital dynamic for single-risk insurer (Hymans Robertson

LLP) (b) Capital dynamic with a diversifying risk (Hymans

Robertson LLP) (c) Capital dynamic with a negatively correlated risk (Hymans Robertson LLP) (d) Capital dynamic with a

negatively correlated risk and “optimal” mix (Hymans Robertson LLP) (e) Capital dynamic with negatively correlated risk and

Fig 13.16 Parties and cashflows involved in an indemnity swap (Hymans

Fig 13.17 Parties and cashflows involved in an index-based swap (Hymans

Robertson LLP, differences versus indemnity swap shown by

Fig 13.19 Framework for assessing basis risk (Hymans Robertson (2014),

reproduced with permission of the Institute and Faculty of

Fig 13.20 (a) Barriers to longevity hedging (Hymans Robertson LLP

online survey of pension scheme trustees and their advisors,

June 2016) (b) Willingness to cede longevity risk (Hymans

Robertson LLP online survey of pension scheme trustees and

Fig 13.21 Breakeven inflation (Hymans Robertson graphic based on

Fig 13.22 Five practical steps to a deep and liquid longevity risk

Fig 15.1 Deaths from communicable diseases and other causes since

Fig 15.2 Proportion of global disease burden in respect of DALYs in

2015 Communicable diseases are separated into “infectious

and parasitic diseases” and “respiratory infectious” together

accounting for 19.1% of DALYs (World Health

Fig 15.3 Deaths by cause in 2015 by World Bank classification of

Fig 15.4 A simple SIR model Susceptible members of the population

are infected at a rate corresponding to the force of infection, λ Infective people recover at a rate γ corresponding to the rate

Fig 15.5 Simple deterministic SIR and SEIR models for smallpox,

displaying populations of each compartment relative to the total population 476 Fig 15.6 Results of the SIR model incorporating demographic

stochasticity for a single infective introduced to a community of

Fig 15.7 A schematic of a metapopulation model and a network model

Fig 15.8 Annualised age-specific mortality rates for deaths attributed to

influenza or pneumonia per 100,000 cases in the USA for

1911–1917 and 1918 Notice the peak in mortality rates among

Fig 16.1 ILS deals outstanding in “market” portfolio on

September 30, 2014 (9/30/2014) Grouped by peril and type

and ordered by original expected loss (EL), excess to remodelled

EL. N.B. AIR remodelling premiums and discounts to original

Fig 16.2 Market risk profile The left panel is based on 10,000 scenarios

Fig 16.6 Risk profile for the optimal solution with limits of 10% of any

deal 517 Fig 16.7 Peril composition of optimum solution with limits of 10% of

Fig 17.2 The Bayesian net associated with the John-slipping-on-path

scenario A represents the probability of rain tomorrow;

B represents the probability of the sprinkler being on;

C denotes the probability of the pavement being wet; and

D is the probability of John slipping 552 Fig 17.3 The effects of uncertainty in the inputs and in the outputs

Fig 17.4 A measure of ‘distance’ between joint distributions (on the

y axis) and the rank of the input conditional probability

Fig 17.5 A measure of ‘distance’ between joint distributions (on the

y axis), and the rank of the input conditional probability

NWS 2017; wind speeds are from Enhanced Fujita Scale

Table 10.2 Country risk sources applicable to Asia, Russia, Argentina

Table 13.3 Basel Committee recommendation for the development of

List of Tables

Table 15.2 Transmission modes and zoonotic origins of infectious

diseases 472 Table 15.3 Basic reproduction numbers of historical influenza pandemics

and other epidemic diseases (Taubenberger and Morens 2006;

Table 15.4 Comparison of the functional components of pandemic models

Table 16.1 Overview of market portfolio (i.e., all outstandings by peril or

region) 500 Table 16.2 Data sheet (partial) illustrating required inputs and

co-measures 506 Table 16.3 Optimum solution with just risk constraints—solution on

Table 16.4 Optimal solution with limit of 10% of any deal versus

Table 16.5a Optimum solution marginal values limit to 10% any deal

Table 16.5b Optimum solution marginal values limit to 10% any deal

Table 17.1 The correlation delivered by Mephistopheles at time T 546 Table 17.2 The second instalment, delivered at time T + Δt, of the

© The Author(s) 2017

M Pompella, N.A Scordis (eds.), The Palgrave Handbook of Unconventional

Risk Transfer, DOI 10.1007/978-3-319-59297-8_1

a handful of other insurers with a dozen or so issues At their most basic, CatBonds is debt whose coupon (and even principal repayment) is indexed

to the intensity of a naturally occurring event At the end of March 2016, the outstanding market for CatBonds and other ILS instruments was $26.5 bil-lion worth, with $2.2 billion of new capital issued from ten transactions in the first quarter of 2016.

