THE MEASUREMENTAND MANAGEMENTOF INTEREST RATE RISK AUTHORS: Linda A. Dembiec Ms. Dembiec is a Consultant in the St. Louis office of Tillinghast, a Towers Perrin company. She holds a B.S. in Mathematics and Economics from the University of Wisconsin. Ms. Dembiec has extensive professional liability consulting experience as well as a broad pricing background in both personal and commercial lines of insurance. Ms. Dembiec is a Fellow of the Casualty Actuarial Society and a Member of the American Academy of Actuaries. James D. Poaorzelski Mr. Pogorzelski is a Consultant in the Simsbury office of Tillinghast, a He holds an M.B.A. ano a B.S. in Business Towers Perrin company. Administration with a major in Accounting from the State University of Mr. Pogorzelski has experience as a Manager of Financial New York. includins resoonsibilities in the financial olanninq orocess, Plannina. portfolro management and trading. Mr. Pogorzelski‘ is a-Chartered Financial Analyst, a member of the National AICFA Society and FAF Society of Rochester. Vincent

T. Rowland,

Jr.

Mr. Rowland is a Consultant in the Simsbury office of Tillinghast, a Towers Perrin company. He is a graduate of St. Mary's College of Winona, Minnesota, with a B.A. in Mathematics. Mr. Rowland has fourteen years experience in the actuarial and financial management departments of insurance comoanies. includino financial manaoement, financial strategies, Mr. Rowland and the structuring of "investment portfol-ios. is an Associate of the Casualty Actuarial Society and a Member of the American Academy of Actuaries. ABSTRACT: The intent of‘this paper is to provide some basic tools for the measurement and manasemen't of interest rate risk. Interest rate risk has been oresent in the P/C-industry since inception of the first insurance policy: Recent (1980's) results of the P/C industry have heiahtened the awareness of the importance of investment income and its associated risk. Proper management of this risk is a key to the economic success of a P/C company. The actuary should play an imoortant role in the evaluation of this risk and in further developingmanagement techniques. While this paper goes beyond the work previously published in CAS materials, there is much need for additional work in this area. Note to Reader:

It is recommended that with recent publications

71

the reader on similar

be reasonably topics.

familiar

THE MEASUREMENTAND MANAGEMENTOF INTEREST RATE RISK

HENRY FORD II.... "NOBODY CAN REALLY GUARANTEETHE FUTURE. THE BEST WE CAN DO IS THE CHANCES, CALCULATE THE RISKS INVOLVED, ESTIMATE OUR ABILITY WITH THEM, AND THEN MAKE OUR PLANS WITH CONFIDENCE."

SIZE Up TO DEAL

INTRODUCTION

Casualty

actuaries

underwriting regard This

to

investment

concentration

of

results of

insurance

is

since

the to

insurance

reflect

income

circ

rices,,

results

(i.e.,

insurance, ignore

if

and we believe

the balance

investment

risk

in the past,

has become clouded to

product.

Many

states

determining actuary

has to

this

performance

any

to be the case, levels,

income

amount

surplus)

interest

lines

of

from

segregation

of

years.

for and

reflected the

in

the

pricing

business, reserves

for

taxes.

of

the

these

for

business

of

Tax

future

Under

responsibility the

little

underwriting

of

the

portfolios.

in recent

require

to discount

federal

the

on

with

asset

directly

For all

the P/C industry

or

segregate

is

income.

expertise

industry

however,

income

contributions

investment

In this

the

and

(P/C) rate

unrealistic

investment

when

efforts

investment

Reform Act of 1986 has forced investment

interest

results

it

lines

their

Property/Casualty

seemed appropriate

tail

investment

the

performance,

and investment

long

pricing

concentrated

performance

underwriting some

have

total writing

then the actuary

can no longer

rate

asset

risk

or the

side

of

sheet.

paper, risk

we will

discuss

of P/C companies

methods

that

through

Asset/Liability

12

can be used to

help

Management

manage the (ALM).

We

I ‘! will

concentrate

on the actuary's

how to measure interest

rate

the

"matching"

to the

investment their

assets

and liabilities

purpose

1

NE

1970's,

income that

contributions

‘I$$;

in order

to i$,#sure

0

/

interest

rates

was predictable.

on underwriting

profits.

to

underwriting

profit

(see chart

Parcentl

and

of I$!

/I':I

late

efforts

shifted

of

in ALM, the overall

risk.

4

Prior

role

from

below

(‘

500 400 300 200

and Exhibit

were relatively

low and

P/C insurance

companies

concent #fed

Over the years,

however,

the rel$f/ive 1;"

income

and

investment

income

ti?ve

1).

Percent of Proflt Derived from Underwriting ond lnveirtments

4

100

of Profit i'

0 -100

-200 -300 -400

8

Underwrltlng Income 0 Inve8tment Income l

h-e-1980 investment The portfolios

strategy

Early 1950s

was yield

sector.

results

This

Late 1950'S Years

oriented

19601980

with

strategy

of the 1980's. 73

contributed,

II, :%-

a buy and hold

long term (20-30 years)

were predominantly

in the Municipal underwriting

19301950

and heavily

in some ways,

mentality. weighted to the poor

In ,the early desire

1980's,

for

additional

P/C companies

In general,

bonds

at

a

alternative

it

The above circumstances

bring

increased

risk

volatility

increased

long-term,

in

statutory

surplus

at higher the

yields.

generate

current,

losses

in a strong

of the higher ways to

extra

low-yielding The

drain.

combined

industry

In

ratios.

took

of and

the magniiude

gone unmanaged in rates

during

the

the past

income

a company's

for

true

on future

invested

products of

derivative

mortgage

14

coupled

with

results

in

to a need for

ACM.

The P/C

ratio

ALM.

ir

of

desired

vehicles,

recent

to

values

financial

obligation

10 years,

This

surplus

to obtain

The

worth.

of

market

rate

net

ALM has become more feasible

financial

collateralized

asset

point

the

interest

P/C industry.

economic

surplus

end,

of

profitability,

than

level

By 1987 year in

that

faster

exposure

Also,

liquidity

as well,

grown

the

large.

in surplus.

availability

to

have

and a 10% change

futures,

resulted

to sell

to the forefront

factors,

such that

is quite

size

had to find

needs to be managed, thus the need for

assets 2)

change

they

on investment

risk

are additional

rates

advantage

accounting

interest

reliance

risk

industry's

in

of

financial

financial

Exhibit

to take

more business

had previously

substantial

There

environment

losses.

