asset liability management in banks by abe2

VIEWS: 290 PAGES: 21

									                           Asset-Liability Management
                           Ian Webb and Robert Gibbons
                         International Insurance Foundation

As the previous presentations have demonstrated, there are many techniques, and
even numerous goals, characterizing the use of asset-liability management.
Consequently, it cannot be described in a neat little box that fits equally well in all
environments. In the United States over the last thirty years, it has gone from a
neglected to a crucial and elaborate aspect of insurance operations.

The Society of Actuaries defines asset-liability management as:
   The practice of managing a business so that decisions on assets and liabilities
   are coordinated. Or more broadly, … the ongoing process of formulating,
   implementing, monitoring, and revising strategies related to assets and
   liabilities in an attempt to achieve financial objectives for a given set of risk
   tolerances and constraints.
The key words here >> coordinated….& ….ongoing process…& …achieving
financial objectives within given set of risk tolerances and constraints.
             Coordinated because the decisions on assets and liabilities are made in
               an integrated, not separate fashion.
             Ongoing because the changing nature of market factors, claims
               experience, and consumer behavior requires continual readjustment of
               these decisions.
             Financial objectives because they are many, not one, and tolerances
               and constraints because these form the boundaries within which
               asset/liability managers must work.

To the extent that every insurance company manager wants to make sure cash flows
are sufficient to pay claims, and that some profit is earned on investments, he/she is
practicing asset-liability management. However, there is a difference between just
making sure ends meet and identifying numerous more precisely defined objectives
and developing techniques to measure success in achieving them.

A number of factors have driven the rise of A/L management in the last two decades.
Computing power has made new forms of analysis possible, and even desirable.
Deepening and broadening of financial markets has increased the variety of financial
instruments available. Competitive forces have pushed companies towards more
aggressive investment strategies. Regulatory restrictions on investment options have
been relaxed in many jurisdictions in favor of a prudent person approach and market-
based self-regulation of asset-related risks.

However, these factors have not affected all regions and markets equally. As a result,
the manner in which A/L management has developed across countries is quite

Both regulatory factors and economic factors have given rise to different A/L
management practices.

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002           1
Regulatory factors
      Rate regulation
      Where tariffs exist for products, the incentive for managing investment
      portfolios is often diminished. This is so inasmuch as decisions affecting the
      pricing of products can take into account expected returns on investments.
      Taking out this interaction by imposing mandatory tariffs may reduce the
      degree of coordinated planning carried out by the industry.

       Highly competitive pricing environments can motivate insurers to undertake
       higher return/higher risk investment portfolios in order to make up for
       technical losses from underpricing products. Investment returns have
       contributed significantly to total operating results in the U.S. market over the
       last 25 years.

       Investment regulation
       Restrictions on type, concentration, mix, and quality of investments all put
       further constraints on the investment strategies available to insurers.

       In Canada, for example, up until 1992, the Insurance Companies Act restricted
       the types of investments life insurance companies could hold by providing a
       detailed list of the asset classes and investment limits. After 1992, the law
       adopted a prudent portfolio investment regulation that allows managers to
       pursue a broader class of investments while employing a prudent manager’s
       discretion. The prudent approach implies that managers must act with due
       diligence using experience and skills that are comparable to other managers’
       actions in similar situations within the industry. This new rule grants
       flexibility to Canadian life insurance companies in matching asset portfolios
       with their liabilities. The Boards of Directors of these companies are required
       to develop and approve written investment policies that encourage prudent
       behavior. This change provides Canadian life insurers with a more modern
       regulatory environment and the ability to invest and operate more actively
       without cumbersome constraints

       Tax regulations
       The tax treatment of alternative investments may restrict their use. Examples
       are heavy taxation of foreign-issued instruments, heavy corporate taxation on
       investment profits, tax-free status for certain securities (i.e. public-sector
       bonds may be tax-exempt, as are municipal bonds in the USA). Such special
       treatments often give the investment manager the decision of weighing the
       gain from not paying taxes on interest income received from tax-free
       securities, versus obtaining the higher interest rate available from corporate or
       other taxable securities, but paying the extra taxation on capital gains.

Economic Environment Factors
     Financial market depth/liquidity
             A fairly liquid market affords investors the price and quality signals
     needed for decisions on asset composition. Without active bond and equity
     trading investors are unable to determine what risks are associated with certain
     types of bonds. Neither is it how they react to changes in interest rates and
     other economic indicators.

INTERNATIONAL INSURANCE FOUNDATION                  Warsaw, 15 March 2002         2
                A fairly broad market provides investors with options for matching
       liabilities with investments of different maturities, and interest rate

       Economic stability
               This stability facilitates the analysis of risks and returns in the financial
       markets. Volatile markets are more difficult to measure, and so manage.
       Stability however is not necessary, and in fact instability has spurred countries
       on to realize they need to manage assets and liabilities more carefully. Yet it is
       desirable for developing the metrics to have stability in markets.