The growth in this unconventional risk transfer market is partly the result

of the great changes and crisis most economies have experienced over the past

20 years We use the term ‘risk transfer’ to indicate that the managers of a firm pay an external group of investors to take on the firm’s risk We use the term

‘risk retention’ to indicate that the managers of a firm keep the risk within the firm and thus implicitly the firm’s own investors pay for the risk Therefore,

in our view, both risk transfer and risk retention are components of the firm’s risk financing consideration

The use of the term ILS is relatively recent (as far as the short history of the unconventional risk transfer market goes) The early market used to refer

to the process of issuing ILS as securitization The practice of ‘securitization’, that is bundling future cash flows from similar risks into portfolios for sale to investors, originated among investment bankers who applied the technique to finance risk ‘off balance sheet’ Off balance sheet because at the inception of the technique, the prevailing accounting regulations did not address how to record the transaction, which allowed some leeway The spread of securitiza-tion into the insurance and other sectors of the economy represents a period

of cross-sector or ‘diagonal’ risk transfer

As a result, the traditional channels for trading risk made room for a series

of alternative channels that feed directly to investors in the capital markets, many of whom are unrelated to the insurance industry The insurance indus-try plays a central role in the success of these alternative channels by pushing the development of dynamic models for analysing the probability and sever-ity of an event These models draw on seismology, meteorology, engineering, actuarial, statistical and financial science They deal with issues of simulat-ing low-frequency events, quantifying associations among risks and balancing the internal cleverness of the model with how well its results reflect reality While many insurers maintain their own models, they all begin the process

of pricing risk from vendor-provided models (from mostly Risk Management Solutions (RMS), AIR Worldwide (AIR), or EQECAT) These models are complex computing devices that are updated regularly with granular data by postal code and in some cases even by smaller geographic divisions The wide-spread use of vendor models has created a standard point of reference for pricing risk, which legitimized, to investors, the purchase of ILS. The legiti-mization of ILS pricing further strengthened the legitimacy of models, which perpetuates the legitimacy of ILS. The refinement of vendor models creates a

general understanding that unpredictable risk can be converted into tradable deals which can be compared with other deals for pricing and placement with investors Thus, even though each tradable ILS is unique in terms of the underlying risks it encapsulates, all ILS are delineated in a consistent way.

It is challenging to parse the evolution of the risk markets from tional insurance-only to today where insurance-centred and alternative, or unconventional risk transfer markets coexist There is a convergence between different types of financial intermediaries, but their boundaries are fuzzy Indeed, regulations clearly segregate types of risk products, but the ideas and processes that support the pricing, marketing and trade of these risk products are impossible to allocate to respective risk products

conven-The title of this work refers to ‘unconventional risk transfer’ Conventional applications of risk transfer almost always involve the use of the insurance mechanism The risk capacity of the insurance mechanism, however, as large as

it is, is still small in comparison with the risk capacity of the broader financial and capital markets This work frames and contextualizes the latest techniques and strategies that are used to unlock the risk transfer capacity of the global financial and capital markets This work adds value to the literature because it presents core topics that either allow unconventional applications of conven-tional risk transfer practices or enhance directly the pricing of unconventional risk transfer practices This duality in the works included in the Handbook is what sets this publication apart This Handbook is a collaborative work that brings together experts from different disciplines and countries On purpose, each expert uses the version of English spelling that they feel most comfortabe with Also on purpose the Handbook preserves instances where different con-tributors discuss an identical concept from their discipline’s perspective Such spelling and instances are few in between as not to distract the reader, but they

do serve to underline the multi-disciplinary and multi-country nature of this collaboartion