This

the

rate

result

was to write current

risk.

that

would

avoid

3.5

to

in order

was undesirable which

chosen

interest

realized

loss,

words,

economic

E

funds

quickly

cash.

other

the high

years

changes assets would

to

cash flows

etc.).

such

interest

surplus

result

through

products

in

(see

was

in a 35%

the (i.e., as

increased growth options,

Further,

certain

states

(Kentucky

which

require

invested

that

these

It

as to the timing

the

rates,

requirements

of

would

regulations

the

in

for

value

apply

future

ALM is necessary

of

receipts

insurance in order

proposed

At

of

opinion

Standards

risk.

two

the matching

Board

on has

including

instruments,

and credit to

or

a statement

financial

fully

of

Accounting

expected

At least

effect

reasonableness

Financial

the

market

have surfaced.

when providing

requirements

as liabilities.

or

payments

this

time,

company financial to appropriately

as the

assets respond

to

issues.

is

not

our

assets.

in

any way

instruct

The management of

invested

assets

professionals instruct

goal

to

in the

or

inform

managing the level

ALM involves

investment the

reader

assisting

objective

of

in

ALM does

assets

and

rather

the prudent

to

not

will

the

It

not

of

always

the

responsibility

need for

invested of

is our intent,

of

assets

investment

achieving

exact

be present.

of

those

however, measuring

to and

and liabilities.

imply the

management

and the

matching

management

is

the

field.

manaaement of mismatch. almost

is

of assets

necessarily It

on the

as to methods

measure

prudent

liabilities.

mismatch

banking

of the "matching"

techniques

thereby

since

address

Also,

issues

have

reserves

reserves.

as interest

as well

actuary

disclosure

information

proposed

the

and loss

loss

proposed

and accounting

and Pennsylvania)

assets

discounted

well

regulatory

match

The focus

and liabilities, portfolio.

a perfect that should

is

The match

important be risk

of but

control

A fully

matched position

assets have

equal

changes

simplified

inflation, Since

consideration results worth

of

treatment

assuming

inflation

can

rate

in the

present (In

of liabilities. rate

interest

to

rate

and

ignore

equals

liabilities

this the

real

applications

assets

will

and liabilities

value

of

paper

we

effect

interest

differently,

may be needed in actual

of rate.

further The

of ALM.)

insulate

economic

net

changes since:

Market Market

of ALM, therefore,

to the extent

changes

interest

assets

Economic Net Worth =

The purpose

of

affect

matching

from interest

value

nominal

of inflation fully

be one where

in the present

the

i.e.,

would

is

management chooses,

value value not

of Assets of Liabilities

to project

to insulate

its

interest

rates

but

rather,

effects.

HOWTO MEASURE "MATCHING"

Methods stages.

of

measuring This

measurement

paper

matching, will

questions,

or

not

be able

but will

take

analysis

as presented

Duration

is one measure of price

as the weighted value asset,

terms. a portfolio

mismatch,

(See Appendix of assets

1 for

in

and a liability

76

developmental answer

of simple

to

the

duration

paper.1

to interest

in which the

the

an ultimate

the method beyond that

sensitivity

maturity

still

to provide

in R.E. Ferguson's

average

are

the weights

calculation stream.)

of

rates. are

It

stated

duration

is defined in present

for

a single

For coupon bearing an indicator

of price

Note that

To

for

not

It

date,

duration decreases

is clear

that

first

(see

discounted increases

Exhibit

3).

with This

maturities,

but with

wide variances

Duration

is not without

to be

per year)]

thus the above is a

relative

price

volatility. measure

There of only

is

interest

understanding

of duration

for

increases,

a bond are the it

may in

In

so does duration.

maturity, since

what

For example,

a 3% bond priced

important

of

However,

rate.

duration.

an increasing

from 0% to

problems.

an

affects

bond (i.e.,

ranging

technique

obtain

and the discount

interrelationship

coupons

measurement

in order

of coupons

MD = Dl,

the components

payments,

seen stated

as a complete

must

coupon bond, as maturity

a deeply

at

to maturity/number

we

duration,

how their

the case of a zero

as follows

duration.

the coupon

be clear

the case of

t (yield

coupon bonds and liabilities,

for

it.

must be modified

movement.

comprehend

influences maturity

zero

formula

help

duration

(MD) = Dl/[l

~$~~i~~

general

bonds,

then

in recent

17% resulting

to yield

15%),

eventually

years

in bonds with

we have the

same

in cash flows.

It

is best when it

are problems, rate

risk.

under the following

77

is used as a measure of

however, Duration(D1) conditions:

with

using

duration

is an appropriate

(1)

Infinitesimal

(2)

Parallel

(3)

Instantaneous

(4)

Flat

changes shifts

yield

in yield shifts

restrictions,

interest

but

Unfortunately, interest

this

is is

B% to 9%), potential

Empirical 70% of

tests

inaccurate

rate

both

duration

measure within

that

close

yield. maturity the actual

(D2) It of

the price

cash

simple

rate

change

as the weighted

of convexity

examples

of

convexity

articles.

G~B~9

concept

from

about (i.e.,

more risk.

Each

of interest

rate

from

any

a type

can be insulated

Convexity

in duration average helps

almost

01 and D2, removes

estimated

be

found

78

in

a

relative

to

of the square

explain

is shown in Appendix can

changing

can remove

eliminate

measures,

in

01 measurement.

matching

model measures

shifts

risk.14

as the

flows.

rates

matching

will

a portfolio

large

the simple

duration(D1)

of a bond and the price

the calculation

only

of stable

environments.

Given

interest

when using

in times rate

most.

(i.e.,

and convexity(D2))

is defined

is calculated

points

best

interest

The use of two duration

to 90% of interest

Convexity

volatile

a multi-factor

risk.

works

The use of a multi-factor

risk.

duration(D1)

interest

analysis

needed the

develop

When used collectively, of

curves

in

when ALM is

errors

matching

type

in yield

duration

indicate

interest

risk.

curves

such as 100 basis

rates,

rates

curves

Because of these rates,

in interest

the

3.

Dl.

Further

number

of

in

of the time to

difference

by using

changes

between

An example of discussions the

and

referenced

The

affect

of

duration's

adding

suggested

representative both

the variance

for

estimation

of

for

price

to

between

a zero

the

this

duration

price

coupon bond.

to

change

to

a more

the calculations

Appendix

of

28 graphically

when duration

alone

is used

When convexity

above calculation.

variance

is

and yield

2A displays

from convexity)

from

formula,

is dramatically

reduced

is

as shown

2C.

Using 01 and 02, the equation be written

convexity

Appendix

relationship.

