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ACTSC 445: Asset-Liability Management

Department of Statistics and Actuarial Science, University of Waterloo

Unit 1 Introduction

What is Asset-Liability Management (ALM)?

ALM can be defined as managing a financial institution so as to earn an adequate return on fundsinvested, and to maintain a comfortable surplus of assets beyond liabilities (from QuantitativeRisk Management, by McNeil, Frey and Embrechts)

ALM is the practice of managing a business so that decisions and actions taken with respect toassets and liabilities are coordinated. (. . . ) It can be defined as the ongoing process of formulat-ing, implementing, monitoring and revising strategies related to assets and liabilities to achieve an

organizations financial objectives, given the organizations risk tolerances and other constraints.ALM is relevant to, and critical for, the sound management of the finances of any organization thatinvests to meet its future cash flows needs and capital requirements. (From SOAs ProfessionalActuarial Specialty Guide on ALM)

Why ALM?

Was initially developed to deal with interest rate risk, which became a major concern in the 1970s, whenrates increased substantially and became quite volatile. For instance, insurance companies often sellproducts that are sensitive to interest rates: an obvious example is the option given to the policyownerto take a loan on the policy at a prespecified interest rate. Before the 1970s, insurers did not expect

this option to be exercised very often, except under special personal circumstances. However, whenrates went up in the late 1970s and early 1980s, several policyowners decide to exercise this optionand invest the loan at a much higher rate than the lending rate. Insurance companies thus needed cashon a much shorter term than anticipated, and often had to borrow money at a very high price to fulfillall the loan requests.

Here are a two recent actual examples of what can happen when an insurance company does notproperly manage its assets and liabilities:

In 1997, Nissan Mutual Life, a major insurance company in Japan covering 1.2 million clientsand having about 17 billion US$ in assets, was offering individual annuities at a rate of 5 oreven 5.5%. The company had a significant portion of its assets invested in government bonds,

and when the rates for those dropped to record (low) levels, the wide gap between the promisedreturn on its liabilities and the one earned on its assets caused the company to go bankrupt (andwas the first japanese insurance company to do so in over 50 years).

In 1999, General American Life in the US had issued for 6.8 billion US$ of short-term fundingagreements at a quite interesting rate, and with the provision that the investors could ask to bereimbursed within 7 days. When Moodys downgraded the credit rating of General AmericanLife from A2 to A3, several investors asked to be reimbursed. In fact, a few days after the

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downgrading, a total of 4 billion dollars needed to be reimbursed, which made it impossible forthe company to sell its assets quickly enough to satisfy all the reimbursement requests. Thecompany eventually was sold to MetLife.

These examples focus on the interest-rate risk, which will be covered in this course, more specifically

in the two first parts of the course. But we will also discuss other financial risks. Namely, we will talkabout risk measures that can be applied to a portfolio exposed not only to interest rate risk but moregenerally to market risk. Then we will discuss credit risk, which is becoming an increasingly importantissue in financial risk management.

Before going over the topics discussed in this course in more details, we give a classification of financialrisks that comes from Quantitative Risk Management, by McNeil, Frey and Embrechts:

Market risk: risk of a change in the value of a financial position due to changes in the valueof the underlying components on which that position depends, such as stock and bond prices,exchange rates, commodity prices, etc.

Credit risk: the risk of not receiving promised repayments on outstanding investments such asloans and bonds, because of the default of the borrower.

Operational risk: the risk of losses resulting from inadequate or failed internal processes, peopleand systems, or from external events.

Underwriting risk (for insurance companies): the risk inherent in insurance policies sold,for instance due to changing patterns of natural catastrophes, changes in demographic tablesunderlying (long-dated) life products, or changing customer behavior.

We will study the two first types of risk here. Another classification sometimes used by actuaries isthe one coined by C. L. Townbridge when he was chairperson of the SoA committee on Valuation and

Related Matters (C is for contingency).

C-1: Asset risk (Risk of asset defaults and decrease in market values).

C-2: Mortality and morbidity risks (risk of losses from increase in claims and from pricingdeficiencies).

C-3: Risk of losses due to changes in interest rates (either in the level of interest rates or theshape of the yield curve).

C-4: Miscellaneous risks (Accounting, managerial, social and regulatory risks).

More details on the four parts of the course are given below.

Part 1: Fixed-income securities, duration, convexity, immunization. Fixed income securitiesform a large class of assets used in ALM. Also, we put an emphasis on bonds and interest rates becausean important part of ALM is to deal with interest rate risk. Then an important question to ask in thecontext of ALM is: what will happen if interest rates change? To answer this, we need to measure thesensitivity of the assets portfolio to interest rates: duration and convexity are two measures that do

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that. Finally, we will discuss some basic risk management tools, i.e., well try to answer the question:how can we structure our assets portfolio so that it is protected against changes in interest rates.Note: This part of the course will be covered rather quickly, especially topics that have already beencovered in ACTSC 231.

Part 2: Interest Rate Models, pricing interest-rate derivatives. When we ask in Part 1 whatwill happen if interest rates change?, if we want to go a little bit deeper, we need to understand howwe can expect interest rates to change, i.e., we need to model them. In particular, good models arerequired to price interest-dependent securities. Here we look at a few simple stochastic models. We willstart with discretized versions of these models, where derivatives related to interest rate (like callablebonds) can be priced using a binomial tree. If you have taken ACTSC 446, this part will be veryfamiliar to you. But we will also look at continuous-time models, and describe techniques that can beused to price interest-rate derivatives in that case, and will see that these techniques are more flexibleand efficient that binomial-tree type methods.

Part 3: Risk Measures. Duration and convexity focus on interest-rate risk. To measure a portfoliosexposure to a wider range of risks, other measures have been defined. One of them is value-at-risk,

which well study here. We will also talk about other measures, like conditional tail expectation (orTailVar), and discuss methods for computing these quantities. In particular, we will talk about the useof simulation and importance samplingprobably familiar if you have done STAT 340for this typeof computation. We will also make sure to cover models that go beyond the simple multinormal linearcase.

Part 4: Credit Risk Credit risk has to do with the risk that a borrower will not pay back a loan to thelender. With the mortgage crisis in the US, this is an area of study that has become very important.We will talk about different models that can be used to study credit risk, and the statistical andcomputational techniques that go with them. In particular, we will talk about copula models for creditrisk.

ALM in practice

Large corporations, insurance companies, and financial institutions typically perform some form of riskmanagement. To give a bit more insight on this, here are a few facts taken from the Results of theSurvey on Asset-Liability Management Practices of Canadian Life Insurance Companies (May 2002):

86% of all companies surveyed view interest rate risk as deemed material for their company, and80% have a formal process to manage this risk.

More than two thirds of medium and large companies have an independent ALM function.

In large companies with an independent ALM function, up to 20 persons are working on ALM.

79% of all companies use modified duration as a risk metric, 51% use convexity; 57% of all largecompanies use value-at-risk.

Second most cited future goal is to implement stochastic scenario generator.

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