       Economic booms
               Periods of rising investment returns heighten insurer management's
       awareness of the role that investment management can have in overall
       profitability. Periods of high interest rates and rising equity values can drive
       competitiveness with regard to investment strategies.

As a result of the many ways the environmental factors affect the options available to
managers for the practice of A/L management, it is not surprising there are many
differences in how it is practiced around the world. In spite of these factors, however,
there is also simply the issue of insufficient exchange of information, education, and
experience with A/L techniques.

Learning from Past Failures

Besides the environmental factors mentioned already, the growth of A/L management
techniques and know-how has also much to do with learning from A/L failures. In the
U.S. there is quite a history of insurer failures, which have led great changes in
regulatory oversight as well as industry self-management. These failures were
accelerated by a highly competitive environment which created a multitude of new
risks for insurers.

Heightened competition in the financial services market in the U.S. in the 1980s, in
which the savings products offered by life insures were challenged by products from
banks and mutual funds, drove insurer management to take bold new strategies. The
methodologies which applied in the more settled environment were no longer
adequate. Riskier investment portfolios, a move to more interest-sensitive products,
greater guarantees on returns, all contributed to much greater risk for companies. Life
insurance contracts which offered a variety of options to policyholders, such as
settlements, policy loans, and surrender or renewal privileges, became more risky for
companies when interest rates fluctuated. This is because the value of the options rose
in many instances with the rise of interest rates. For example, policyholders
guaranteed loan options at 4 percent interest were being offered 6 or greater percent
return on government bonds. Thus, life insures lost as there was great financial
disintermediation. As interest rates fluctuated greatly, it was only natural that some
companies approached financial crises.

The leading causes of insolvencies in the U.S. during the last 15 years have been
inappropriate investments in high-yield non-investment grade bonds, commercial

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002           3
mortgages, and real estate. However, inadequate liquidity, poor management of
investment function including insufficient analysis and reporting of the investment
function to top management, also contributed.

Baldwin United Life Insurance Company went bankrupt in 1983, having annual sales
of 1.6 billion dollars the previous year. Two primary causes were unrealistic promises
on interest rate returns on insurance and annuities to customers, mismatching assets
and liabilities.

First Executive Life Company went insolvent in 1991, with 60 billion dollars in
coverage in effect, and billions in liabilities. High-risk investments in high-risk bonds
was largely at fault.

Mutual Benefit, the 6th largest life insurer in the U.S., had assets of $13.1 billion when
it was taken over in 1991. A high concentration (37% of its investment portfolio) in
real estate, contributed greatly to the demise of a company that had been in business
since 1846.

A more recent lesson of inadequate A/L management can be found in Japan. Nissan
Mutual life, a Japanese company with 17 billion dollars of assets, sold annuities
paying guaranteed interest rates of 5 percent or greater without hedging these
liabilities. A drop in government bond yields created a large gap between the interest
rates Nissan Mutual promised and the returns it was making on its investments. In
1997 the company was taken over by the Japanese Finance Minister, with losses of
2.5 billion dollars.

From this experience and the competitive forces, methods have been developed to
provide insurers with greater investment returns while ensuring a degree of liquidity
and cash-flow balance. The methods vary by line of business, as there are significant
differences in how A/L management is practiced for Life and Non-life. While life
insurers generally focus on interest rate risk, some non-life insurers are taking a
broader view through the application of Dynamic Financial Analysis.

Interest rate risk, which is essentially a firm's vulnerability to interest rate fluctuations,
has been the major contributing factor to fluctuation in the value of fixed income
assets of insurers over the last two decades. As life insurer asset portfolios in the U.S.
are heavily weighted by these bonds, it is natural that this focus on interest rates be so
strong. Interest rates, however, also affect the liabilities of life insurers (i.e. options),
and to some extent P/L insurers.1

 This section draws from, “Asset-Liability Management in the Life Insurance Industry”, LOMA,

INTERNATIONAL INSURANCE FOUNDATION                       Warsaw, 15 March 2002             4
Some differences between Property/Casualty and Life Assets and Liabilities
Property/casualty insurer liabilities - auto, fire, homeowners policies - are usually
short-term coverage periods (one to three years). Property/casualty insurers can
generally meet liquidity needs with current income. Their common investment
strategy is therefore cash and short term investments, short-term bonds, and stocks.

Life insurer liabilities - whole life, endowment life policies- are longer-term liabilities
with implied investment returns. Life insurers look for longer-term investments that
will provide attractive returns, such as long-term bonds, stocks, mortgage loans, and
real estate.

Investment activities of financial institutions involve buying primary securities and
issuing secondary securities. Often, the primary securities have different maturity and
liquidity characteristics than the securities issued. This mismatch in assets and
liabilities exposes the financial institution to interest rate risk.