(gain/(loss)

added to the pricing

of

relationship

and convexity

displays

in Appendix

element

linear

curved

duration

the

the

for

the change in price

of a single

bond can now

as:

chgP

=

-DDl(chgI)

chgP

=

Change in price

DDl

a

Dollar

chgI

=

Change in interest

DDE

=

Dollar

R

=

Residual

t l/2

DD2 (chgI)2

+ R

where:

For an entire measured present

portfolio,

similarly. values

duration

convexity

(price

of

Dl

of each.

79

duration)

rate (price

the change in present The values

x modified

x convexity)

value

and D2 would

or market merely

value be the

would be weighted

Like

to

duration,

fully

understand

convexity

we need

to

understand

its

characteristics:

(1)

Positive

convexity

a larger

percentage

rates.

(This

Negative

(2)

Given

relationship

Doubling

(4)

The mere matching from are

interest quite

convex-shaped

volatility. of

opposite

(positive

stated

would

this

ensure

It

80

opposite

the higher

as liability

cash

the

the convexity.

protection

company assets is

value

of the P/C industry.

be the case because:

the

convexity.

does not

market

yield

curve.)

the coupon,

(as well

more than double

convexity.

in

in

curve.

coupons

P/C insurance

convexity)

5, exists

will

result

increases

employ

-- the higher zero

rates

in a convex

would

have the least

duration(D1)

shown in Exhibit that

will

the duration

of

rate often

Therefore,

than

result

a concave

duration

in yield

price

therefore,

Bonds of equal

streams)

in

would

and produce

the convexity. flow

when decreases

movement

convexity,

relationship

(3)

exists

reasonable profile

D. F. Babble

surplus

and liabilities to

of

of

assume that liabilities, and R. Stricker

a as

(1)

When interest

rates

may be slowed costs

(2)

down by the

(increasing

When interest

rates

fall,

this

a concave-shaped

convexity

higher

yields

instruments.

basis

In

Products,

points

order

determine

required

liabilities

is

determine

the

appropriate current

Assets rate

market

Treasury

should of

interest liabilities of risk

free

with with

to

for

negative

(MBS),

Callable

investors similar

are

quality

approximately

the same

a yield

spread

present

values using

asset.

The

discount

Since

changes

have

our

purpose

on the

be discounted

securities.

81

display

attract

relative

of

One reason

value

that

should

to

profile

to present

forward. rate

frequency

value

Backed Securities

convexity,

be discounted for

in claim

values

of

50-150

security.

or

return

market

in securities

MBS security

duration

effect

rates

claim

a P/C company.

may be purchased

so straight

of

for

securities

a typical

not

value

on ultimate

market

The enticements

these

above a comparable

determined. market

for

as Treasuries

to

convexity)

investments

etc.

For example,

strength

values

in liability

of an increase

such as Mortgage

offered

market

hazards.

5) is typical

characteristics, Derivative

credit

in moral

many of the industry's

Bonds,

inflation

the increase

(negative

(as shown in Exhibit is that

of

by the effect

caused by an increase

assets

effect

in liability

severity).

may be accelerated

Conversely,

the decrease

rise,

in

must the

be

implied rate

for

ALM is

to

market

values,

the

to present

value

using

Additional

complications Some of

and convexity. Appendix

arise

in the actual

the

more

practice

common ones

of calculating are

duration

discussed

further

in

5.

APPLYING ALH TO THE P/C INDUSTRY

There

are

basically

industries.

The first

most banks designed

sophistication. which

is

further

is a maturity

and thrifts. modeling

methods

three

Second,

still

in

the

in Appendix

6.

simulation

In this

which

of

which

stage. 4

the

The three

paper we will

which

apply

duration methods

other used by

are

varying

have

is

in

is currently

approaches,

and most modern,

development

used

ALM applications

gap approach,

each

techniques, The third,

of

computer

levels

of

gap approach, are

the duration

described

gap approach

to the P/C industry.

The first

step

in the P/C industry

of assets

that

are required

exercise

is

following

not

trivial

application

to be specifically and requires

at

least

of ALM is to select matched with

liabilities.

temporary

resolution

the subset This of

the

runoff

or

issues:

(1)

How should ongoing

(2)

the

operation

be reviewed

(liquidation,

concern)?

Which assets

and liabilities

should

82

be included?

(3)

How should expense

does

not

that

probably

the best

views

that

this

is

only

be considered

with

the less

associated

payout

for

a liquidation

approach

(including

most companies

and most sophisticated

situation.

to

and

value,

approach

loss

expected

of the

This

concern

sufficient

it

limit

an

this

is

is our position

approach

experience

paper will

day-to-day

recommends taking

however,

runoff

with

their

Theoretically,

concern.

approach;

by an organization

complex

loss

ultimate

W. H. Penning

mentality.

extension

the

pattern)?

the company as an ongoing

an advanced

with

and should and expertise

the discussion

to the

scenario.

Since

the

surplus assets

objective

is

asset

other

premiums,

bills

tax

of these

future estate, purchase

side,

naturally of

income

rate

the

steam of

other

assets

such

reinsurance receivables

of

expected

in lieu

of

owned

invested as

extent

definition

to which of

whose market

from

parents into

to be received.

the periodic

83

real

assets

agents'

the company has entered

cash is

the

estate,

included value

is

uncollected

payments,

subsidiaries,

an agreement In the case

to use a portion cash payment

of of

above

as the market or

on loss or

the

as well

balances

recoverable

management has made the decision property

changes,

exception all

receivable,

assets,

rate

and manage the

encompass any sub-category

includes

recoverable,

determine

changes.

with

reported

to

interest

should

On the definition

ALM is

from

or liabilities by interest

value

of

imunized

affected

all

and selected

seem desirable

management with

runoff

uncertainty

amounts be considered

payout

It

the

etc.

For

in which

some

of

their

rent.

federal

owned assets

real

to

Management

in

has,

"matched"

essence,

Therefore,

for

practical

mortgage

liability)

reasoning

can

processing

equipment).

be

extended

side,

this

loss

Additionally, fees,

funds

borrowed

liability

other

payments

applicable asset

liability.

(as well This

ALM analysis. assets

"non-invested"

as any line

data

(i.e.,

require

loss

and loss

adjustment

reserves.

In

one should

estimate

and include

the

that

the inclusion

of

would

premium reserves,

are associated

such as contingent

money, drafts

commissions,

outstanding,

etc.

with other

should

of numerous

these

reserves.

expenses,

be included

taxes,

within

the

(i.e.,

the

category.

