ALM Property Casualty Insurers

ASSET LIABILITY

WATCHING FOR PROPERTY/CASUALTY INSURERS by Sholom Feldblum

BIOGRAPHY: Mr. Feldblum works at the Allstate Research and Planning Center in Menlo Park, California. He was graduated from Harvard University in 1978 and spent the next two years at a visiting fellow at the Hebrew University in Jerusalem. He became a Fellow of the CAS in 1987, a CPCU in 1986, and an Associate of the SOA in 1986. He currently serves as President of the Casualty Actuaries of the Bay Area, Vice President of Research of the Northern California Chapter of the Society of CPCU, and as a member of the cAS Education and Testing Methods Task Force. Previous papers and discussions of his have appeared in Be&z's Review, the CPCU Journal, the Proceedings -of the Casualty Actuarial Society, and the Actuarial= In addition, he submitted one of the winning papers to the 1988 Insurance Data Management Association call paper program. ABSTRACT : Asset-liability investigated by and non-life immunization Property/Casualty matching, long known to life insurers, is currently being Several crucial differences between life casualty actuaries. modification of traditional insurance operations require when applied to and duration matching techniques insurers:

terms; nominal expressed in 1. Life insurance liabilities are Inflation Property/Casualty insurance liabilities are inflation sensitive. sensitive liabilities are similar to short duration assets with regard to the effects of interest rate fluctuations. bonds provide 2. With a normal, upward-sloping yield curve, short duration lower returns than long duration bonds provide. In other words, duration matching with fixed income securities would reduce investment returns for Property/Casualty insurers. with inflation, in 3. Common stock prices directly expected vary which vary inversely with expected contradistinction to bond prices, inflation. Thus, both coxrumx stocks and Property/Casualty insurance liabilities are inflation sensitive. 4. Property/Casualty insurers do not segment funds, expect a steady premium inflow, and do not face disintermediation problams. Losses and expenses are generally paid from insurance cash flows, not from liquidation of assets. 5. On statutory financial statements, fluctuation. But when marked-to-market, amortized bonds show little price long-term bonds are risky assets.

A superficial acquaintance with asset/liability matching theory would indicate a short duration fixed iip!t ,,I'? :z,et portfolio to back a Property/Casualty insurer's liabilities. .% CS..; ~:nr&al consideration of the factors listed above indicates a portfolta. 1.f o+ :.;::I oecnrities and long-term bonds. ** ---------l * I am grateful ',.n :B,~j.;~..~;~ :--!fkowitz and Richard Wall for extensive ,a1 ?.bis Paper. corrections to an excl..~.-. The rem,%.i.ning errors, of course, are my own. 117

3SSETLIABILIT!fHATCRINGPORPROPRRTY/(ZA5JWTy

INSURERS

Asset-liability managers. ro?rp=inies' rate

matching has long been known to life Casualty stability actuaries as well. now wonder whether

insurers it can

and pension plan improve their

The answer is complex. both liabilities

Cash flows, and assets.

interest But the must

changes, life

and risk insurance

influence techniques

ctandard he applied

of immunization

and duration

matching

differently

to Property/Casualty

companies.

I. THE ASSET LIABILXTY MATCBXNGPROBLEH

why is writings profits

interest are large will

growing

in asset-liability and its

matching? returns

If

a life

insurer's then its

and stable,

investment pricing

are steady,

depend primarily arise

on internal rate8

and external If to rates satisfy

competition. decrease, its the

Put complications insurer's obligations. policies forced

when interest income increase, may be

change.

investment If rate8 to obtain to sell will

insufficient

policy

insureds

may take policy elsewhere.

loans or lapse their The insurer Clearly, may be these

higher

investment losses

returns

bonds at capital adversely affect

to meet its returns.

cash neede.

scenarios

operating

Life

insurers

have responded

to these uncertainties instead 118

in three

ways:

(1) SOme The short

inr....:xs

are pi-omoting

term policies

of permanent policies.

duration shifting universal matching effect

of term policies investment insurance durations of interest

reduces

interest

rate

risk.

(2) Some insurers
through And some
variable

are
and

reward and risk policies

to the policyholder
(3)

and annuities. of liabilities on operating

insurer6

are

and cash flows
rate

and assets returns.

to mitigate

the

fluctuations

Characteristics

of Property/Casualty

fnaurers:

For first-party In this regard, In lines Auto

coverages,

insurers

pay claims policies however,

soon after are the

the accident to term

date. life

such Property/Casualty the past - General Liability, two decades, Liability,

similar long tailed

insurance. Xability Commercial importance. +he accident loss reserves

coranercial Malpractice,
in

Products

Liability, Multiple is paid risk

Medical Peril

and Commercial loss in these
lines

- have grown years

The average date.

about four

after the

Moreover,

the investment to

on the assets
For

supporting these

can not

be shifted

policyholders. and insurance

reasons,

incurers

seek ways to match their

investment

portfolios.

Property/Casualty repertoire payout operating addition But there of

canpaniee immunization

have

begun

to High

investigate interest vital

the rates

life

insurance loss

techniques.

and slow

patterns

have made investment Actuaries

strategy

to a liability cash flow liability

insurer's patterns products. of in

profitability. to loss are frequencies several and life

must now examine when pricing .betueen

and severities .afforences

cruciaL

%he characteristics

Property/Casualty

insurance

operations: 119

(1) Traditional nominal pension 65. date. ultimate inflation the market inflation terms.

life

insurance

and pension a deferred

fund liabilities annuity may obligate lifetime at

are expressed the insurer beginning the

in or

For instance,

fund to pay $500 a month for Casualty Inflation liability. sensitive. values rates fall. of loss obligations, the

the insured's

at age

however, accident words, rates

are determined

settlement the are whereas true when

between In

and settlement Property/Casualty rise, liabilities

dates

influences liabilities

other

When inflation long-term

increase,
is

bonds decline.

The reverse

(2)

Asset-liability equals this

matching the duration

involves

holding

an

asset

portfolio

whose

duration insurer, with

of the liabilities. duration assets bills these

For the Property/Casualty also paper. vary directly a

means short

whose returns

inflation,

such as Treasury yield curve,

and commercial assets

But with

normal,

upward-sloping assets,

have lower Clearly, yield.

returns

than do the

long duration benefits

such as corporate with the overall

bonds, portfolio

one must balance

of immunization

(3) Many actuaries stocks. current This

and financial if

analysts

ascribe only

long durations

to connnon from

seems true

one examines but

the cash flows

resulting

and expected

dividends,

not price rates.

changes. or expected

dividend prices are

changes due to changes in interest inflation rates year, sensitive, just

However, ccnnuon stock are. period A rise

as insurance But after generally

liabilities an i.nitiol i,: ._

in interest

depresses a rise

bond prices. rates

of a few weeks to a

in interest

^- ..~cw'.x sti.ck Prices.