Risks Faced by Insurance Industry
Six general types of financial risks face the insurance industry. These include:
      Actuarial
      Systematic
      Credit
      Liquidity
      Operational, and
      Legal risks
As these risks vary with the type of services provided, management of life insurance
companies work very hard to define the inherent financial risks that can alter their
course of success.

Actuarial risks arise from raising funds by means of issuing policies and other
liabilities. The two risks that affect companies are (1) paying too much for the funds
received and (2) receiving too little for the risks taken.

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002           5
Systematic risk, also called the market risk, deals with changes in value of assets and
liabilities. These include interest rates and basis risk. Life insurers measure and
manage their vulnerability to interest rate movements. Companies with common stock
holdings, large corporate bonds, and mortgages watch closely swings in the basis rate.
Any movement in the rates affects the yields on those instruments. Life insurers invest
in assets that vary in credit quality, liquidity, and maturity which subjects them to
market value variations independent of fluctuating liability values.

Credit risk takes considers that borrowers will not fulfill their obligations and is
affected by borrowers’ financial condition and the value of their collateral. Life
insurers need to be concerned with this type of risk, because investments in bonds
form part of their asset portfolios

Liquidity risk may present potential funding crises connected with unexpected events
in the market. Because of the long-term nature of risk associated with this type of
business, life insurers undertake long-term investments to fulfill their contractual
obligations as they fall due. Unexpected situations such as disintermediation can arise
when policyholders make increased withdrawals and surrenders due to high interest
rates offered in the market. Such actions taken by policyholders could force
companies to sell off long-term assets at losses to pay for these unexpected events.

Operational risk not only looks at management and employees but also at
management information systems used for processing data and record keeping.
Inefficiency in this area can produce costly outcomes for life insurance companies.

Legal risk should be of great concern to the life insurance industry. New legal trends
can be observed in litigation outcomes, especially in the U.S., and globalization adds
new meaning to the legal environment. Other reasons such as fraud, violation of
regulations, and misinterpretation of contracts by policyholders add to the complexity
of this kind of risk. This legal risk can result in catastrophic losses to life insurance

INTERNATIONAL INSURANCE FOUNDATION                  Warsaw, 15 March 2002          6
Actuarial Categorization of Risks
Actuaries categorize risks into four different classes:
      C1 - Asset depreciation risk concerns itself with losses caused by the decline
       in market values. Life insurance companies hold many different
       assetsincluding bonds, real estate, and policy loansthe market values of
       which are sensitive to fluctuations in interest rates. Market values of these
       assets have an inverse relationship to interest rates.

                         Bond price

                                         Interest rates

      C2 - Pricing risk incorporates various elements including mortality,
       morbidity, and operating expenses. These calculations are used to determine
       adequate premiums so that life insurers can meet their contractual obligations
       to their policyholders. Examples of pricing risk include:
   o            Wrong mortality table
   o            Charging too little.
   o            Expenses higher than expected.
      C 3 - Interest change risk affects companies’ cash outflows and inflows. For
       example, life insurers could face insolvency if the impact of fluctuating
       interest rates is different on assets than on liabilities because values of assets
       and liabilities will change by different amounts. Examples:
   o            Withdrawals (financial disinertemediation)
   o            Prepayments of mortgages or bonds when int. rates decrease.
      C 4 - General business risks including regulatory changes, changes in tax
       laws, and venturing into new lines of business. Legal interpretations that can
       greatly affect a life insurer’s future obligations.

Measuring Interest Rate risk:
Banks under the BIS Accord (Bank for International Settlements) can calculate capital
requirements due to changes in the market interest rates (general market risk) using
the "maturity" and the "duration" methods (standardized approach).

Maturity Model:
The maturity model takes into account the effects of interest rate changes on the
mark-to-market value of assets and liabilities. An example drawn from "Financial

INTERNATIONAL INSURANCE FOUNDATION                    Warsaw, 15 March 2002         7
Institutions Management"(Saunders 2000) will be used to understand the dynamics of
fixed income securities relative to interest rates changes.

The financial institution has a position in one bond with the following characteristics:
    - Maturity of 1 year.
    - One single annual coupon of 10% (C).
    - Face value of $100 (F) to be paid at the end of the 1-year period.
    - Yield to maturity of 10% (R).
So, the current value of the bond is:

VB1 = (F + C) / (1 + R) = $100
Now, suppose that the yield (R) rises to 11%. Then the market value of the bond falls
. VB1 = ($100 + $10) / (1 + .11) = $99.10
a)  rise in the required yield to maturity reduces the price of the fixed income

     Market Value




                               0%   10%   20%         30%           40%    50%         60%
                                                Yield to Maturity


Now suppose that the maturity period is two years and the bond keeps paying coupons
at the end of the first and second year. With a yield to maturity of 10%, the value of
the bond is:

VB2 = ($10/ 1.1) + (110/1.12) = $100.
Now, suppose that the yield (R) rises to 11%. Then the market value of the bond falls
VB2 = ($10/ 1.11) + (110/1.112) = $98.29

b) The longer the maturity of a fixed-income asset or liability, the greater its fall in
price and market value due to an increase in interest rates. Furthermore, the decrease
in the value of longer-term securities increases at a diminishing rate for any given
increase in interest rate.