The remaining uncertainty addition

issues in

involve

ultimate

to the "best

ALM should development. management's

include

the

values,

estimates" "safety

adversity additional

quantifying

such "safety

to

reduce

the

is

recommended

loss

of

to

amounts

payout

and

of these

values,

the liabilities

to

these

account margins

(as

margins". for

the

should its

needs to

Another

payout

for

respects

research

rate

expense

actual

risk

actuarial

discount

and loss

margins"

The magnitude

Significant

is

to

definition

and expense

the estate

from further

to the stated

the case of the unearned

with

the owned real

purposes,

in addition

projected

assets

can be removed

On the liability liabilities

these

be

be done

below

the

In

utilized risk

of

for

adverse

a reflection

remaining

way of reflecting

liabilities

patterns).

in

of

surplus). this

area

"safety risk

of

margin"

free

market

rate.

It

categories.

that

The first

the category

assets,

once

(Asset

84

I)

defined, is that

be segregated of assets

into

at market

two

value,

supporting

the

II)

(Asset

is that

net worth measure

market

of the

levels

the surplus

Exhibit

6 displays

matched

reported factor

implement vehicles. entire interest

the

present

total

of

with

category

to the economic

we are able

assets

the

to

separately

liability

funds

Alternatively,

the

of

available

reflect

are

it

claims.

places

duration(s)

it on the

while

rates or

still

value

is

only the

change

in

of

assets

there

will

While

cash flow

not

the

of

liabilities,

the

is

matched

investments

present

durations

equal,

immunity,

the

assets

modified

to cover

to

the minimum value

in interest

firm's

totally the

Here,

be equal

the

rate

limitations

insurer.

to

terms,

interest

always

cost

selection

and be

to

investment

can utilize

effectively

a

matching

effective of

approach

value

the

controlling

risk.

Once the assets

and liabilities

measured

appropriate

following

of

If

the

rate

second

corresponds

associated

a change

will

value

value

due to

universe

risk

value

convexities).

for

assets,

that

measurement

market

required

the

has been determined

equal

sufficient

which

our typical

Assuming

in

assets,

rate

graphically

can alter

liabilities,

The

liabilities.

funds.

duration

(assuming

is

interest

liabilities.

modified

the

By segregating of

assets

that

of

of the remaining

surplus.

versus

of

value

using

examples

we have

have been determined, duration used

discussed

on page 6) measurement

section,

actual

application

in

measures the

for

modified

and market duration

simplicity.

the

convexity.

85

P/C

the duration

industry

values. (MD,

As discussed should

as

gap can be

In the previously

in the previous normally

include

In order

to calculate

the dollar dollar

value

duration

affected

durations.

assets,

in market

and liabilities years.

of assets other

of Appendix

4A also

and liabilities

words,

in the true

surplus

thus

equal

is

of

economic

value

the modified

of surplus

duration year

of surplus.

duration

derive

the proper

is

mismatch In

an approximate

The modified caused

assets

surplus.

produce

effect

for

to

mismatch

gap of 16 for will

(DD).

respective

duration

the

points

compounded by a levered

by their

whose ratio

in a duration

100 basis

duration

for

duration

when assets

for

are

not

to liabilities.

Given the

above assumptions assets

Appendix

4B shows

the

calculation

scenario

(A) [using

all

assets].

are greater

in order

we can easily

(MD) for

than

of liabilities.

to totally

surplus)

insulate of

surplus

the

proper

Due to the levered

the required

Under scenario

duration

Value

of Assets

Changes in the Market

Value

of Liabilities

(B)

maintain

the

segregates same insulated

any remaining

(see Appendix

the

assets

assets surplus into

into

4C).

86

duration

interest

asset

MD to

be 3 under

(i.e.,

when assets

impact

of assets

will

rate

risk.

not equal

that

the following:

=

the

position cash

modified

from

(A) we have now achieved

Changes in the Market

Scenario

places

an insurer

respectively,

can result

we must account

values

shows how the above three

a change in rates

16% change

market

is 25%. Given

and four,

surplus,

known as dollar

rates,

4A displays

terms,

seven

for

by multiplying

Appendix value

duration

by interest

is calculated

modified

three

the modified

(Asset

two

categories.

as in Scenario

II),

having

In (A),

order

Scenario

a duration

of

to (B) zero

What remains yields

is

change

assumptions

to

derive

by

for

100 basis

the

the

interest

rate

quantify

the

interest

risk

effects

rate

(i.e.,

implied

assets

risk

under

how much basis

from

At this

point

II.

risk

(or

surplus

stockho7ders

and policyholders

underwriting

obligation

amount of

assets.

exposure

Maintenance strategy.

wi'll

To avoid

this, durations

reduced

if the

"the

convexity

liabilities"8.

tend the

present

of

assured

matching

apart, must

rate

Under

scenarios.

changes

is

isolated

to the as to

is acceptable.

In this

way,

the

of

company's

of

fulfillment liabilities

line.

The

convexity

is

utilized.

assets assets

Some observations

is

the

with

the

better

the

required control

of

(under

resulting

in dollar

should of duration

Dl)

duration

of

dollar

In a totally the

of the assets

periodically

problem

exceeds

87

by no means a buy-hold

durations

be rebalanced

in

these

to

4C shows how to

duration

portfolio

the dollar

of

required

risk.

portfolio

value

not

management has been given

to drift

back

are

investment

becomes a management decision

asset/liability

passes,

dollar

where

rate

a matched

As time

liabilities

dollar

of

the

Additionally,

to interest

which

the

I

volatility) are

by

altering

if

=

interest it

on surplus

has been maintained:

Value of Asset

surplus

impact

Appendix

relationship

Changes in the Market

of Asset

II),

different

Value of Liabilities

exposure

when

(Asset

Changes in the Market

on economic

the

on liabilities.

B, C and D the following

The impact

its

basis

points)

remaining

immunize

Scenarios

the

present

exceed drift

mismatch.

to

bring

the

duration

drift

is

immunized value the

and

of

liabilities,

convexity

of assets

scenario,

follow:

of

the

(1)

As time

the

passes,

change in interest

duration

of

any

asset

shortens

(given

no

rates).

(2)

Zero coupon bond durations

(3)

Coupon bond durations

shorten

shorten

linearly

more slowly

year

to year.

than

zero

coupon

bond

durations.

For P/C industry particular

the

age of the

liability

portfolio

will

duration

drift,

line's

However,

due

accident that

liabilities,

to

year

duration

as an accident

always

the

new accident

If

be generalized. its

duration

payments

are

heavily

may have a shorter

done by Goldman Sachs, the durations

general

liability

other the

hand, accident

medical year

malpractice ages.

should

duration

The duration

remains of

Mix of business

(2)

Relative

(3)

Pattern

age of loss of growth

in new business

88

line.

age

might

first

and

appear

year,

a

year.