120

In sum, common stocks and liability sensitive to inflation dates.
rate

insurance the

reserves

are similar.

Both are and the

between Asset/liability changes.

acquisition/occurrence matching risk stems from

disposal/payment other than interest stock factors

factors factor iS the of

For common stocks, For

the principal liabilities,

systematic principal coverage.

market

fluctuations. risks

insurance

are contagion

and changes in legal

interpretation

(4) Property/Casualty that life insurers

insurers face.

do not face the same disintermediation Regardless expect a steady of interest of rate premium Investment any given

problems changes, inflow. returns block of

Property/Casualty Moreover,

insurers

stream

Property/Casualty for

insurers

do not segment funds. not for

must be sufficient policies.

the company as a whole,

(5) Measurements example, nominal long-term returns.

of

asset

risk

often

concentrate

on nominal

returns.

For

bonds with But insurers

amortized for

book values statutory returns.

show high financial By this

and steady statements,

except

Property/Casualty term
bonds are risky

depend upon real

measure,

long

assets.

Property/Casualty inflation vary assets yields influence

insurers

have a difficult and settlement rates. short-term

balancing

act.

The effects loss fixed

of

between the accident with interest

dates mean that theory for

reserves income

directly

Ilnmunization bonds. Moreover,

reconnnends holding than long-term

But these interest

securities rates

have lower have a minor

;ionds have. cash flows,

on insurance

since premium income does not vary greatly 121

wi.th investment invest market. heavily

returns in

for

most lines bonds,

of business. risky

As a result, assets risks

insurers

long-term

which are

when marked-to-

yet insurers

do not want to add investment cycle.

to the fluctuations

of the insurance

underwriting

A common solution stocks and real

is estate.

to diversify Real estate

into

equity

investments, are limited investment

such as common by state expertise. statutes, Co-n so their

holdings considerable

they are illiguid,

and they require at their

ctocks must be reported hook values are the fluctuate

market values

on Annual Statements, bong-term

more than those of bonds do. of choice for

bonds therefore accounting

investment

the Property/Casualty

industry,

for about half

of admitted

assets.

Were bonds reported amortized invest values,

on the Annual Statement at their their in actual riskiness

market values,

instead

of

would be apparent, In other words,

and insurers accounting

would rules

more heavily

common stocks.

influence security selection as much as operating income does.' ___________________----------------------------------------------------------1 Federal income tax laws also influence Tax law financial portfolios. changes affect asset holdings in ways that asset/liability matching theory does not recognize. The 1996 federal income tax modifications provide several example5 : (A) The tax rate on long term capital gains used to be lower than the rate on net investment income. As a result, growth Current law taxes both equally. stocks have lost their tax advantage over income stocks and corporate bonds. The reduced tax exemptions for municipal bond and corporate dividend reduces the tax advantages of these securities over corporate bonds, federal bonds, and growth stocks.
income

(9)

(C) The strengthening of the Alternative Minimum Tax rules reduces the tax advantages of municipal bonds and income stocks over corporate bonds, federal bonds, and growth stocks. Asset selection depends on current tax law as much as it does on the liability portfolio. Nevertheless, taxes are ignored in this paper, because tax laws 122

TI.NCX4INAL'JERSUSINF'LATIONSENSITIVELIABlLITIES

Asset/liability conventional disintermediation. in nominal terms, life

matching

theory

is

grounded

on

two valued

characteristics liabilities

of and

insurance First.

policies: life

nominally insurance

traditional

liabilities

are stated returns. If enough

but are funded at least rate used for pricing is sufficiently little years, in their risk.

partially the policy

by investment

the assumed interest - that rate volatile is,
if

is "conservative'! returns

it

below actual But

investment returns

- interest

changes pose in recent

investment pressures assumptions. insurance

have become more insurers to be

and competitive interest effect rate

have forced

J.ess conservative rate

Consequently,

interest

changes have a large

on life

profitability.

Second,

many

actuaries risks

believe in the 1970's. as financial

that

life this

insurers

faced

strong it

disintermediation characterized in the industry. disintermediation policy terms are life

Although underdogs,

view is not correct,

insurers

and so was widely of this.) insurers,

accepted

(See below for does not apply
short

further

discussion

In any case, because the

to Property/Casualty reserves

and policy

do not accumulate.

There is a sharp contrast a property/Casualty insurer

between a life with inflation

insurer

with nominal liabilities.

liabilities

and The life

sensitive

insurer may issue a $100,000 policy for a level net premium of $1,000 per ----------------------------------------------------------'-------------------change frequently and unexpectedly. This paper concent r&.$6 on the continuing characteristics of the property/Casualty industry. However, actuaries must be cognizant of factors such as tax treatment and accounting regulations when providing financial investment recommendations. 123

annum.

Policy to

exclusions

(e.g.,

war and insurrection), (e.g., epidemics), make

a sufficient

spread of enough risk

risk

eliminate portfolio

contagion of

factors

and a large the mortality

insurance insignificant

homogeneous

insured6

for young applicants.

But interest determined fall for

rate

risk

remains.

The $1,000 net annual premium may have been on policy reserves. If interest rates

a 5% per annum return returns

below 5%, investment

may not cover the expected

loss.

Surprisingly, benefit January

the

converse

can also

occur: issued

a drop

in

interest

rates certain

may on

the insurer. 1, 1987 for paid

Suppose an insurer $1,000;

a one year annuity rates

new money interest 1, 1988.

were 10% per annum; and suppose the insurer

the annuity

$1,100 on January corporate

Moreover,

bought a lo-year

bond that paid

10% annually

to fund the annuity.

What would happen if corporate insurer's value . bonds

interest

rates

fell 1,

to 1988,

5% per
would

annum during pay

1987?

New The par

issued

on January

5% coupons. its

old bond, which has 10% coupons, Its market price discounted

would be worth more than value

on January 1, 1988, would be the present

of the

cash flows

at 5%, or

Price

=

$100

+

$100

*

0.952

+

$100

l

0.9522

+

.

.

.

+

$1,100

l

0.952=

=

$1,455.