The first two contributions set a framework for risk and its management, from a conceptual and a practical perspective, respectively Both of these con-tributions point out two challenges when dealing with risk One, while indi-vidual risks can be measured, the interpretation of whether operating at a given level of risk is prudent ultimately depends on the decision maker’s view

of the environment Two, even though risks interact with each other and the environment, there is insufficient ability to quantify such risk associations.The contributions that follow—in Sect II, which explores the origins of unconventional risk transfer; Sect III, which looks at risks according to their class of origin; and Sect IV, which examines society’s tolerability to risk, mar-ket solutions and the social implication that arise—provide context for indi-

vidual risk transfer techniques and/or strategies The last part of the work, Sect V, focuses on potential solutions to quantifying risk The reader will notice, however, that almost all of these contributions (directly or indirectly) confront the two overarching challenges identified earlier in this work: How

to interpret risk and how to capture the interdependencies of risk

The last two contributions, particularly, provide a solution to these two overarching challenges They both deal with bundling individual risks into a portfolio and point the way forward They both offer practical advice One

of the contributions examines how to assemble a portfolio of risks that mizes return without taking ‘excessive’ risk The other contribution shows why application of Bayesian nets lends itself particularly well to the need for

maxi-a prmaxi-acticmaxi-al wmaxi-ay to stress test maxi-a portfolio of risks

University of Siena, School of Economics and Management (SEM), Italy He has been a researcher, lecturer, senior lecturer and associate professor since 1991, and

is the Dean of MSc in Economics and Management of Financial Intermediaries Certified as a stand-by professor at the LUISS—Guido Carli in Rome in 2014,

he serves as an adjoint professor at Charles University in Prague (CZ) since 2012, OMSU (Ogarev Mordovia State University of Saransk, RF) from 2015 and SibSU (Siberian State University of Krasnoyarsk, RF) from 2016 He served as a book reviewer for the Journal of Risk and Insurance, published by ARIA (American Risk and Insurance Association), and contributed to the ARIA Newsletter Pompella has been teaching banking, finance and insurance at graduate and post-graduate levels in Italy, Eastern Europe, Latin America, the Middle East, Russia and China His areas

of expertise include insurance economics, banking and monetary economics, finance, structured finance, alternative risk transfer, financial innovation and stability, and project financing.

Actuarial Science (SRM) at St John’s University in New York His research helps insurance managers judge the risk/uncertainty/value dynamic in their evolving oper- ations When he served as the chairperson of the SRM, he founded the Masters

in Risk Management and Insurance He was sought out by the US Congress for expert testimony on financial services integration Scordis has a BSc in Insurance from Florida State University, an MBA from the University of Georgia and a PhD from the University of South Carolina.

Part I

Risk Management Strategies and

Perspectives

© The Author(s) 2017

M Pompella, N.A Scordis (eds.), The Palgrave Handbook of Unconventional

Risk Transfer, DOI 10.1007/978-3-319-59297-8_2

a theoretical foundation for understanding why risk management can add value to a firm and also characterize different means of managing risk—for instance exploring hedging with derivatives and operational hedging

The relevant literature is immense and parts of it quite technical—by necessity our survey is therefore limited in scope We try to present a broad and encompassing view of the motivations for, and means by, which risk, broadly construed, can be managed We strive to survey the relevant theo-retical literature with a light hand and give some references to indicate the flavour of empirical work To aid intuition we present the results in an essen-tially static setting, where we can equate firm profits with the value of the firm

man-age risk or not One view, often associated with Modigliani and Miller

it is better that investors put together a portfolio that best represents their

Stockholm School of Economics, Stockholm, Sweden

preferences towards risk This is indeed a key insight and it remains an important backdrop for understanding when risk management by a firm is motivated.

In public discussions there has been an increasing emphasis on the fact that the future is becoming harder to predict and terms like “unknown unknowns,” ambiguity and black swans are increasingly part of our vocabulary In Sect

risk as randomness that follows a probability distribution whereas uncertainty pertains to randomness that cannot be described by a probability distribution Making a forward-looking decision is clearly much harder if we cannot rely

on probability distributions While some may see this form of uncertainty as

an analytical dead end, we believe that the distinction is valuable, in particular for understanding the limits of financial contracts as a means of managing uncertainties

Thus having set the stage, we turn to different ways of managing risk in

natural starting point and the focus of much theoretical work in risk ment and corporate finance The empirical evidence indicates that derivatives are only one of the many ways used to manage risk, however We therefore

manage-proceed and explore less conventional ways of managing risk: operational

hedging, investing in flexibility and ensuring access to liquidity and to new funds

The central role that we assign to Knightian uncertainty in ing the whys and hows of risk management is a bit unconventional but hopefully the reader will agree that it provides a useful prism A book-