INTERNATIONAL INSURANCE FOUNDATION                       Warsaw, 15 March 2002     8
The before mentioned rules apply equally to a portfolio of securities. The maturity of
the portfolio is equal to the weighted average of the maturities of the securities that
compose the portfolio.

The net effect of the variability of interest rates on a financial institution depends on
the direction and magnitude of the mismatching maturities of assets and liabilities.

E           =             A               -           L
(Change in net worth) = (change in market value of assets) - (change in market
value of liabilities)
                                                    Maturity Gap

Therefore, when the maturity of the assets is greater than the maturity of liabilities,
any change in interest rates will affect the value of assets more than it would the value
of the liabilities. The maturity method, by determining the maturity gap (direction and
magnitude), would tell us about the impact of changes in interest rates on the equity or
net worth of the firm. However, hedging strategies based on matching maturities
would not always eliminate all interest rate risk because the cash flows of the
instruments in the portfolio are not considered, only their time until maturity.

Asset-Liability Statistics
The life insurance industry has the opportunity to consider statistics for financial
instruments to facilitate management's task. Such statistics recognize information
regarding several different assets and liabilities in a single value. Such recognition is a
major step toward managing assets and liabilities more efficiently. The most
important statistics used in analyzing both assets and liabilities are:
       Macaulay duration
       Modified duration
       Option-adjusted duration
       Convexity

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002           9
In the past, life insurance companies did not fully incorporate interest rate sensitivity
of cash flows in estimating asset and liability durations for each line of business. In
recent years more attention is being paid to the effects that interest rate changes have
on the value of shareholders’ wealth. A mismatch between the durations of assets
and liabilities places the value of equity at great risk to increases in the interest
rate. Because of the relationship between maturity and the interest rate, the longer the
term-to-maturity on a fixed income investment, the more sensitive is the value of that
investment to any interest rate changes, keeping everything else constant.

The Macaulay Duration is defined as the present value weighted (i.e. discounted
with interest) average time to maturity of the cash flows of that financial
instrument. The most commonly used duration is Macaulay’s duration, or Simple
Duration, and is calculated as follows:

                                                             t  CFt
                                                       (1  r )    t
                            Macaulay Duration          t


                                   where P  
                                               t   (1  r ) t              
                                             P 1    t  CFt 1
                   Modified duration                       
                                             r P t (1  r )t 1 P
                                          Macaulay duration
                                 (1  r )

Macaulay’s duration computes the present value weighted average time to maturity of
the cash flows of a certain financial instrument.

The duration method is more appropriate than a maturity method to measure interest
rate risk because it not only takes into account the maturity but also the timing of the
cash flows of the instrument or portfolio exposed to interest rate risk. It measures the
"average life" of the asset or liability.

INTERNATIONAL INSURANCE FOUNDATION                          Warsaw, 15 March 2002   10
 Consider the following example:2An insurance company has the following position in
 a bond:

          0                                      6 mos.                                     1 year

Insurance Company                         Insurance Company                Insurance Company receives
    loans $100                            receives$50                      $50 principal + interest ($3.75)
                                          principal and interest           + interest on reinvestment of
                                          of $7.5 for a total              cash flow received in month 6 =
                                          amount of $57.5.                 $53.75 plus interest on cash
                                                                           flows received in month 6

 Interest rate = 7.5%

 At 6 months it receives $50 principal and interest of $7.5 for a total amount of $57.5
 At 1 year it receives $50 principal + interest ($3.75) + interest on reinvestment of cash
 flows received in month 6 = $53.75 plus interest on cash flows received in month 6

 The cash flows of the bond are:

              0                                    6                                             1 year
                                                  CF1/2 = $57.5                                 CF1 = $53.75

 We want to compare the sizes of the cash flows to find the "average life" of the bond.
 The present values (relative terms amounts so they can be compared) of the cash
 flows are:

        CF 1/2 =           $ 57.50                     PV 1/2 =          $ 53.49
        CF 1 =             $ 53.75                     PV 1 =            $ 46.51
     CF 1 + CF 1/2 =       $111.25                  PV 1 + PV 1/2 =      $100.00

 To determine the simple duration of this bond, it is necessary to weight the timing of
 the cash flows relative to their importance in terms of their present value. The weights
 of each cash flow is calculated as follows:

       Cash Flow
        Timing                          Weight (W)
         1/2 year          W1/2 = PV1/2/(PV1/2+PV1) 53.49%
          1 year            W1 = PV1/(PV1/2+PV1) 46.51%

     Values for the example taken from A. Saunders, Financial Institutions Management (2000).

 INTERNATIONAL INSURANCE FOUNDATION                           Warsaw, 15 March 2002               11
The table above suggests that 53.49% of the cash flows are received at the end of six
months, and 46.51% at the end of the year. By definition the weights have to add up
to one.