In other words, the insurer pay $1,100 to the annuitant, insurer can lose its as easily liabilities

Could

sell

the bond for $1,455 on January the remaining from interest nominal terms, $355. rate

1, 1988, the The

and pocket as it

Of course, changes.

can gain
in

reason is that

are fixed 124

but its

investment

returns interest differently, mismatch,

fluctuate rates the

with affects liabilities

interest the

rate market

changes. values

When a change in new money of liabilities and The greater assets the

and assets rate

are "mismatched." risk.

the greater

the interest

Note that well its

this

is a speculative rate

risk,

not a pure risk: An aggressive changes, insurer

the insurer insurer,

can gain a6 confident seek of an

as lose from interest ability to forecast mismatch.

changes. rate

interest

may consciously would attempt

asset/liability

A conservative

to match

assets and liabilities

more closely.

Hatching

Techniques:

Two common methods of matching and duration portfolio insurance securities matching. Exact to interest from its

assets

and liabilities matching changes. of business provide the

are cash flow matching creates an asset/liability forecasts fixed net income at the

cash flow rate book

impervious cash flows

The insurer and buys

whose coupons and maturities For instance, if the insurer

needed monies that its

needed times. cash outflow portfolio

estimates

net insurance its in that financial year.

10 years hence will

be $S,OOO,OOO, it would arrange provide $5,000,000

such that

coupons plus maturities

Exact cash flow matching may closely better yield. &.hrih liability :C:?erest

can be cumbersome, inefficient, cash flows, rate but an alternative

and costly.

One bond a

bond may proviaa risk for the insurer,

changes are a speculative 125

not simply

a possibility

of loss.

Exact cash flow matching outweigh the costs

is worthwhile of lower yields

only and

when the benefits administrative

of risk

reduction

expenses.

This is rarely

the case.’

Duretion Nat-:

Duration

Watching hedges against rates

small interest

rate

changes. First,

A change in new coupons rise, are the

money interest reinvested

has two effects

on bond prices. rate. When interest When interest the rates bond's fall.

at the

new money interest at higher returns.

rates rates fall,

coupons are reinvested are reinvested rates at rise

returns. Second,

coupons when

lower

price

declines

interest

and rises

when interest

If

a fixed

j.nccme security

is used to fund

a nominal returns

liability, and prices

then

the

relative the bond's

importance term, its

of changes in reinvestment coupons,

depends on If a is

and the date of the liability year, total

payment. then there value

nominal liability no reinvestment from the price entire

of $1,100 is due at the end of the first of coupons. change. The only change in the bond's used above,

results gains the

In the illustration

the insurer

$355 price

increaee.

At a bond's

expiration

date , only the par value

is received.

Interim rate

price do

changes have no effect on the proceeds. But reinvestment ----------_-_-----------------------------------------------------------------

changes

a See, for example, Martin L. Leibowits and Alfred Weinberger, %ptimal Cash Plow Matching: Minimum Risk Bona Portfolios for Fulfilling Prescribed Schedules of Liabilities" (New York: Salcam Brothers, Inc., n.d.). 126

influence

the final

wealth.

Suppose a 10 year bond were used to fund a nominal liability ln years. together If with interest rates

of $2,594 due in

remain at 10% per annum, the $100 annual coupons, of the bond, accumulate rates fall to $2,594 at the

the $1,000 par value But if

end of 10 years. fir6t declines year, the

new money interest value will wealth. of the lose

to 5% per annum in the the maturity value

accumulated

coupons plus

to $2,258.

The insurer

$336 - the difference

between the

nominal liability

and the final

There is one date when the change in the bond's market value change in its reinvestment returns , as illustrated in Figure

just 1.

balances

the

_---_----_---_---------------------------------------------------------------Figure $400 200

1: Insurer From an Interest

Gain or Loss Rate Change

Insurer Gain or Lo86

0 -200 -400

Liability Payment Date to 5% during first year.

10 year 10% annual coupon bond; interest rate6 decline -------------------------------------------*---------------------------------Thus, if the liability inaurer
1066S,

payment date is one year from purchase it is ten years five from the
years

of the bond, the the insurer the

gains. If it is

If

date of purchase, date

approximately even.

from the

of purchase,

insurer

just-breaks

127

Hacaulay Duration:

The point interest

at which rates just

the positive balance

and negative

effects duration

of a a of the bond.

change in Formally, is

is the "Macaulay"

the Macaulay duration the weighted values

of a bond, or of any group of assets

or liabilities,

average of the cash flow dates,

where the weights

are the present

of each cash flow.

Consider flows principal

a 10 year 10% annual coupon bond issued on January 1, 1988. of the $100 coupon payments 1, 1997. figure each January values for yieLds 1, and the

The cash $1,000

consist

repayment

on January yield;

The present

of the cash flows of 10% and 5%.

depend upon the current

2 illustrates

--_-___----------_-----------------------------------------------------------Figure Date 1,/l/88 l/1/89 l/l/90 1/l/91 l/1/92 l/1/93 l&J94 l/1/95 l/1/96
l/l Jw

2: Bond Duration Present Value at: 5% ) 95.2 90.7 86.4 82.3 70.4 74.6 71.1 67.1 64.5 675.3 $1,386.20 Principal Repayment 0 0 0 0 0 0 0 0 0 1,000 10% $ 90.9 82.6 75.1 68.3 62.1 56.4 51.3 46.1 42.4 424.1 $l,OOO.OO

years Since Issue 1 2 3 4 5 6 7 8 9 10

Coupon Payment $100 100 100 100 100 100 100 100 100 100

Total

(10 year 10% annual coupon jond; current yield rates of 10% and 5% per annum.) ---e---s ------_-__.. c ,, .-__.. -. _-----------------------------------------------128

At a 10% current

yield,

the bond'6 duration

is

(l"90.9

+ 2'82.6

+ . . . + 10'424.1)

/ (90.9 + 82.6 + . . . + 424.1)

= 6.76 yr6.

At a 5% yield,

the duration

is

(1'95.2

+ 2*90.7 + . . . + lO"675.3)

/ (95.2 + 90.7 + . . . + 675.3)

= 7.29 yrs.

Suppose the bond were purchased 6.76 years. Then a small

to fund a nominal rates

liability

of $1,905 due in

change in interest or loss,

- say to 10.2% or 9.8% price would

would cau6e no net gain balance

because the change in market income.

the change in reinvestment

The duration durations, assets the flows

of

two bond6

is

the

weighted

average

of

their

individual

where the weights

are the current their either average

market prices.x durations.

You can match First determine annual cash

and liabilities

by equating

(overall)

duration

of the liabilities, the weighted

by examining

the total of all

or by computing fixed

of the durations

policies. the

Then purchase duration

income securities

whose overall

duration

matches

of the liabilities.

Duration interest

matching

eliminates

asset/liebility

mismatch

risk

only

for

small as

rate changes. 3.