Managing Risk and Uncertainty: A Strategic Approach and the present

sur-vey can in many ways be seen as a summary of this area as presented in

2.2 Why Should a Firm Manage Risks?

We commence with the question of why a firm should manage risk While similar arguments can be made for the case of uncertainty, they are more transparently illustrated for the case of risk, and risk that can be captured

by a probability distribution is also the case that the academic literature has focused on We therefore take this as a starting point

2.2.1 A Point of Departure: Risk Neutral Owner

opera-tionalize higher risk as a mean preserving spread—redistributing probability weight to the tails of the gold price distribution while keeping the mean fixed

It can be seen as a generalization of a case where we capture an increase in risk

The spot price of gold is denoted by s and clearly a higher price of gold

leads to higher profit If the gold price is 0.8 ducats, profit is 80 ducats; if the gold price is 1.2, profit is 120; and if the gold price is 1, profit is 100 ducats

Consider the first case where the probability is 0.6 that the price of gold is 1,

and 0.2 on each of the more extreme outcomes We will refer to this as the low

risk case The expected value of the gold price E(s) is equal to 1 since 0.2 × 0.

8 + 0.6 × 1 + 0.2 × 1.2 = 1 and expected profits are equal to 0.2 × 80 + 0.6 × 

100 + 0.2 × 120 = 100 ducats

If we instead consider a mean preserving spread in the price of gold such

that the probabilities of s = 0.8 and s = 1.2 are both 0.5, the expected value E(s)

is still equal to 1 We refer to this as the high risk case We easily establish that

expected profits are unaffected by this change since 0.5 × 80 + 0.5 × 120 = 100 ducats The finding that expected profits are unaffected by a mean preserving spread holds generally for linear functions and in such a situation there is no motivation to manage risk Profits can be high or low, but in probabilistic terms the good and bad outcomes perfectly balance

2.2.2 Risk Aversion on the Part of the Owner: A Reason

to Lower Risk?

Now instead assume that the owner of the firm is risk averse and has a strictly

Higher profits are thus attached to a lower weight in the utility A string tied between two points on the function would everywhere lie below the function when it is strictly concave If all the individuals’ income came from this one gold mine, the expected utility in the low risk case would thus be

0 2 × 80 0 6+ × 100 0 2+ × 120 9 98≈ and in the high risk case the

util-ity thus falls with a mean preserving spread, and managing risk, in the sense

of lowering the variability of profits, would be valuable for an undiversified risk-averse owner This result holds generally for strictly concave functions.But, and this is a large but, she need not have all her wealth tied to this single firm If capital markets function well and she is risk averse, why not diversify? Why not maximize the value of the gold mine from the perspective

of the market and allow others to invest in the mine and then, as a pletely separate decision, construct a portfolio of assets that maximizes her expected utility? Loosely put, this is the intuition behind the Fisher separa-

whatever investments that maximize its net present value, irrespective of the preferences of the owners That firm policy should be independent of the risk profiles of owners is also associated with the theorems of Modigliani and

of a number of frictions, the value of a firm is independent of its capital

structure A corollary is that hedging with derivatives cannot add value in the frictionless Modigliani-Miller world In practice financial markets are not likely to work in a frictionless manner however and distortions due to, for instance, taxes may play a role Nevertheless, the reasoning behind the Fisher and Modigliani-Miller results represents an important benchmark Even in the absence of perfect financial markets the intuition of the theorems remains important: If owners are highly risk averse it often makes sense for them to strive for a diversified portfolio rather than having the firm engage in exten-sive risk management Note however that the argument just presented relies

on the fact that the owner’s preferences are the source of concavity of the value function Concavity, and thereby a value of lowering variability, can also arise from other sources—an issue that we turn to now

2.2.3 Why Variability Might Lower the Value of the Firm

Assume for simplicity that the owner is risk neutral but that profit is not linear over the entire relevant range Let us therefore consider a case where profits, or more broadly the value of the firm, fall sharply as the gold price drops below a certain threshold It may for instance be the case that moral hazard problems imply that the firm needs to have sufficient own funds, sufficient “skin in the game,” to be able to access external finance Such moral hazard problems are