To calculate the simple duration (D) of this bond we need to use the present value of
the cash flows represented by their weights. It follows that:

                    D = [(W1/2 x 1/2) + (W1x1)] = 0.7326 years.
                           [(.5349*1/2) + (.4651*1)] = .7326

Note the difference between a maturity measure of one year compared to the duration
or “average life” of the bond of 0.7326 years. This difference between both measures
arises because a higher percent of the cash flows are received before the bond
matures. Maturity would equal the duration of an interest sensitive financial
instrument only when the cash flows are received at the end of the period when the
instrument matures.

Modified Duration

The modified duration of financial instruments is a measure of price sensitivity of a
fixed set of cash flows to small changes in the single interest rate. This statistic
captures how small changes in the interest rate will affect changes in the price and is
expressed as a percentage. It is equal to the Macaulay Duration divided by one plus
its effective annual yield to maturity.

Modified duration can be defined alternatively as a direct measure of the sensitivity of
the value of a financial instrument to changes in interest rates. The higher the measure
of duration, the more sensitive (elastic) is the value of the financial instrument to
changes in interest rates. The idea behind duration is simple. Suppose a portfolio has a
duration of 3 years. Then that portfolio’s value will decline 3% for each 1% increase
in interest rates – or rise 3% for each 1% decrease in interest rates. Such a portfolio is
less risky than one which has a 10-year duration.

For instruments that pay fixed cash-flows, such as non-callable bonds, there is a
particularly simple way to calculate duration. For such instruments, duration is just
the average maturity of the instrument. A 5 year zero-coupon bond, for example, has
an average maturity of 5 years, and so a duration of also 5 years.

To illustrate how to calculate modifed duration, consider a 10 year non-callable bond
with a nominal yield of 10%. The cash flows will be $50 payable every 6 months per
$1000 face, plus an additional $1000 return of principal at maturity. The modified
duration is calculated as follows:

                              ½ x CFt x (1 / ( 1.05))t
                          x CFt x ( 1 / (1.05))t

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002         12
where the summation sign is from t =1 to t =20. The result = 5.934 years. The prices
of this set of cash flows should change by .05934% for a one basis point change in
effective interest rates.

Option-Adjusted Duration
The option-adjusted duration, like the modified duration, is a measure of price
sensitivity. The difference is that option–adjusted duration is a much more accurate
measure of price sensitivity if the cash flows depend upon the path that interest rates

Option-adjusted Duration = -d Price/ di
This expresses how much the price will change (dPrice) as a result of small changes
in interest rates (di), and is expressed in terms of a ratio by dividing by the beginning

Features of Duration:
- The duration of a bond is always smaller than its maturity. The only exception is
   with a zero-coupon bond where its duration and maturity are equal.
- Increasing the coupon rate while keeping its maturity and the yield constant will
   decrease the duration of the bond. Bonds with higher coupons distribute relatively
   more cash flows earlier decreasing the ”average life” of the bond.
                                                Duration v. Coupon Rate

                                           0%   5%    10%     15%    20%    25%     30%

                                                       Coupon Rate

-   Increasing the yield of a bond while keeping its maturity and coupon rate constant
    will decrease the duration of the bond. The rational in this case is that with a
    higher yield the discount factor would decrease, giving those cash flows closer to
    the maturity of the bond less relative weight, therefore less “average life” for the

INTERNATIONAL INSURANCE FOUNDATION                          Warsaw, 15 March 2002         13
                                                             Duration v. Yield




                                                   0%   5%   10%        15%       20%        25%         30%


Shortcomings of Simple and Modified Duration Measures

The Macaulay formula as well as the Modified Duration formula assume all cash
flows are fixed. For instruments that do not pay fixed cash flows, such as callable
bonds, mortgage-backed securities or interest rate caps, the Macaulay and Modified
formulas for duration will not work. For these instruments other means must be used
to calculate duration.

Most liabilities as well as assets of insurers have cash flows which are not fixed, but
vary with changes in interest rates (i.e. assets with imbedded options.) As a result,
another means is needed – this is what is called “Effective Duration.” Effective
duration measures are based on stochastic interest rate valuation models. Because
most stochastic interest rate processes do not have closed form solutions for duration,
numerical procedures are usually employed to estimate duration. Perhaps the most
conventional approach to measuring duration is a numerical procedure where three
valuations are performed, with each valuation performed by an interest rate lattice (or
simulation path) being positioned at a different level of interest rates. Then each short
rate is the entire tree is increased by 50 basis points and a new valuation is performed.
Again, each short rate is reduced by 50 basis points from the initial tree levels, and a
third valuation is performed. Finally, the percentage change in price is scaled by the
change in interest rates, which in this case amounts to 100 basis points, resulting in a
measure of Effective Duration.
For many financial instruments, the traditional duration measures, Macaulay and
Modified, produce durations that are close to those generated by effective duration.
This is true for many government notes, bonds, and non-callable corporate notes and
bonds. As credit quality is reduced and call or prepayment options introduced, the
traditional measures diverge more from the effective measures.3

Convexity is defined as the second derivative of price with respect to interest rates
divided by the price, and is a measure of how the duration changes as interest rates

  This section draws on “Effective and Ineffective Duration Measures for Life Insurers”, David Babbel,
in Investment Management for Insurers, Frank Fabozzi Associates, (1999.)