As the rate6 change, the bond durations

change too,

shown in Figure
----e-m

-----------_-----------------------------------------------------------

3 More precisely, the weight6 are the sum6 of the discounted values of each bond's cash flows. Barring marketplace imperfections, these are the market prices of the bonds. 129

--_---__-____--_________________________-------------------------------------Figure Current Yield 3: Bond Duration versus Current Yields (10 year 10% annual coupon bond) Duration Current Yield 7% 6 5 Duration 7.07 yrs 7.17 yrs 1.27 yrs

10% 6.76 yrs 9 6.86 yrs 8 6.97 yrs -___-------__--__------------------------------------------------------------Even when the interest tnterest. its rate, rates asset they and liability portfolios

have the

same duration

at one

may have different change slowly,

durations giving

at another.

Fortunately,

generally

the insurer

time to "rebalance"

asset portfolio.4

Duration

Hatching

for Property/Casualty

Insurers:

If duration

matching

reduces mismatch risk as well?

for life out,

insurers,

does it work for determine either from

Property/Casualty loss payout patterns internal

insurers by line

To find

you must first

of business.

Such data are available Annual Statements. durati0ns.e

company reports

or from statutory

Some analysts

have used this data to estimate insurance portfolio -------__----_---___---------------------------------------------------------4

Durations of whole life policies generally exceed the durations of longterm bonds. This complicates duration matching. the Moreover, rebalancing asset portfolio may be difficult when interest rates change sharply. To solve these problems, some financial analysts have suggested taking long positions in futures and buying call options to lengthen the duration of the asset portfolio. In practice, however, unless there are other reasons for investing in futures and options (such as hedging), the additional cost of these transactions outweighs the gains from more accurate duration matching. Few actuaries examine the costs of asset/liability matching. Fewer sti1.1 seek to balance these costs against the benefits of a more stable operating income and the reduced risk of insolvency. See below for further discussion of this. 130

Richard Woll has shown how to estimate business for from Annual Statement P lines data.6

loss reserve In brief,

payout patterns loss reserve for

by line

of

payout patterns 10 years. Loss Loss

the Schedule after

of business

can be determined by an exponential

payouts reserve

10 years may be estimated are then determined investment rate.

decay mode1.7

durations

by discounting

the nominal loss payments

at an appropriate

We illustrate Liability patterns future loss

the traditional reserves.

calculation Part

of liability

"durations"

for General loss payout expected

2 of Schedule P shows historical Using prior year experience (using

by line payout

of business. for

to forecast a paid

patterns

each accident

loss development 4.e

analysis},

Richard Woll calculated

the percentages

shown in Figure

-------_----------_----------------------------------------------------------5 See, for for Property

Management Strategies example, Peter 0. Noris, "Asset/Liability & Casualty Companies," Morgan Stanley, May 1985.

6 Richard G. Wall, "Insurance Profits: Keeping Score," in Financial Analysis of Insurance Companies, CAS 1987 Discussion Paper Program, particularly pages 505-514 and 522-523. -J The exponential decay assumption simplifies the mathematics, but it is not crucial for the estimates of reserve duration. Any reasonable model, such as simply dividing the remaining loss payouts equally over the next five years, produces approximately the same durations. The exponential decay model is described by Charles A. McClenahan, !'A Mathematical Model for Loss Reserve Analysis," Proceedings -of the Casualty .-Actuarial Society, Lx11 (1975) pp. 134153.

e Richard Wall, 9. cumulative payments. Wall's percentages.

cit., p. 511 (Exhibit IX, Page 1). Wall's exhibit shows The numbers in Fi.gn-: ! are the first differences of 131

____-__________--___---------------------------------------------------------Figure 4: General Liability Loss Reserve Payout Pattern Development Year Accident Year
1983

1

2

3

4

5

6

I

8

9

10

lli 10.5% 10.3 10.2

1984 1985

16.1% 15.3% 14.6% 11.9% 9.2% 7.0% 16.4 16.3 14.3 11.7 9.1 6.8 17.3 16.1 14.2 11.6 8.9 6.8

5.3% 4.2% 3.3% 2.6% 5.2 4.1 3.3 2.5 5.1 4.1 3.2 2.5

Notes : Since these are loss reserve payout patterns, the first development For example, year is the first calendar year subsequent to the accident year. development year #l for accident year 1985 is calendar year 1986.

The numbers shown are the percentages of required reserves for each accident year that are paid in each development year. For instance, 16.1% of required General Liability reserves for accident year 1983 were paid in 1984; 15.3% were paid in 1985; and so forth. The percentages for calendar years 1986 and onward are estimates based on historical loss payout patterns. -----------------------------------------------------------------------------The timing of loss payments within the tenth calendar each calendar year, year, as well as the pattern effect on the

of payments after "duration." year,

do not have a major all after

For simplicity, loss reserves five

we assume that still held

loss payments are made at mid10 years year are paid out evenly

and that

over the subsequent loss pattern reserves

years.held after

For accident 10 years. 15.

1983, 10.5% of required assume a payout

are still

We therefore

of 2.1% for years

11 through

P The exponential decay model used by Richard Woll is more accurate. However, the loss payout patterns are then more difficult to calculate. The simplified method in the text is sufficient for the heuristic purposes of this paper.

Similarly, the average General Liability 1066 payment is not made midpoint of the policy year or of the succeeding years. Rather, the payment date is c!.ose to the end of the policy term during the initial and it gradually recedes towards the midpoint of the policy term development years continue. This phenomenon has little effect arguments in the text, and it unduly complicates the mathematics. 132

at the average year, as the on the

In

1983 and 1984, between of

new issues

of

Moody's annum. assets,

grade Since

Aaa corporate

bonds were

yielding percentage rslculate

11% and 13% per investable "duration."'O

such bonds form a large rate to

insurers'

we use a 12% interest

the reserve

The General Liability

1983 loss reserve

"duration"

is therefore

16.1*0.5*(1/1.12)"-5 + 15.3*1.5*(1/1.12)'.5 + 15.3 * (l/1.12)1-5 16.1 * (1,/1.12)-5 or 3.2 years. This figure is substantially

+ . . . + 2.1*14.5*(1/1.12)'"-" + *.. + 2.1 * (l/1.12)=.5 the same as that derived by other

actuaries and analysts for liability reserve "durations."'1 _________-__^____---____________________-------------------------------------10 Richard Wall uses a 5.9% interest rate for 1983, based on short term Treaa1x-y bill rates. The risk free rate is appropriate for discounting loss For duration reserves, thereby separating insurance and investment returns. matching, however, we must use the same interest rate for the liabilities as we use for new investable assets.