In

compensation

and

accident

declining. its

a

Such is not

in the

a P/C company's

and LAE reserves

it

shorter.

ultimately below

that

claim

glance

of both workers'

depend on the following:

(1)

get

comprise

of

between

than an older

before

that

the duration

At first

duration

dramatically

years

concentrated

a study

increase

affect

relationship

ages,

year

case. year

cannot

the

accident

original liabilities

On the level

as will

The actuary

is now challenged

(1)

Determine its

(2)

ALM methods to:

the P/C company's

current

Asset

to utilize

liabilities

level

by measuring

I and liabilities;

rate

rate

the

risk

amount of

underlying mismatch

of

and

Aid company management in its interest

of interest

risk

understanding

inherent

in the

of the total

company's

level

current

of

investment

strategy.

Once the knowledge

of investment

be managed through investment

policies.

established

policy

specific

rate

risk

investment

In addition, objectives

for

a company is understood,

strategies

actual

that

results

to determine

if

correspond

can

to overall

can be measured

a portfolio

it

against

strategy

the

was truly

effective.

Through ALM, management can assess on the true making

economic

certain

a desired

level

assumed interest

the adequacy potential

surplus.

of reserves. growth

Additionally,

the

implied

of acceptable rate

forecasts,

Positive in premium since

the level

the

sales

it

is

This

in economic supported places

rate

informed

risk

in order

is a composite

strength

of surplus

net worth by growth

a premium

risk

decision

has assimulated

the perceived

market

89

risk

returns.

changes

of interest

Only through

of the company.

can a company understand

to attain

that

net worth

and control

will in

of and

ensure

statutory

on consistency,

sustained

growth

should

allow

for

higher

acceptable

P/E ratios

for

a firm's

stock.

With

certain

financial

institutions

interest

rate

survival)

of

understand

and control

ALM, a link

control

this

risk.

its

It

portfolio

strategy

management to limit underlying

existing

value.

thoughts

should

play

day-to-day

However,

a key

role

in

of rate

with

to which

considerable

within

developing

management tool.

90

similar worth

the

to

base,

growth

other

subject

to

surplus

(and possibly

management's

ability

to

risk.

can be established

external

stated

market

to bring

that

utilizing

of an

goals

forces

together

additional tool

to

the creation

company's

the P/C industry. and

is

asset

the mechanism for

and meaningful

basis

invested the future

paper has attempted

be done to make ALM an effective on a practical,

its

net

and liabilities

provide

the extent

on ALM.

of

to interest

consistent

This

economic

income,

assets

can also

inherently

be a function

exposure

between

is

true

on investment

a P/C company will

Through

true

its

Because of the size

risk.

the dependency

allow

P/C industry

and thus

leverage,

objective

the

exceptions,

and

affect

is

many of the

research

needs to

can be implemented The actuary this

very

can and important

PROPERTY AND CASULAlY

INSURANCE INDUSTRY PROFIT BREAKDOWN UNDERWRITING -vs.- INVESTMENTS

1987 (millions)

1987 (percentage)

Underwriting

($10,620)

-80%

Investments

$23,960 --_---__ $13,340

180% --__ 100%

Net Profit

1930 - 1950

Early 1950's

Late 1950's

-

1960 - 1980

1980 -1987

-

Underwriting

63%

40%

10%

-15%

-343%

Investments

37% ___-_ 100%

60%

90%

115% e---v 100%

443% __-__ 100% --s-m

Net Profit

im

loos

Source : Best's

91

Aggregates

& Averages

Property

& Casualty Ins. Industry Assets vs. Surplus

Growth

Billions 500 -

300 200 100 -

45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87

Years --

Source:

Best’s

Aggregates

Assets

8 Averages

-+

Surplus

Duration vs. Maturity Duration selling

14

to Yield

15%

12 selling

15% coupon

10

to Yield

6%

8 3%Coupon - Selling

to Yield

15%

6

/-_.

1

5

-----

10

15

I

I

I

I

20

25

30

35

Years to Maturity

40

Various Yield Curve Shifts Yield

P

Assessment Market

of Basis Risk in Surplus

Value

Liabilities

Assets

(Decrease)

(Initial)

Change

in Yield

Determination Dedicated $1000

-

Market

of Assets

to Liabilities

Value Exposed Net Worth

C B

$800

A

Hfnimum Hatching Requirements for Policyholders

$600

Assets A B c

Initial Estimate of Liability Adjustment for Variance Error Adjustment for Variance Error

Liabilities Harket Value in Ultimate Payout in Payout Pattern

WEIGHTEDAVERAGE TERM TO KATURITY (Assuming Annual Interest Payments) Bond A __---$1,000 Face Value with 4% coupon Maturing in 10 years, discounted at 8% 2

1 Year

1 2 3 4 5 6 i 9 10

Present Value 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632

Weighted

4

3

PV of PV as % Duration FlOW of Price Components (1 * 5) (2 * 3)

Cash Flow

40 40 40 40 40 40 40 40

37.04 34.29 31.75 29.40 27.22 25.21 23.34 21.61 20.01 481.72 ___--731.60

10%

Average

6

5

5.06% 4.69% 4.34% 4.02% 3.72% 3.45% 3.19% 2.95% 2.74% 65.85% ___-__ 100.00%

Term to Maturity

0.0506 0.0937 0.1302 0.1608 0.1861 0.2067 0.2233 0.2363 0.2462 6.5845 ____-_ 8.12

: 8.12 years

Bond B _---_$1,000 Face Value with 10% coupon Maturing in 12 years, discounted at 8% 1 YMLK

1 2 3 4 2 7 8 9 :"1 12

2 Present Value

0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971

Weighted

3 Cash Flow

100 100 100 100 100 100 100 100 100 100 100 1100

Average

4

5

6

PV of PV as % Duration of Price Components Flow (2 * 3) (1 * 5) 92.59 85.73 79.38 73.50 68.06 63.02 58.35 54.03 50.02 46.32 42.89 436.83 __- _- _ 1150.72 --

8.05% 7.45% 6.90% 6.39% 5.91% 5.48% 5.07% 4.70% 4.35% 4.03% 3.73% 37.96% _ _- _ _100.00%

Term to Maturity

91

0.0805 0.1490 0.2070 0.2555 0.2957 0.3286 0.3549 0.3756 0.3913 0.4025 0.4100 4.5553 _____7.81

: 7.81 years

ia WEIGHTED AVERAGE TERM TO MATURITY (Assuming Annual Interest Payments) Given: Bond A $1,000 Face Value with 4% coupon Maturing in 10 years, discounted Priced at $731.60 Weighted Average Term to Maturity

at

8%

- 8.12

years

$1,000 Face Value with 10% coupon Maturing in 12 years, discounted at 8% Priced at $1,150.72 Weighted Average Term to Maturity - 7.81

years

Bond B

Calculation: Portfolio Weighted Average for Assets A and B

Term to Maturity

(D)