INTERNATIONAL INSURANCE FOUNDATION                           Warsaw, 15 March 2002             14
Convexity is a property associated
with most fixed income instruments
such as bonds. For example, as the
yield-to-maturity on a financial
instrument decreases, its price
increases at an increasing rate.
Convexity measures how the
duration changes as interest rates
change. There is a convex
relationship between the price of a
financial instrument and the interest
rate. The graph on the right shows
the relationship between the price of
a financial instrument and its yield.
The curve gets steeper at higher levels of price. The slope of this curve can be used to
estimate the change in price for very small changes in the yield. A positive convexity
is a good attribute for an asset to have, for example if the interest rate increases by
200 basis points the asset will gain more value than if the interest rate falls by the
same amount.
Liabilities, on the other hand, benefit from negative convexity. This graph illustrates a
price curve for an asset and a liability financial instrument.
Duration only works well for small interest rate changes. The poor approximation of
duration for larger interest rate changes is due to the convex relationship between
price and yield. Duration is a first-order approximation of the price change. We can
improve the approximation by adding a second term convexity.
Duration and convexity are factor sensitivities that describe exposure to parallel shifts
in the yield curve. They can be applied to individual fixed income instruments or to
entire fixed income portfolios.


To address interest rate risk, insurers have relied on measures of duration and
convexity, and the principle of immunization. Immunization seeks to match interest
rate sensitivities of assets and liabilities. By so doing, the company will hopefully be
protected from a change in interest rates.

We consider again a company (such as an insurance company) which has a future
liability stream, and which wants to fund these by a bond (or some other fixed-
income) portfolio. We look for an asset portfolio which has sufficient value to fund
the liabilities, but we relax the requirement of cash-flow matching. Instead, we require
that the sensitivity to changes in interest rates is equal on the asset and liability
sides. That is, we immunize against interest rate changes.
Many insurance (and other) companies got into trouble in the late 1970's and early-
1980’s where interest rates in the U.S. rose. Consider the following example. An
insurance company in 1985 sold a GIC (Guaranteed Investment Contract), worth

INTERNATIONAL INSURANCE FOUNDATION                  Warsaw, 15 March 2002          15
$1,000,000, maturing in 1992 at a rate of 5%. That is, in return for the investment, the
insurance company promises to pay

in 1992, 7 years later. To ensure this liability, the insurance company (in this simple
example) purchased the highest-yielding zero-coupon they could find, a 30-year,
yielding 7%. The face value of this investment was

In 1992, the general level of interest rates had risen by 2%, so the (now 23-year) zero
now had a yield of 9%, and hence the company's investment was worth

--- 358,300 less than the liability! A very modest change in interest rates lead to a
large shortfall, or asset-liability mismatch. The problem here was that the assets and
liabilities were duration-mismatched, i.e., reacted very differently to changes in
interest rates. This problem is precisely what immunization attacks.

Duration Gap Report

Many insurance companies produce a report describing the results of their duration
analysis, called a “duration gap report.” This report provides a snapshot of the
insurer’s asset/liability match at the time of the report. Information in these reports is
highly time-sensitive, as even a small change in interest rates and other economic
factors can cause a dramatic change in the asset/liability gap.

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002           16
                                       Duration Exercise

Duration of a Six-Year Eurobond

Annual coupon rate                    8%
Face Value                    $     1,000
Current Yield to Maturity             8%
Time to Maturity                  6 years

                                                                        Present Value x Duration
                               Time         Cash Flow   Present Value
                                                                             Time        (years)

                                  1         $ 80.00     $      74.07    $   74.07      0.074074
                                  2         $ 80.00     $      68.59    $ 137.17       0.137174
                                  3         $ 80.00     $      63.51    $ 190.52        0.19052
                                  4         $ 80.00     $      58.80    $ 235.21        0.23521
                                  5         $ 80.00     $      54.45    $ 272.23       0.272233
                                  6         $1,080.00   $     680.58    $ 4,083.50     4.083499
                                                        $   1,000.00    $ 4,992.71      4.99271

                            Duration =       4.99271 Years

Asset-Liability Management Strategies
Life insurers operate either as mutual or stock companies and their overall financial
objectives generally involve a target return on capital and the ability to provide
prompt payments to their customers arising out of contractual obligations. Thus,
management’s role in a life insurance company is to be proactive in scanning the
Some technical approaches used in ALM programs include
   Portfolio segmentation by product line
   Cash-flow management
   Portfolio gap analysis, including maturity analysis and interest rate sensitivity
   Simulation analysis, including cash flow testing and dynamic solvency testing
   Optimization analysis
   Hedging strategies for investing