While this may not be crucial for a gold mining firm, there are many plausible situations where low profits may trigger additional difficulties Valuable employ-ees may be more likely to leave and customers may require rebates to compensate for the declining value of the firm’s products in second-hand markets In a highly

to creating a value of staying above a lower threshold for profits Let us again consider the gold mining firm, but let there be such a threshold at a profit of

we now have profit of only 20 ducats when s = 0.8 Expected profits for the low

risk case are now 0.2 × 20 + 0.6 × 100 + 0.2 × 120 = 88 ducats as compared to

further lowers expected profit, and in the high risk case expected profit falls to 0.5 × 20 + 0.5 × 120 = 70 ducats Increasing risk lowers expected profits and thereby the value of the firm when the profit function is strictly concave It is important to note that here the concavity is not because of preferences of the

owner It is properties of the profit function itself that lead to concavity here and

thereby the result that higher risk lowers the value of the firm In this case the ative relation between risk and expected profits will not vanish if owners diversify

neg-Factors that make the profit function concave thus provide a motivation for

that taxes might be a reason for why profits would be a concave function of profits and thus create a value for risk management While much of the sub-sequent literature has focused on financial constraints and taxes, it deserves

to be emphasized that many other mechanisms can lead to a concave relation between a risk factor and profits For instance, under a fairly broad set of functional forms profits will be a concave function of the exchange rate for an

linear case that we depicted in Fig. 2.1 implicitly assumes that quantities are unresponsive to price Profit then changes one-for-one with changes

in the price of gold Now instead consider a firm that is more flexible than this When the price of gold is high would the firm not want to expand quantity and make the most of the good times? Conversely, when price is low would a profit maximizing firm not want to cut back on production?

A firm that was flexible in this way would presumably do better than a firm that followed a “passive” strategy We illustrate such a flexible situa-

Assume that profits for this flexible firm are 140 ducats when the price

of gold is high and 85 ducats when the price is low Expected profits are now 0.2 × 85 + 0.6 × 100 + 0.2 × 140 = 105 ducats under the low risk case and 0.5 × 85 + 0.5 × 140 = 112.5 ducats in the high risk case A mean preserving spread thus increases expected profits when profits are a strictly

that expected profits of a price taking firm are increasing in price ity for precisely this reason A function is strictly convex if an imaginary

Profit if not flexible

Fig 2.3 Profits under flexibility—strictly convex profits

string tied between two points on the function is everywhere above the function Another way to express this result is that strict convexity means that profits are increasing at an increasing rate as conditions become more favourable.

A particular case of convexity is linked to what is termed real options

opening and closing of gold mines The opening and closing of a mine can

price is low you mothball the mine with some minor cost which is dent of the gold price, and profit is thus a flat function of the gold price up

indepen-to the point where the price of gold is high enough that you want indepen-to reopen the mine From this point on the relation between gold price and profit is upward sloping The result is a convex relation and in consequence the value

of the real option is increasing in the variability in s Many business decisions

related to real options feature such strict convexity (see Chevalier-Roignant

2.3 Sources of Changes in Profit—Risk

and Uncertainty

Implicit in the discussion up to now is the existence of a well-defined

prob-ability distribution for s One need not ponder long to see that this requires a

stretch of the imagination for many variables that affect the future profits of a firm An early and eloquent observation pertaining to the limits of probabilis-

By “uncertain” knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable The game of roulette is not subject, in this sense, to uncertainty; nor is the prospect of a Victory bond being drawn … The sense in which I am using the term is that in which the prospect of a European war is uncertain …, or the obsolescence of a new inven- tion … About these matters there is no scientific basis on which to form any calculable probability whatever We simply do not know.

Several others have throughout the last 100 years stressed that there is a ence between the type of randomness captured by the cases where we can rely

differ-on objective probability distributidiffer-ons and the cases where there is “no tific basis on which to form any calculable probability whatever.” The Chicago economist Frank Knight highlighted the distinction between risk and uncer-tainty in 1921 and following him we sometimes make the distinction that risk pertains to the case where a variable follows a known probability distribution and (Knightian) uncertainty to the case where the variable does not follow a probability distribution The latter may be because we are uncertain about the exact probability distribution as in the experiment discussed below—a situa-tion sometimes referred to as ambiguous The lack of probability distribution may also refer to a failure to ex ante be aware of the possibility of some pos-sible states of the world (“unknown unknowns”)

scien-How then should a rational individual make forward-looking decisions when there is uncertainty that cannot be described by objective probability

distributions? We are interested in outcomes in the future and these outcomes depend on our actions as well as the realized states of the world Some notion

of the likelihood of different states of the world appears to be a crucial input

previous research by John Von Neumann and Oskar Morgenstern and lished an axiomatically founded framework within which we could model a rational decision maker as using subjective probabilities (reflecting the bets

estab-he is willing to enter) westab-hen lacking objective probabilities Testab-he approach has

proven tremendously useful and is the foundation for mainstream work in economics and finance Two limitations deserve to be highlighted however.