Formula: Portfolio

(D) -(Price

Portfolio

(D) = j9731.60

Portfolio

(D) = 7.93

A * Duration A) + [Price (Price A + Price B) l 8.12) ($731.60

years

98

+ ($1.150.172 * $1,150.72)

B * Duration * 7.811

B:

Appndix

WEIGHTED AVERAGE TERM TO MATURITY (Assuming Midyear Payments) $1,000 Loss Reserve Discounted at 9%

1 Year

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5

2 Present Value

0.9578 0.8787 0.8062 0.7396 0.6785 0.6225 0.5711 0.5240 0.4807 0.4410 0.4046 0.3712 0.3405 0.3124 0.2866 0.2630 0.2412 0.2213 0.2031 0.1863 0.1709 0.1568 0.1438

3

4

Payment Cash Flow Pattern

9.2% 16.2% 14.7% 15.1% 11.0% 8.9% 5.1% 4.3% 2.2% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 0.3%

_---__ Average

88.12 142.27 118.35 111.83 74.50 55.47 29.13

42.7

22.37

21.6 10.1 10.1 10.1 10.1 10.1 10.1 10.1 10.1 10.1 10.1 10.1 10.1 10.1 2.6

10.38 4.45 4.09 3.75 3.44 3.16 2.89 2.66 2.44 2.24 2.05 1.88 1.73 1.58

1000.0

0.37 __--__

689.1

Term to Maturity

99

7

PV as a Duration of Price Comments (l'* 6) * 4)

92.0 161.9 146.8 151.2 109.8 89.1 51.0

------

6

PV of Flow

(2

100.00% -Weighted

5

12.79% 0.0639 20.64% 0.3097 17.17% 0.4293 16.23% 0.5680 10.81% 0.4865 8.05% 0.4427 4.23% 0.2747 3.25% 0.2435 1.51% 0.1281 0.65% 0.0614 0.59% 0.0623 0.54% 0.0626 0.50% 0.0624 0.46% 0.0618 0.42% 0.0609 0.39% 0.0597 0.35% 0.0583 0.32% 0.0568 0.30% 0.0551 0.27% 0.0532 0.25% 0.0513 0.23% 0.0494 0.05% 0.0122 _- - - _ _ __- _ - 100.00% 3.7 -: 3.7

years

ic

DURATION and CONVEXITY CALCUIATIONS (Assuming Annual Interest Payments)

Bond C -____$1,000 Face Value with 0% coupon Maturing in 10 years, discounted at 10% 1

2

Year

Present Value

3

4

Cash Flow

PV of Flow

5

6

7

PV as % Duration of Price Components (1 * 5)

(2 * 3) 1

0.9091

0

0.00

0.00

: 4 5 6 7

0.7513 0.8264 0.6830 0.6209 0.5645 0.5132

z 0 0 0 i

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

i 10

0.4665 0.4241 0.3855

100:

0.00 385.54 _- _- - _- - _ 385.54

Weighted

Average

Term to Maturity

Weighted

Average

Term to Maturity

0.00 1.00

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 10.0000 _- _ _ _ _ _ - _ 10.00

Squared

Convexity Components (12*

5)

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 ~0.00000 - - - - - __- -

100.00

: 10 years

(Duration)

: 100

(Convexity)

interest % Channe

Rate Sensitivity

in Price

140% 120% Qaln From Convexity

100% 80%

Positive

60%

Convexity

40% 20% 0% -20% -40% -60% -80% -60%

-80%

-40%

-20%

0%

% Change --

Estimated

Change

Price Based Duration

on

in

20%

40%

60%

in Yield +--

Actual

Change Price

in

80%

Interest % Change

Rate Sensitivity

in Price

Estimated Changa in Price and Convexity

Actual

-80%

-60%

-40%

Based on Duration

Change in Price

-20%

0%

% Change

20%

in Yield

40%

60%

80%

K. 0”

DURATIONand CONVEXITYCALCULATIONS (Assuming Annual Interest Payments)

Appendix

3

Bond D __.__$1,000 Face Value with 10.65% coupon Maturing in 5 years, discounted at 10.65% 1

2

Year Discount Rate

3

4

Present Cash Flow Value

5

6

8

7

Convexity Components

PV as % Duration of Price Components

PV of Flow

2 (1 * 6)

(1 * 6)

(3 * 4) 1 2 3

10.65% 0.9038 10.65% 0.8168 10.65% 0.7382

106.5 106.5 106.5

96.25 86.99 78.61

0.10 0.09 0.08

0.0962 0.1740 0.2358

) 1 (

45

10.65% 0.6671 0.6029

106.5 1106.5

71.05 667.11 ----w-.-m 1000.00

0.07 0.67

03%: . e-e*.*-..4.13

I

: 4.13 years Squared : 18.97

Weighted Average Term to Maturity Weighted Average Term to Maturity

1

(Duration) (Convexity)

Maturing

$1,000 Face Value with 10.65% coupon in 5 years, discounted at implied Term Structure

2

3

Year Discount Rate

4

Present Cash Flow Value

5

6

PV of Flow

8.00% 9.05% 9.86% 10.42% 10.89%

0.9259 0.8409 0.7542 0.6727 0.5964

106.5 106.5 106.5 106.5 1106.5

98.61 89.56 80.32 71.64 659.92 __-----__ 1000.00

Weighted Average Term to Haturity Weighted Average Term to Maturity

103

8

7

Convexity Components

PV as % Duration of Price Components

2 (1 * 6)

(1 * 6)

(3 * 4) 1 2 3 4 5

0.096 0.348 0.708 1.137 16.678 _- - - _- - 18.97 -m--s

0.10 0.09 0.08 0.07 0.66

0.0986 0.1791 0.2410 0.2865 3.2994 -_--_---4.10

: 4.10 years Squared : 18.82

1 ( 1 ) 1

0.099 0.358 0.723 1.146 16.497 __--- -_18.82 w-m--

(Duration) (Convexity)

CALCULATIONOF MODIFIED DOLLARDURATIONS

(2)

(3)

MODIFIED DURATION

MODIFIED DOLLAR DURATION

(1) MARKET VALUE

ASSETS LIABILITIES SURPLUS

EFFECTOF YIELDS INCREASING 100 basis points

ASSETS ,

LIABILITIES SURPLUS

MARKET VALUE

CHANGE

CHANGE

$930

($70)

-7.00%

$720 __.__ $210

($30) __-__ ($40)

-4.00% --____ -16.00%

104

Agzendix

4A

Appendix

I

4-B

~

DERIVATION OF MD FOR TOTAL ASSET PORTFOLIO TO IMMUNIZE SURPLUS

Initial

Scenario

IA) (5) Modified Duration

Portfolio

(2)

(1) Market Value

Modified Duration

(31 Dollar Duration

fk!r?et Value

(1)x(2) Assets

$1,000

7

$7,000

750

4

3,000

250

16

$4,000

Liabilities Surplus

$

Effect

of Yields

100 Basis Market Value

Increasing Points

Change

(61/(4)

$1,000

S

3

$3,000

750 *

4*

3.000

250

0

Effect

of

Yields

100 Basis

Chanqe

DJfi)ar Duration

Market Value

s

Increasing Points

Change

Chanoe

Assets

$ 930

($70)

-7.00%

$ 970

($301

-3.00%

Liabilities

720

1

-4.06%

.Jj.Q

f-al.