The first step in developing an ALM approach is to set up an ALM committee. After
management has developed comprehensive and understandable asset-liability
portfolios, it is necessary that these are communicated to all levels in an organization.
Suggestions for achieving the determined objectives include appointing a high level
asset-liability committee and appropriating segmentation of investments and financial

ALM Committee

INTERNATIONAL INSURANCE FOUNDATION                          Warsaw, 15 March 2002              17
A high level ALM committee is also called a risk committee. It is comprised of senior
level executives and is responsible to monitor and manage life insurance companies’
asset and liability risks on an ongoing basis. Its tasks include reviews of investment
strategies, pricing, and product development as well as market developments. Life
insurance products sold in the market are sensitive to disintermediation in a high
interest rate environment and interest rates established by life insurers may fall below
those on competing products. The responsibility of this risk committee is to evaluate
products so that pricing and investments can be set to meet companies’ required
returns on equity and other established objectives.

Segmentation of Investments and Financial Measurements
The main approach to ALM over the years has been to create mathematical models of
both the products and of the assets associated with those products. In this effort,
insurers typically classify their products into distinct lines of products having similar
cash-flow patterns and risk characteristics, a process known as portfolio segmentation.
Once analysts have identified and described the characteristics of a given product,
they go about selecting a portfolio of assets that will provide cash inflows that match
timing and amount the insurance company’s cash obligations from the product and yet
also offer a target profit margin.

Segmentation decisions, for example, can be based on the size and risk and
profitability characteristics of the product or line of business. Along with these
decisions many operational issues need to be considered which include: establishing
rules for trading assets among segments; restructuring or refinancing shared
investments; and allocating taxes and expenses. In addition, it is necessary for
companies to have good financial information systems in place because management
needs to know the cash flows from the segmented lines of business in order to make
appropriate investments. Such a segmentation approach can facilitate a life insurer’s
corporate wide-analysis by re-assembling the investments and other segmented
factors. This procedure should provide management with quicker insights to
weaknesses or opportunities in companies’ portfolios and reveal certain offsetting
risks among product lines in given environments.

Life insurance companies have many options to structure adequate asset-portfolios to
match their liability structures and maximize firm value. In a stable environment
where interest rates are constant this would be an easy task, because the outcomes
would be more predictable. However, falling interest rates and fluctuations in the real
estate market values over the last seventeen years have challenged life insurance
companies to develop adequate solutions to achieve their objectives. In addition,
government regulations, agency ratings, and informed customers have further
challenged life insurers’ business strategies.
When evaluating exposures, life insurers should be looking at the aggregate risk
exposure and formulate asset-liability management processes that incorporate all
levels of an organization. With the help of computer technology and sophisticated
software programs such as simulation, life insurers are able to perform different
situational analysis with investing little time before choosing an alternative.

INTERNATIONAL INSURANCE FOUNDATION                  Warsaw, 15 March 2002         18
The Dedication, or Cash-Flow Matching (CFM) Model.
Cash-flow testing became a regulatory requirement in the U.S. as a way to manage
interest rate sensitive products. It is not considered an A/L management technique by
some, but it is worth mentioning as a valuable tool for determining reserve adequacy.
In 1993 the NAIC adopted a Standard Valuation Law which requires insurers to
perform CFT to verify they have sufficient reserves. The testing must follow practices
set down by actuarial standards board, and include the testing the impact that 7
interest rate scenarios would have on reserve sufficiency. The testing must follow
practices established by the Actuarial Standards Board and take into account the many
effects that interest rates have on liabilities and assets. The standard Valuation law
requires insurers to test the cash flows related to all their life products. Once this
testing is completed, the insurer’s valuation actuary is required to sign an actuarial
opinion and memorandum (AOM) that attests to the actuary’s opinion that the
reserves are adequate, given the assets backing them.

Companies such as insurance companies often face a liability stream reaching several
years into the future, for instance, representing future payouts on insurance products
such as life insurance. Usually such future liability streams are stochastic, that is, it is
not known today precisely when they will occur, or how big they will be. For a life
insurance, this depends on customers' longevity and possibly on options built into the
product, such as cancellation rights. Other examples of future liability streams are
home owner mortgages (with fixed or variable payments over a typically 15-30 year
period), lottery payouts (for instance, the Texas Lottery pays out larger prizes in 20
annual installments), etc.