11 For 1983, Richard Woll calculated the General Liability loss reserve Schedule P loss reserve duration as 2.1 duration as 3.2 years, the overall years, and the all lines loss reserve duration as 1.95 years; see Wall, E duration of 2.5 year6 for a, p. 523. Peter Noris obtained a 1983 liability Automobile Physical Damage, an insurance portfolio of Automobile Liability, Workers' Compensation, Multi-Peril, and General Liability, weighted in the same proportions as the overall industry portfolio (see Noris, op. cit., pp, 8 and 26). This is longer than Wall's 2.1 years for all Schedule P lines combined, since Noris assumes slower payout patterns. For instance, his General Liability payout pattern assumes that only 32% of losses are paid in the first three years. Wall estimates that 4b% of initial General Liability loss reserves are paid within the first three subsequent years. This discrepancy results from the type of loss payout pattern used by each analyst. Noris uses the loss payout pattern for losses incurred during a specific accident year. In agreement with Noris, Woll estimates that 31% of General Liability losses are paid In the first three years. But for liability durations, Wall uses the payout pattern for loss reserves, not for incurred losses A The +.wo types of loss payment patterns are quite different. Many losses are paid during the year of occurrence, and do not appear as reserve liabilities on the year end accounting statement. Those losses that remain outstanding as of December 31 as generally the slower settling ones. Thus, the loss reserve payout pattern iS usually slower than the -incurred loss payout pattern. ----Thus, 133

The apparent liability duration

conclusion

is

that

to

duration

match

a General

Liability an average

portfolio, of 3.2 years.

you should invest

in medium term bonds with

Interest

Rate Changes:

This conclusion interest true rate

is misleading. changes.

Asset/liability

matching mitigates outlined

the risk

of

But the procedure rate

above does not model the loss payments.

effects

of interest

changes on insurance

--_-__-___-_____-___----------------------------------------------------------

Richard Woll shows an average payment date for all lines combined of 1.72 years for incurred losses and 2.33 years for loss reserves (see Wall, c cit., p. 510, Table XIV). Wall shows the opposite and Medical Malpractice, For General Liability relationship: significantly longer average payment dates for incurred losses than for loss reserves. Perhaps this is due to differences in the loss dates in the two calculations: loss reserves include losses from older accident years, while incurred losses are from the current accident year. The implication in the past, would be that General Liability and Medical Malpractice claims were settled more quickly, but average payment dates have lengthened in recent years. However, Wall's Exhibit VIII on page 506 does not support this hypothesis: average payment dates have remained constant for these two lines of business between 1977 and 1985. For further discussion of this topic, see Wall, op. cit., p. 513.

The proper payout pattern depends on the type of matching. If one matches assets held as of December 31 with liability obligations aa of the same date, then one should use the loss reserve payout pattern. If one matches assets purchased with liabilities incurred, then one should use the loss incurred payout pattern. The discount rates used by Noris and Wall do not differ much, and do not account for the duration discrepancy. Noris uses the municipal bond rate to estimate an after-tax return. Woll uses an after-tax short-term Treasury bill rate to estimate the risk free return. These two rates are close enough that their difference has little effect on the liability "duration." 134

Suppose an insurer years hence for

has a General Further,

Liability

loss

reserve inflation

that

will

be

paid

5

$100,000.

suppose that

is 5% a year, loss cost trends

but are

both medium term corporate several percentage points

bonds and General above the general

Liability inflation

rate.

For simplicity,

assume both are +lO% per annum.12

To fund this bonds that - just

liability,

the insurer

invests

$62,092 in five

year zero-coupon years for $100,000

yield

10% per annum.13

The bonds mature in five

enough to pay the liability.

What happens when interest per annum shortly and it after remains inflation,

rates the at

change? is

Suppose inflation set

accelerates

to 10% bond is and

reserve 10% for

up and the zero-coupon five years.

purchased,

the next

Bond yields

'Loss costs follow

with each increasing

to 15% per annum.

The expected the bond still

ultimate matures

loss is now $125,000 ( = $100,000 * (3.15/1.10)5 for $100,000 in five the risk years. rate Duration changes. matching

).

But

has not

helped the insurer

mitigate

of interest

I2 The assumption that the bond yield equals the loss cost trend is made for simplicity only. The three assumptions that underlie the argument are: (1) Inflation affects General Liability date. (2) General Liability loss cost trends (3) Bond yields vary with inflation. loss payments through the settlement vary with inflation.

2.3 The term of a zero-coupon bond equals its duration. For the illustrative bonds in the text, both the duration and the term are five years. 135

Inflation

Sensitive

Cash

Pbw6:

The mistake duration traditional Asset/liability

was in estimating theory. insurance matching either

the

liability from are

loss fixed

reserve income in

duration, securities nominal

not in and terms. nominal

matching life

Cash flows products

expressed insurance

(a) balances

and investment

cash flows or (b) balances cash flows plus capital

the insurance

cash flows with changes in investment

gains and losses.

The

cash

f 'lows If date

from liability (with

General losses

Liabil are

ity

losses, to

however, inflation

are

inflation the

sensitive. settlement

sensitive inflation with

through

no lag between

and its

effects

on losses)

then the reserve That is, should Treasury

is equivalent

to an asset of interest securities are

a duration

of zero years. you and

to eliminate invest Bills) either or in

the influence in short securities estate). term

rate changes on net worth, (e.g., also commercial sensitive paper

that

inflation

(e.g.,

common stocks

and real

In practice, settlement

most reserves date. Workers' date.

are

not

fully

inflation

sensitive

through

the fixed bills the of

Compensation Bodily

indemnity Injury

payments are largely wage loss a year which and medical or two before

a+ the accident may be determined settlement insurance iM!prac,:ica, Injury, -e--w... date.

Automobile

soon after Nevertheless, in

the accident "general Liability, liability

- often damages,"

form the bulk Liability,

payments

General

Products coverages,

Medical Bodily

Commercial Multi-Peril

and Automobile

,a?'~ inflation sensitive through the settlement date.ld .____-___-_______-___^__________________--------------------------136

Inflation settlement suffering" settlement

is increasingly date. awards, date,

important

for insurance are not easily

liability quantified, the value bills

losses

through

the

When the losses juries are

such as "pain of
money at

and
the

influenced date.

by

not at the accident between

Medical

depend on the time dates. Even in instead effects of of

of treatment, disability by statute, inflation

which falls cases, the

the accident

and settlement

as long as the reparations plaintiff's earnings reserves attorneys

are decided by a jury incorporate the damages.

usually

and expected

changes in the demand for are inflation reserves, are paid out sensitive; on the quickly,

In other to not have

words, most liability short inflation duration

they are eguivalent other hand, are they

assets.