should be seen as relevant only for what he termed “small worlds,” sion problems that were relatively simple and isolated Second, an insightful

prefer bets featuring known probabilities (“risk”) to bets featuring unknown probabilities (“uncertainty”) They prefer to bet on the colour of a ball drawn from an urn with known proportions of balls of different colours over betting

on a draw from an urn with unknown proportions In short, many viduals are ambiguity averse (many later actual experiments confirm this; see

The distinction between risk and uncertainty did not have much impact

on research or advice until recently when advances in economic theory (see

the dangers of relying on short backward-looking time series data to model risk In the present survey we will make use of the distinction

Strictly speaking, risk is restricted to cases where the probability distribution

is based on repeated experiments under identical conditions such as gambling

at a roulette table While theoretically sound almost no corporate decisions feature such risks and in this survey we therefore make a broader interpreta-tion of risk, using it to also describe movements in the prices of commodi-ties and financial assets We associate higher risk with more volatile prices of inputs or outputs We associate more uncertainty with situations where there

is greater scope for strategic interaction, unpredictable regulation or potential for drastic innovations to crowd out existing products Essentially, the more unique a situation is, the more the scope for uncertainty

For an asset or commodity price that is subject to risk, financial markets are in many circumstances likely to develop derivative instruments that can

be used to manage such risks Options, futures, forwards and swaps offer sibilities to manage many risks due to exchange rates or swings in the price

pos-of commodities By creating an pos-offsetting exposure, the firm shields prpos-ofit from the effect of unexpected changes in such variables For instance, losses for an exporter that stem from weaker earnings as the domestic exchange rate strengthens can be counteracted by gains made on a forward contract

complete if there exist financial instruments like this to potentially protect

against all risks In contrast, we have incomplete markets if there are many

states of the world for which no state contingent contracts exist Why might such contracts fail to exist? First, the benefits have to be sufficiently large for it

to be worthwhile to create such instruments Second, the experience of eralized debt obligations (CDOs) from the 2000s illustrates the difficulties of correctly pricing and evaluating the riskiness of new state contingent claims Third, at a deeper level, many of the uncertainties that affect firm profits are subject to asymmetric information which in turn hinders the development of markets for state contingent claims and insurance A firm itself knows much more about the uncertainties that it faces, and how it will respond to them, than what outside parties do.

collat-To highlight such asymmetric information let us illustrate with the help

of a specific case: Southwest Airlines The US Securities and Exchange Commission (SEC) requires that public firms above a certain size publish annual reports in the 10-K format Under heading 1A in form 10-K firms are

to discuss the “risk factors” that they are facing (in the SEC terminology “risk” pertains to both risk and uncertainty) Of the risk factors that Southwest mentions, 13 relate most clearly to factors that we might most aptly describe

as uncertainty and 3 to what we would describe as risk An example of the

sig-nificantly impacted by high and/or volatile fuel prices, and the Company’s operations are subject to disruption in the event of any delayed supply of fuel; therefore, the Company’s strategic plans and future profitability are likely to

be impacted by the Company’s ability to effectively address fuel price increases and fuel price volatility and availability.” Clearly for risk due to fuel prices there are derivative instruments that can be used to hedge such exposures and indeed Southwest is prominent in the airline industry for its extensive use of

Company had fuel derivative instruments in place for up to 15 percent of its fuel consumption The Company also had fuel derivative instruments in place

to provide coverage for up to 63 percent of its 2016 estimated fuel tion, depending on where market prices settle.” It also had partial coverage of fuel price risk for 2017 and 2018 and used derivatives to manage interest rate risk as well

consump-That 13 of the points measured can be categorized as uncertainty, relative

to 3 for risk, cannot at face value be taken to imply that uncertainty is more important than risk But it does point to the fact that many important uncer-

label as uncertainty we can for instance highlight the following (Southwest

impacted if it is unable to grow or to effectively execute its strategic plans” What if Southwest would want to insure against this uncertainty in financial markets? One difficulty is that the firms which would be most likely to want

such insurance are precisely the ones which are most likely to have problems

in executing their strategic plans This is hard to observe for potential insurers

and thus the development of such instruments is hampered by adverse

selec-tion (Akerlof 1970)