It is often of interest to determine a portfolio of bonds (obligations) whose cash-flows
replicate that of the liability stream. Regulatory committees often require insurance
companies to demonstrate solvency, and one way to do this is to determine a “fair
market value”' of their liabilities by finding a replicating portfolio consisting of
default-free bonds, such as Treasuries. This is similar to determining the present value
(or “expected present value”' in case of stochastic liabilities) of the liabilities using,
for instance the zero-coupon yield curve, but is a more realistic measure because
actually trading bonds, such as par bonds or even corporate or municipal bonds could
also be used (although then credit risk needs to be addressed). Such a market value
could also be used to sell the liability stream. This is done by many lotteries that pay
out over many years but are not in the business of (or are prohibited from) money

The cash-flow testing process consists of four basic steps.
   1. Match the products or product segment liabilities to be tested with the assets
       corresponding to those products. If the cash flow testing is performed for the
       entire company, it is not necessary to separate products and assets.
   2. Select the scenarios to be tested.
   3. Project cash flows. Using the different scenarios, and accounting for the ways
       variables are interrelated, the cash flows would be estimated.
   4. Analyze the results. There are various possible objectives, relating to solvency
       and profitability, that may drive the cash-flow testing.

INTERNATIONAL INSURANCE FOUNDATION                    Warsaw, 15 March 2002           19
The seven interest rate scenarios mandated by the Standard Valuation Law are:

    1. Interest rate remains level
    2. Interest rates increase 0.5% per year for 10 years and then remain level.
    3. Interest rates increase 1% per year for 5 years; decrease 1% per year for 5
       years; then remain level.
    4. Interest rates increase 3% immediately and then remain level.
    5. Interest rates decrease 0.5% per year for 10 years and then remain level.
    6. Interest rates decrease 1% per year for 5 years; increase 1% per year for 5
       years; then remain level.
    7. Interest rates decrease 3% immediately and then remain level.

Consequences of interest rate changes
The importance of analyzing interest rate movements has been shown by experience
in many countries. When market interest rates rise, life insurers may experience the
following financial effects:
     Customers may demand higher crediting rates on their life products, or
       exercise their options to withdraw funds and invest in other higher-yielding
     If excessive surrenders occur, insurers may need to liquidate assets
       unexpectedly or to borrow short-term funds when interest rates are high.
     When interest rates rise, insurer’s experience “spread compression”. This
       refers to the situation when insurers are forced to take a smaller spread
       because customers demand higher rates immediately, even though the average
       yield on insurers’ investment portfolios rise only very slowly.

When market interest rates fall, life insurers, life insurers may experience the
following financial effects:
     Bonds held in the insurer’s portfolio, if purchased earlier at higher market
       rates, gain market value.
     When market interest rates fall, then insurers can lower customers’ crediting
       rates immediately, whereas the average rate of their return on their investment
       portfolio only falls very slowly. Insurers experience “spread expansion”.
     Whenever interest rates fall, callable bonds become more likely to be called,
       and mortgages become more likely to be prepaid. This is essentially because
       owners of mortgages and issuers of bonds will most likely refinance their
       debts at lower rates if they have the option to do so. This means that the
       insurance company will have to accept lower interest rates on their mortgages
       and bond investments.
     When fixed-period investments mature, the insurance company will face a
       reinvestment risk.
     Lower interest rates can raise the market value of insurance companies (due to
       the inverse price-yield relationship). This is turn can reduce insurance
       companies’ cost of capital, leading to greater capital influx and expansion in
       the industry.4

 This section draws from “Managing for Solvency and Profitability in Life and Health Insurance
Companies”, LOMA, (1996.)

INTERNATIONAL INSURANCE FOUNDATION                         Warsaw, 15 March 2002             20
Constructing a model that will predict the relationship between changes in interest
rates and asset and liability cash flows is often a highly specialized, and sophisticated
task. The effect of interest rate changes on the cash-flows of life companies can be
analyzed by considering how these interest rate changes would affect each of the
following cash in and outflows.

             Asset Cash Flows                          Liability Cash Flows
          In                  Out                     In                 Out
Interest income       Asset purchases         Premium income      Claims, settlements
Loan repayment        Transactions costs      Annuity income      Surrenders
Dividend income       Operating expenses                          Operating expenses
Capital gains         Capital losses                              Guaranty-funds

Cash flow matching is deemed an imperfect solution for several reasons:
   Cash flow matching is difficult because of the uncertainty of cash flows.
   Liabilities of life insurers are hard to predict inasmuch as they will be affected by
   consumer's reactions to interest rates changes and the options imbedded in their
   policies. Liabilities of P/L insurers are even more unpredictable because of the
   effect that changes in the economic and legal environment, not to mention
   localized disasters, have on expected claims.

   Matching can also reduce the return on investments. For example, bonds that
   are purchased very close to their issue date are often priced to yield a little less
   than bonds that have already progressed through their term (to make up for the
   decrease in liquidity of such bonds in progress). Buying only bonds at maturity
   may allow insurers to match better, but at the cost of higher return. Moreover,
   some insurers may try to outguess the changes in interest rates to their advantage,
   something which is made difficult if they have an inflexible portfolio of matched

INTERNATIONAL INSURANCE FOUNDATION                   Warsaw, 15 March 2002         21

To top