Property Since they

sensitive.

however,

equally short durations." _-_--__-__-_---_-_-----------------------------------------------------------14 For a more complete discussion of the timing of inflation on insurance "The Effect of Inflation on Losses and Premiums losses, see Robert P. Butsic, for Property-Liability Insurers," Inflation Implications for Property-Casualty Insurance, 1981 Casualty Actuarial Society Discussion PaprProgram, p. 51.

When the insurance payments indemnify economic losses, such as work disability and medical bills in automobile personal injury claims, the "loss date," or "treatment date I1 should replace the accident date in Butsic's model. If the loss date is c&erminous with the accident date, this revision has only a minor effect. Sometimes, however, the lVloss date" or "treatment date" is closer to the payment or settlement date than to the accident date. For instance, suppose a motor vehicle accident victim in a no-fault compensation state suffers an injury requiring extended medical treatment. The medical bills may continue for years after the accident, and the insurer will reimburse the victim soon after the treatment. Butsic notes that both interest rates and loss cost trends vary closely with inflation. Butsic's reviewer takes him to task for this, claiming that interest rates and inflation are not as well correlated as Butsic implies. In the short term, this is correct, since numerous factors besides inflation affect interest rates. Over the long term, however, interest rates do vary closely with inflation. One may infer, as both this paper and But&c's paper expected interest rates are directly correlated with expected do, that inflation. 16 Steven D'Arcy makes the same argument in his excellent review Ferguson's "Duration" in the Proceedings -of the Casualty Actuarial 137 of Ronald Society,

Short-term Liability loss

connaercial loss reserves. increases.

paper If

has

a duration rates

similar increase,

to

that

of

General expected paper's

interest

the ultimate corunercial

payment

Reinvestment similarly.

returns

from the

maturity is little

payments increase

Since the assets In other words,

are short the assets

term, there (commercial If loss cost

change in market price. and liabilities and connnercial (GL losses) paper yields

paper) trends

change in the same direction. change by approximately

the same amount,

the magnitudes

of the asset and liability

changes are also equal.'e

This

is

by no means a recommendation buy long-term incurs higher bonds.

for

investments

in

commercial

paper. lower income We first

Most insurers yields securities. turn, however, and

Short-term costs

commercial paper provides than do other fixed

transaction are discussed estimates

These issues to duration

in the following securities.

sections.

for equity

_______-____________----------------------------------------------------

--em--

Peter Noris also notes the inflation sensitivity of LXX1 (1984) pp. 8-25. insurance losses, but he believes that conservative reserving obviates this problem; see Noris, op. cit., pp. 43-45. However, conservative reserving and asset/liability matching are different types of solutions to the general valuation problem. The former says, "Make reserves sufficiently redundant so that they will be adequate even under adverse conditions." The latter says, "Keep reserves accurate, but choose matching assets 60 that changes in conditions affect the two sides equally." When conservative reserving is used to guard non-financial against uncertainties, it may be used even with asset/liability matching. For example, American courts have interpreted the pollution exclusion in General Liability policies in diverse ways. The insurer may set up a large bulk reserve for such "extra-contractual" liabilities that the courts discern in the policy and impose on the carrier, This is unrelated to the asset/liability matching problem. I6 The similarity in magnitude assumes only that the yields change by the the same amount, not that they be equal. General Liability loss cost trends in the 1970's and 1980's have exceeded commercial paper yields. If inflation accelerates, however, the changes in trends and yields may be about equal. 138

III.

EQUITY DURATIONS

The previous loss payments. and maturity

section

distinguished

between are similar. nominal life

nominal

and inflation with fixed

sensitive coupons products. whose and

Asset durations repayments are like

Securities insurance

and annuity

Macaulay durations annual payments interest liabilities. rates,

are weighted and "maturity" such as

averages values

of payment dates. directly are with like

Securities inflation casualty rates

vary

conunon stocks, are misleading

insurance matching.

Macaulay durations

for asset/liability

This is the crux of this the effects in market interest of interest value rate. is

section. rate

Asset and liability

durations

help quantify the change in the

changes on market values. to the duration

In general, times the

proportional

change rate

Long-term

bonds are more sensitive bills are.

to interest

changes

than commercial paper and Treasury

Figure five

5 illustrates

this

phenomenon. respectively.

Consider

two zero coupon bonds, of $1,000,

with and

and ten year terms,

Each has a par value therefore,

each pays 10% per annum. = $621 and $1,000 * (l/10)'*

The issue prices,

are $1,000 * (1/1.1O)5

= $386, respectively.

Suppose that after isaue.

new money interest Figure

rates

change by one percentage

point

the day

5 shows the new market prices

of these bonds.

139

___-----______--____---------------------------------------------------------Effects of interest Figure 5: rate changes on market values Market value: Zero-coupon bonds at 10% at 9% f Change % I at 10% at 11% $593 352 Change d % -4.5% -8.8

+4.7% 1 $621 5 year term: $621 $650 $29 +9.3 1 386 36 386 10 year term: 422 --------___---_-__-_---------------------------------------------------------A zero coupon bond's and 10 years, duration equals its term.

$28
34

Thus, the two durations

are 5 for the

respectively. that

Accordingly, for the five

the change in market price

ten year bond is double rates change slightly.17

year bond when new money interest

Ccamm Stocks:

How should

the

duration

of

common stocks

be measured?

Stated

differently,

17 Mathematically, the change in price equals the negative of the Macaulay duration times the market price times the change in the interest rate, or

Change in Price

= -1

l

Duration rates

l

Price

l

Change in Interest

Rate. in

For a decline in interest market price should be

from

10% to 9% per = = $38.60 $31.05

annum, the changes

Ten year bond: -1 * 10 * $386 l 0.01 Five year bond: -1 l 5 * $621 * 0.01

These figures differ from the actual market price changes because the change in the intereat rate is not "infinitesimally" small. For a n-ore extensive treatment of this subject, see G. 0. Bier-wag, George G. Kaufman, and Alden Toevs , "Duration: Its Development and Use in Bond Portfolio Management," Financial Analysts Journal, July-August 1983, especially pp. 17-18.

"What definition interest rate

of

cormnon stock

duration

helps

quantify

the

effects

of

changes on market values?"