Another difficulty is that a firm that is covered from business risks is also likely to be more reckless since it is partly sheltered from the consequences

of an ineffective strategy Such moral hazard will also hinder the development

of state contingent instruments that could be used to manage such tainty There is a clear link between whether a risk factor is seen as risk or uncertainty—and whether financial instruments are available for hedging that exposure—either via standard contracts or via tailor-made instruments Simplifying somewhat we conclude that risk is often hedgeable on financial markets whereas uncertainty is much less likely to be hedgeable with financial instruments With the above as a foundation let us now proceed to an over-view of the means available to manage risk and uncertainty—both offering a theoretical motivation and highlighting some empirical results

uncer-2.4 Ways to Manage Risk and Uncertainty

For clarity let us consider a highly stylized situation with a firm that exists

in two periods only—period 0, “today” and period 1, “tomorrow.” Today the firm decides on strategy and on how to manage risk and uncertainty Tomorrow’s realized profits depend on

1 the strategy (i) chosen with respect to “real decisions”

2 the realizations of random variables (s, A) that affect profits and

3 the risk management tools (rm) chosen.

We assume that tomorrow’s profits can be affected by two random

vari-ables: s and A The variable s is risky: described by a probability distribution,

and we assume that there exist derivative instruments that can be used to

hedge exposure to s For A we assume that there does not exist an objective

probability distribution and that derivative instruments are not available—it

is thus a source of uncertainty No matter the source of profit fluctuations the

firm wants to keep realized profits above a lower threshold K In a very stylized

way we can write the decision problem of the firm in period 0 as

The firm wants to choose risk management (rm) and strategy (i) so as to maximize expected profits (Π) subject to a constraint that ex post realized profits are above a lower threshold K Both the part of profit that depends on risk (Π) and the part of profits that depends on uncertainty (A) can depend on the choices of firm actions (rm and i) For example, assuming that s represents

an exchange rate, profits of a firm will depend on the share of production that

is located abroad For the part of profits that depend on s we can use expected values, while for the part that depends on A we cannot rely on expected val-

ues For now we skirt the issue of how to think of forward-looking decisions when we do not have a probability distribution and instead turn to a concep-tual view of different ways of managing risk and uncertainty

If the firm does not find it worthwhile to engage in risk management we say that it follows a benchmark strategy This would be relevant if the conditions for the Fisher separation theorem held or if the firm was sufficiently uncon-

cerned that ex post profit may fall below K Simply following the benchmark

and refraining from risk management is a perfectly respectable alternative if the situation is such To make the risk management decision consequential

enough to fall below K The motivation for managing risk here can thus be

a willingness to lower volatility per se

We consider four different ways of managing risk and uncertainty We distinguish between risk management with derivatives, operational hedging, flexibility and liquidity management As with many classification schemes other divisions are possible but we believe that the present one is useful for

par-To illustrate the intuition behind the use of state contingent contracts note that financial hedging strives to make the value of the firm insensitive

to changes in s To highlight this we depict the case where hedging totally

rela-tively minor cost of the financial hedging strategy but clearly if s equals E(s),

the profits are lower under the financial strategy One important issue to note

is that derivatives do not in themselves insure against shock due to

uncer-tainty (A)—which we may think of as shifts in the operating profits, the curve

marked with benchmark Derivatives do however work in the direction of helping the firm keep profits up in the face of uncertainty shocks By neutral-

izing the effect of low s on profits, hedging would give a more stable position

from which to survive a negative uncertainty shock

against weak realizations of s but also takes away the upside By using options

the firm may of course keep the upside alive while purchasing insurance against the downside Nevertheless, survey evidence (such as Bodnar et al

on the notional amounts of different contracts from the Bank of International Settlements (BIS) all indicate that linear contracts (such as forwards and swaps) are used to a much greater extent than options

Profit with financial hedge

Fig 2.5 Hedging with derivatives—a stylized example

The literature also indicates that derivatives use is a common way of

taught in typical courses on risk management, with a clear focus on pricing and using financial instruments, this should come as no surprise It is also consistent with a simple interpretation of the Fischer separation theorem—make whatever “real” decisions that maximize expected profits and then deal with risk issues separately by having dispersed ownership or using derivatives Nevertheless, several puzzles remain before we can settle on the view that derivatives are the supremely important conduit whereby firms manage risk and uncertainty