-4.00%

Surplus

$ 210

($401

-16.00%

* Constant

105

$ 250

SO

0.00%

* 0

ApLzendix4c

ASSESSMENTOF BASIS RISK ON SURPLUS

ZERO BASIS RISK DERIVED FOR TOTAL PORTFOLIO

ALTERNATIVE ZERO BASIS RISK DERIVED FOR TOTAL PORTFOLIO

SCENERIO(A)

SCENERIO (B)

(2)

(1)

ASSET (I) ASSET (II) TOTAL

--m--a

-se.

$1,000

3

(5)

(4)

$3,000 $0 -----

$3,000

(6)

MARKETMODIFIED DOLIAR VALUE DURATION DURATION

MARKETMODIFIED DOLLAR VALUE DURATIONDURATION

I

__--__ _--i1 $1,000 3

_.___ $3,000

I LIABILITIES SURPLUS

$750 -m---e $250 --

4 -.me 0

BASIS RISK :

$3,000

$750 me---_ $250 m--

I

4 .m_0

0.00%

0.00%

IMMUNIZE INTEREST RISK ON LIABILITIES (7)

ASSET (I) ASSET (II) TOTAL LIABILITIES SURPLUS BASIS RISK :

(8)

$3,000 --_-$0

(10)

(9)

ONLY

12)

(11)

MARKETMODIFIED DOIJAR VALUE DURATIONDURATION

MARKETMODIFIED DOLLAR VALUE DURATION DURATION

SCENERIO (C)

SCENERIO (D)

;::i -e--e_ $1,000 $750

.-----

$250 m-

41 .-__ 3.25

$3,000 $250 ----o-m $3,250

/

4

$3,000

I )

1

$250

I

.-__ 1.00%

Basis Risk defined : The impact on Surplus

_______ -I

if yields

106

1 (

$750 $250 _____. $1,000 $750

1: __-_ 5.5

$3,000 $2,500 ___ ___$5,500

4

$3,000

$250

10

$2,500

---

10.00%

__----

__-_

change by 100 basis

__-___-

points.

Appendix

5-A

CONSIDERATIONS WHEN APPLYING ALM

Exhibit

4 graphically

(additive); by

Dl

simultaneously

and

are

can

protecting

small,

safeguarded

by additionally

of

flows

cash

multiple

minimize

and control

measures

would

P/C companies,

this

Like

type

a matter

Policy

will

of

both

non-callable

portfolio

would

not

risk

of

small

02

twists. agree

that

This

type

of

average

time

to maturity

duration

A perfect

the and

cash

risk

measures

on the

other

of primarily convexity

change

of

when compared

bonds.

107

the

match

flow

is

(Dl,

will

Mortgage

convexity to a portfolio

of

for

Backed

is of

style. will

goals.

judgmental.

securities

will

interest

rate

different (D3)

most

portfolio.

and desired be less

to

duration

matching

investment

aversion

under

all

management

of

hand,

ability

But,

and type

type risk

of

match.

portfolio

degree

the

management's

and negative

situation

and

management

be an acceptable

positive

in this

risks

Matching

most would

three

allows

a true

policy

of

shifts

world.

these

risk. to

composed

rate

of

management,

a company's

The

real

rate

shifts.

D3, the weighted

rate

a portfolio

environments.

the

[parallel

interest

comforting,

duration

characteristics,

For example,

important

the

rate

shifts

risk.

of

be a reflection

The portfolio

exhibit

the

interest

of

is

The matching

measures

steer

to

matching

95% of

Managing

any other

closer

cubed.

D2 and D3) removes

be

are

of

parallel

shifts

rate

type

interest large

parallel

interest The

random].

against

against shifts

possible

parallel

protect

multiplicative

the

three

multiplicative;

protected

While

displays

relatively pure

fixed

more income,

Appendix

The

assumption

discounted cash

at

flow

average

a flat

the

duration

would

this

may lead

material

(A)

of

the

a more cases.

implied

had led

entire

some to

bond's

is

when

yield

believe to

structure the

accurate

measure,

Appendix

3 derives

cash

flows

are

that

since

each

maturity,

the

The way to

inaccurate. term

all

of

eliminate

interest

this

rates.

increase

in

above

measures

the

weighted

While

precision

is

of

Dl

not

and D2

two methods:

Derives

zero

the

is

at the

portfolio

with

following

the

(B)

discounted

to

most

on the

curve This

is

be to work

in

yield

same rate.

stream

bias

based

of

5-B

and uses

the

relationship coupon

Assumes

term

structure

between

bonds

a flat

(spot

yield

the

yield

of

interest

of

a par

rates bond

implied

and yields

by in

rates).

curve,

discounting

at

the

bond's

yield

to

maturity.

It This

can be seen that can

supported

be

the

extended

in an article

and Quantitative

Analysis,

relative to

portfolio

difference

(Dl)

analysis.

by D. R. Chambers March,

in

1988.

108

appearing

and (D2) This

is

insignificant.

conclusion in the

Journal

is of

further Finance

Appendix

Another

consideration

portfolio

(i.e.,

overall

portfolio

identical. change

the

portfolio

weighted

this

value

overall

portfolio

For

of

durations value

of

If

there

different

the

is the

exists duration

be first

(i.e.,

a relationship would

taxable

by 0.8

spreads

if

the

it

a 0.8% average of

is

for

spreads

constant, the

are

be multiplied times

the

present

greater

adding

the

calculation

of

the

proportional

to

the

by the than

by 1.20

In

spread

factor.