The traditional discount perpetual assumed to model"

measurement of equity

of

common stock This for

duration

use6

the

"dividend as a are

valuation.

model views

a common stock If dividends

bond that
grow

pays dividends

an infinite

term.

at G% per annum, and values value of the stock's dividends

are discounted is

at K% per annum,

then the present

(current

dividend)

l

(1 + G) / (K - ,).I,

The duration of the natural rate-l9

of a fixed logarithm

income security of its present

equals value

the negative with respect

of the derivative to the equals discount

Using this

equation

for common stocks,

the duration

- d (ln

(current

dividend * (1 + G)) - In (K - G)) d (K>

=

(K _1G)

Sn the mid-1980's dividends grew at about 6%. A discount -----_--------____-_---------------------------------------------------------3.e

rate

of 10% implies

The sum of the discounted

dividend

payments is (1 + G)date. This reduces to the

t=t where "t" is the number of years since the purchase formula in the text. For further exposition, Finance, eighth edition formula, ‘*KS’ represents growth rate.

E

current

dividend l (1 + IQ=

see J. Fred Weston and Thomas E. Copeland, Managerial (Chicago: The Dryden Press, 1986), pp. 609-X). In the the cost of capital and "G" represents the dividend

19 See, for example, Martin L. Leibwitz, et al., "A Total Differential Approach to Equity Duration," (New York: Salomon Brothers, Inc., n.d.), p. 3. Leibowitz similarly concludes that traditional measures of equity duration give meaninglessly high figures. 141

a duration duration

of

25 years

for

the

average bonds.

common stock.

This

exceeds

the

of even long-term

corporate

Market Price

Changes:

What happens duration direction

to

connnon stock that stock

prices prices

when interest will shift

rates strongly

change? in the

A long opposite

implies

of the change.

This is true for long term bonds, but it

is not true

for common stocks.

Tnterest ways.

rate

and inflation

rate

changes affect

common stock prices

in several

1. ---value should

of the firm: not be affected

In theory, by

the real

value If

of the firm's

major

assets rates so that

inflation.

inflation

and interest accordingly,

accelerate, its

the nominal value of the firm value

should increase

inflation-adjusted

remains constant.

I

2. Supply -and Demand: In practice, and costs. increase, When inflation

the value of a firm depends on its rates accelerate,

revenues

and interest

supply

costs is

but demand may or may not. If inflation

If inflation

is V'demand-pull,Vt there

excess demand. rising reducing interest demand.

is "supply-push," households

demand may be weak. to save, not consume,

Xoreover, further

rates

encourage

142

In sum, accelerating increase stock will demand. decline.

inflation

and interest the values

rates

increase

costs but may not and of its common

In such cases,

of the firm

3. Investment holdings

strategy:

When interest

rates

rise,

investors in"

often

shift

their

from connnon stocks

to long-term

bonds, to "lock

the high rates.

The lessened demand for ccmmon Stock6

reduces their

market prices.

The first

effect

is long-term; and interest but rise

the next two are short-term. rates rise unexpectedly,

In other

words, prices

when inflation
decline

common stock

at first,

later.

We quantify stock capital

this

phenomenon by correlating appreciation and (b) long

inflation term

rates government

with

(a)

cormnon capital

bonds

appreciation. The correlations below used 1962-81 annual returns.Z0 ------_------_---------------------------------------------------------------20 Annual Singuefield, (Charlottesville, Ibbotson and appreciation

and monthly figures are from Roger C. Ibbotson and Rex A. Stocks, Bonds. Bill6 and Inflation: The Past and the Future _---Virginia: Thxanzl Analysts Research Foundation, 1982). Sinq-uefield do not provide a long-term corporate bond capital series.

Ibbotson and Sinquefeld's series begin at 1926. The 1929 depression, as well as the post World War II economic prosperity, caused major fluctuations in common stock prices, which overwhelmed the effects of interest rate changes. The 1962-1981 period is more representative of current conditions. This paper uses the Consumer Price Index (CPI) as a proxy for new money interest rates. An alternative series available from Ibbotson and Singuefield is the Treasury Bill total return series. However, this lags inflation by up to half a year, and so it is less useful for the correlations. These series are used only to illustrate the argument in the text. To accurately determine the correlations among new money interest rates, longterm bond prices, the following adjustments would be and conrnon stock prices, needed: (1) New money interest rates should issued high quality corporate bonds. be measured as coupon rates on newly

143

The correlation accumulation market price rates

coefficient series

between

the

long

term government

bond capital

and the consumer price bonds varies

index is -50%.

In other words, the with inflation

of long-term

strongly

and inversely rates).

(and by implication,

with new money interest

If

the long

term government

bond capital

accumulation strongly initial

series negative

is

lagged

one

year,

the correlation words, Rather, there

is reduced but is no "rebound"

is still

(r = -25%). in market from two as the by past

In other values. factors.

from the

decline results

the reduction

in the correlation

coefficient their

(1) The market values shortens. rates.

of bonds move towards

par values

time to maturity changes in interest

(2) Newly issued bonds are not affected

The correlation series

coefficient

between index

the

common stock

capital

accumulation

and the consumer price varies

is -19%.

In other words, the market price inflation rates.

of common stocks

inversely

but weakly with

However,

if

the coaxson stock capital turns positive hurts (r

accumulation = +17%).

series

is lagged an

one year, initial decline. so nominal

the

correlation

Presumably, equity

acceleration

of inflation

most firms,

and their

values

After several months, however, firms adjust their costs and prices, ----____-_______-------------------------------------------------------------(2) Smoothed monthly
or quarterly

rates

should be used. lengths, with point. depending

(3) One year lags should be replaced by lags of differing on the ease with which the firm can pass on cost increases. (4) Interest rate changes should be examined in conjunction values of the interest rates. See the discussion in the text for elaboration 144 of the third

the fbso1ut.e - -_.-

cornnon stock values

vary directly

with recent

inflation

rates.

In sum, common stock prices similar to casualty reserves,

are sensitive

to inflation.

common stocks of mOney.2'

are

in that both track

the real value

Why does the traditional traditional dividend change, growth calculation payments the rate dividend will in

duration

formula

give

stocks a 25 year duration? growth rate

The

uses the current future growth years. rate will But

dividend if

to determine rates the

inflation

and interest The change in since firms

change as well. rate,

lag the change in the inflation rate too frequently. discount

dislike

modifying rate,

the dividend

Once a firm changes the dividend model" rate. valuation of the firm will

though,

the new "dividend

vary in the same direction

as the inflation

The effect fim.

of

inflation

upon cosunon stock

prices

depends upon the type prices when inflation

of

For example, Its

a retail

store can quickly

increase

accelerates.

nominal rates.

value

should move rapidly utility

in the

same direction for rate

as

new money interest the state regulatory with

A municipal

must apply inflation

changes to

department.