First, much of derivatives use is for relatively short horizons up to one year and derivatives use is more common among larger firms This is at odds with expectations if we believe that financial derivatives are the main way of managing risk based on the discussion above We expect risk management

to be more important for the long haul and we believe that the motivation for managing risk should be stronger for smaller firms, which are likely to have less diversified ownership and be subject to tighter financial constraints Second, an additional finding that is hard to square with a dominant role for

establish that at the time of their study the derivatives portfolios held by large

US firms were not sufficiently large to act as an important hedge with regard

to the overall exposure of these firms Third, survey evidence is also

firms view operational hedging as a more important way of managing risks than derivatives for most sources of risk and uncertainty

One way to interpret the empirical results on derivatives is that using them simplifies short- to medium-run liquidity management This can be seen as the key motivation for their use rather than them providing a crucial role in limiting the risk of default and financial distress per se This means that for

a firm that wants to manage risk other measures may be explored, which we now proceed to

2.4.2 Operational Hedging

“Operational hedging” is a common term even though it is rarely defined in

a precise way In the present survey we define “operational hedging” as tional decisions with the explicit aim to make profits less sensitive to both

opera-changes in s and to uncertainty shocks For instance, serving foreign markets

by having sales for that market produced locally instead of via exports is a

form of operational hedging, since it lowers exposure to exchange rate changes

to have cost and revenue in the same currency Locating production in the market country also serves as protection against tariff shocks and many other policy shocks Many other choices with respect to what products to carry, how

to price them and how to produce can be modified because of risk concerns and would thus amount to operational hedging

An empirical example of operational hedging is examined by Treanor et al

airplanes This limits the harm of high prices of jet fuel—but also makes the impact on profits of falling prices of jet fuel lower We illustrate the situation

the price of an input, such as jet fuel, is likely to have a negative relation to

profit (for clarity we may think of s as 1/(price of jet fuel)) For operational

hedging not to be a free lunch we would need more fuel efficient planes to be less profitable when the price of jet fuel is close to its expected value

Why would a firm use operational rather than financial hedging? From the logic of separation theorems the firm should take a “real” decision to maxi-mize expected profit Adjusting the portfolio or using derivative instruments

Profit

110

100

Benchmark profit

Profit with operational hedge

would then appear to be the preferred way of dealing with risk Distorting real operations to deal with risk seems ineffective and one might ask, why not sim-ply use financial instruments which are likely to be relatively cheap to use and are likely to be easier to revert than real decisions? There is a lot of substance

to this logic but four provisos should be highlighted

First, to the extent that financial constraints, or other factors, create cavity of the profit function, lowering variability will increase expected profits Operational hedging may thus be directly related to an increase in expected

con-profits, even if realized profits at the expected value of s would be lower Again

it matters if concavity stems from the fundamentals of the firm profit or from risk aversion on the part of a non-diversified owner

Second, firms may need to post collateral to use derivatives In their study

the need to post collateral can explain why the most financially constrained firms do not hedge jet fuel prices at all

Third, as we depart from simple settings with a first and second period the

issue of when to initiate hedges becomes crucial Think for example of a

pro-longed cycle in the euro-dollar exchange rate—cycles may easily cover a period

of several years A US exporter that purchased forward contracts at the time the dollar was weak, in the summer of 2008 would do very well as the dollar appre-ciated with an associated lower value of foreign currency earnings Conversely,

a US exporter that locked into the strong dollar at the millennium’s turn might

be cursing itself when the dollar subsequently depreciated Thus, a firm that routinely hedges with linear contracts does not truly insulate cash flows from variability Instead, such a practice largely amounts to a reshuffling of profits

but in a comparison of several common hedging schemes (such as covering a share of next period’s exposure and then decreasing shares further out into the

com-monly used strategies, such as one-period cash-flow hedges and long-term fixed hedges, may leave the firm very exposed to foreign exchange risk One possible explanation for the popularity of one- period cash-flow hedges is that the firm may shift its operations in response to an exchange rate change We argue that the opportunity for such shifts may help to explain the use of short-term hedges.” By using options these concerns could be circumvented but long-term options tend to be costly to tailor and we see relatively little use of them.Fourth and last, but not least important, many of the shocks that affect the value of the firm take the form of uncertainty rather than risk as discussed

instruments