AAA yields,

before

being

the present

duration.

are

of the

of the

be multiplied

109

before

not

AAA, BBB, etc.).

are

be correct

a portfolio between

duration

(i.e.,

multiplied

assets

value

The

the

are

may imply

a present

a mixed

in using

sectors

rate

inaccurate.

in

portfolio

case where

assets

1.20

investment

qualities

should

are

overall

durations

develops

of

duration.

would

durations

BBBs should

is

difference

However,

the

An issue

situation,

asset

durations

BBB yields

into

this

duration

the

the

portfolio

the

duration.

example

of different

that

rates,

in

the

be multiplied

different

if

weighted

A final

involves

interest

example,

first

overall

weighted

in

duration

should

assuming

present

In

rate.

the

bonds).

changes

portfolio

into

example

case,

level

the

determining

a 1% change

municipal

municipal

Another

if

example,

of

is

and tax-free

duration

calculation

value

practice

taxable

For in

in

5-C

same quality

5 and 30 years

5 year

and 30 year

by the

appropriate

and type,

U.S.

but

Treasuries).

securities, factors.

the

All

of

the

preceding It

Treasuries). correlated

with

important

to

respect

to

the

interest

rate

address total

addressed

rate

in portfolio

value.

how each

as well,

(i.e.,

that

is

30 year

AAA

most

value

these to

5-D

closely

Additionally,

asset

Naturally,

rate. side,

is

rate

a reference

reviewing

reference liability

the

pick

in

on the

to

to

been

to

movements

selected

issue

contribution have

best

assume some reference

be consistent

of total

The final

is

projected

be incorporated measure

examples

Appendix

it

varies

with

adjustments

obtain

the

is

should

most

accurate

risk.7

the

asset

calculation

of

duration.

by several

the

equity

Duration There

authors.

duration

and its

calculations

are

for

generally

stocks

two

approaches

Dividend

discount

presented.

One method models As

is

will

a dividend/earnings

transform

shown

duration

use of

before, is

a stock given

straight

estimates

of

A second

method

presented

used can

and accepted for

market

returns,

between would

the

two

an

the

estimated

cash flows,

most

stocks

asset

the

into

once

asset

classes.

this

specifically,

Leibowitz allocation

of

bond

The resulting

be as follows:15

110

of

stream,

with

determinations

variance

model.

a stream

payment

The problem

by M. L.

within

be derived

stock

investment

forward.

credible

discount

the

is

rates

returns, formulas

and from

of

of dividends.

routinely

A duration

made of

flows.

determining

upon parameters

studies. are

cash

calculation

method

growth

draws

future

the

measure

variance

the this

of

correlation approach

Appendix

Formula:

De= ( sd )

@(E,B)

5-E

Db

GG-T Where:

De = estimated sd, = standard

duration

for

the

deviation

of

stock

sdb = standard

derivation

@(E+B) = correlation Db = duration

Dtp = ( Wbp x Dbp )

Where:

Dtp = total

asset

Bep = beta

The calculation relating final of

of the

stock note,

insulate

surplus

and measure measured

market

although

many variables

that

above

it

is

(i.e., from

of the

stock

stock

duration

to movements that

interest via

returns

two markets

of the

bond market

rate

changes.

its

correlation

and stocks

component

is a statistically in long-term return

It

derived interest

the

makes sense to

interest

concept As a

rates.

of stocks

conditions),

measure.

111

to bonds

portfolio

the total

economic

bond market

index the

duration allocations

bond component

of equity

true

measure

of the

general

influence

by a broad-based

portfolio

value

returns

returns

+ (Wep x Bep x De )

fractional

Dep = duration De = duration

market between

a broad-based

Formula:

market

bond market

of returns

of

Wbp and Wep are

of

equity

is

goal then rate

a function here

is

to

isolate

movements

to

as

Appendix

6-A

THREE METHODS OF ALH APPLICATIONS

The maturity to

match

and

gap approach or

intentionally

liabilities

maturity those

began

mismatch

which

dates that

are

(i.e.,

will

experience

interest

income.

For

example,

one year

from

interest

equal want

to

to take

One major the

if

advantage

problem

while

of

is

that

liabilities called

that

increase

would

problems

still

if

it,

exist.

on one target,

a single

does not

on

of

methods

interest are

period's

basically

interest

112

the

maturity

static income.

a gap

period

and

that

exact

number.

timing 1st

has buckets

management.

for

one year

on February This

a

on net

some positive

30th).

risk

during

income

your

over

for

mature

Here,

of are

exclusively

set

gap to

September

range

interest

to rise

account

assets

is

assets

rates

is

you would

your

gap approach.

precision These

set

sensitive

interest

hedge

rates

approach

assets/liabilities

in

to

this

a specified

approach

changes,

(e.g., due

within

this

want

of

interest

sensitive

interest

method

periodic

the

you

you would

the

are

the

mature

of

rate

of

change

The focus

repricing

refinement

to Interest

you expect

assets/liabilities

year;

focus

period.

Or,

zero.

dollars

a contractual

accounting

of

the

O-1 year).

The intent

1970's.

scheduled

selected

period

in the

But,

approaches

of

of

led

the to

a

are used overall, and only

Appendix

Simulation They

models

incorporate

Additionally, Simulation method,

results

models,

however,

are

most

serious

of

magnitude.

cash It

gap models. measurement

is

does Most

of

It ignore

importantly,

Balance

Sheet,

or

time

without is

rather

looking

Also,

at one point

As with

they

are

they They

Context. scenarios).

rate

than

fault.

that

goals.

forward

interest

(i.e.,

structures.

being

an index

not

not

faults

internal

flows.

a dynamic

over

other

the company

analysis of

of

and ignore unknown

in

assumptions

measure

having

Duration series

future

income

environment

results

they

the

interest boxes"

provide

the

mainly

are rarely

in time.

maturity

gap

focused

often

6-B

sold

on net

as "black

simulate

the

actual

modeled.

measure(s) takes

into

timing with

of

interest

account mismatch

respect

as well

113

to

as Income

rate both

which the

sensitivity

cash is

flow

present

P/C industry,

Statement,

items.

for timing in it

any and

periodic permits

BIBLIOGRAPHY

1)

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E. Ferguson.

2)

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3)

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Management Strategies New York: Morgan

4)

Alden L. Toevs, William C. Haney. Measuring and Managing Interest Rate Risk: A Guide to Asset/Liability Models Used in Banks and Thrifts. New York: Morgan Stanley. 1984 Alden L. Toevs. of Interest Rate

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PCAS. Volume

of Duration New York:

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An

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Asset/Liability Sachs. 1987

Introduction.

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the

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12)

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--

Corporate Management

Policy I --

Policy II

Problems

14)

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Maginn, Donald L. 1985-1986 Update.

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for

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in

for

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Revolutionizing

Drops

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Pensions

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The Handbook

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of

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Investment

&

116