Unexpected of utilities."

should

be inversely

correlated

cosunon stock prices

How, then,

should a Property/Casualty

insurer

divide

its

assets

among

comon

21 If through inflation. market neither

inflation affects insurance losses only through the accident date, not the settlement date, then trends in paid losses also lag economic It is not clear whether the lag is greater for the overall stock However, portfolio or for the industry-wide insurance portfolio. lag is large enough to affect the conclusions in the text. et al., "Total Differential," 145 a cit., make a similar

Leibowitz, argument.

stocks, bills

long-term

bonds,

and short-term

bills?

Common stocks rate

and short-term loss to

have a similar
a0.

relationship

to interest

changes as liability

reserves the risk higher

Long-term

bonds have long durations changes. bills loss stock this risk. Common stocks do, allowing cost trends.

and so expose the insurer and long-term an investment Common stocks

of interest yields than with

rate

bonds provide return expose more the

short-term liability

connsensurate insurer

to "systematic" against costs.23

market

risks.

Short-term long-term

bills

and long-term the lowest

bonds protect transaction

Finally,

bonds entail

The following transaction important,

section costs,

examines

these

investment

attributes: Asset/liability investment

expected

yields, is

cash flows,

and market risks.

matching strategy.

but it

is only one aspect of an insurer's

-----------------------------------------------------------------------------Up until the 1970'6, institutional investors were not active traders of stocks and bonds in the secondary markets, so transaction costs were low. During the past decade, institutional investor trading has grown markedly, particularly in common stocks. 146
13

Iv.

EXPECTEDYIELDS, TRANSACTIONS CVSTS, INSURANCECASH F-Law, AND RISKS

ogsetjlisbility in short-term reserve portfolio

matching securities.

theory

tells

the Property/Casualty Noris reconunends that He notes the

insurer

to invest loss some so in yield

For example,

the entire that "while

be backed by short-term might perceive that

bonds. shortening

investment dramatically tax-exempt curve), this

managers

bond portfolio

could result bonds, where

in a reduction
there

in investment a steep,

income (particularly positively sloped

is

typically

should not be a major concgrn."'4

Expected Yields:

On the contrary, deals greater investment with or

this

is

indeed risk. income with

a major

concern.

Asset/liability may provide provides.

matching either The of

speculative lesser analyst net deals

A mismatched than

portfolio portfolio

a matched returns.

expected

Shortening investment

the duration income.

the bond portfolio

generally

reduces the expected

The yield usually

differences offer

can be great. points

High quality

long-term

corporate bills

bonds and

2 to 5 percentage offer. portfolio

more than short-term
matched

Treasury

commercial with

paper

James Tilley of three

a Guaranteed l-year

Inccene Contract bonds yielding 8%. He concluded

an investment

types

of bonds:

?.5%, 2-year bonds yielding 1.X%, and 3-year bonds yielding _----------------------------------------------------------------------------* Noris, op. cit., p. 33.

147

that percent

"to

cover for three

the

interest

rate

risks

associated annual

with

guaranteeing privileges

7.65 without

years

and providing charges

withdrawal

asset-liquidation of the assets rate of return rate

(surrender) in the three is 7.84%.

. . . II the insurer

can invest

only half

year bonds. The insurer

The matched portfolio's must forgo fully

net weighted of the

one third

interest

spread between short

and medium term bonds.a5

Transaction

Costs:

Transaction expenses, involve analyze continual financial

costs particularly

are equally if

important.

Long-term

bonds entail

the least

the bonds are held

to maturity. investment

Common stocks department requires of the to

greater individual

trading

expenses as well Accurate
money

as a larger asset/liability rates

equities. of new

matching and rebalancing

monitoring portfolio.

interest

Disintermediation:

What risk does asset/liability matching guard against? Answers like -----_------_-------_________________^__-------------------------------------IS
the

"the risk

James A. Tilley, "The Matching of Assets and Liabilities," Transactions of Society of Actuaries, XXXII, p. 293. Note also the fourth criticism 2 oonventional-bnization theory that Tilley cites: "Ieununisation theory in its conventional form places rigid constraints on investment operations, leaving investment officers with too little latitude for making policy decisions" (p, 264). Tilley believes, however, that the resolution of this problem is "largely a matter of education." 148

of interest rate

rate changes" or "the C-3 risk,"
the

beg the question: insurer?

How do interest

changes affect

Property/Casualty

Life fall

actuaries below the

answer:

"When interest interest

rates yield in

decline, the

investment life

returns

may When loans

guaranteed rise,

whole

policy.

interest (i.e., Either

rates

insured6

may withdraw insurers

funds by means of policy to sell bonds at capital

"disintermediation"), way, the insurer loses."

forcing

losses.

This

is misleading. that

Guaranteed there is little

interest chance

rates that

in whole life they will

policies exceed

are so

conservative returns policy expected illustration

investment above the

over the long term. loan interest rate,

And when new money interest insurers of clear. the receive extent investment of

rates

rise

income above their An

return

regardless

disintermediation.

should make this

Consider annuitant

a one year deposits

annuity

certain

with

a contract on January investment 1.

loan

provision.

The promises

$1,000 with

the insurer

The insurer returns

to pay $1,040 on December 31, but it the year, for a net profit of $10.

expects

of $50 during the cash value

The annuitant subject

may withdraw

of the annuity

as a loan at any time,

to 6% interest

per annum.

149

If new money interest might Clearly, because it loan,
$10.

rates

increase

from 5% to 8% on January 2, the annuitant the money at the higher annuitant not take the rate. loan,

take a $1,000 contract the insurer

loan to reinvest that the

would prefer

would earn $40 ( = $1,060 - $1,040). profit is $20 ( = $1,060 - $1,040).

But even with

the contract of

its

exceeding

the expected profit

What about the capital loss simply allow occurs forces before

loss on 5% bonds purchased requests

on January

l?

The capital

the annuitant

the loan. Statutory

The disintermediation financial statements capital
loss

realization

of the capital

loss.

amortization

of bonds in good standing,

so the unrealized The reduction

does not appear on the insurer's net income that statutory insurer results

income statement.

of statutory of the

from disintermediation principles. Determining

is caused by the vagaries the economic worth of

accounting requires

marking bonds to market. to obtain higher returns

The withdrawal from other

of funds by insureds does not have a

and annuitants

investments

significant adverse effect on economic worth.26 ______________-________________________c-------------------------------------26 For participating policies, the issue is more complex. Suppose the premiums on a participating whole life policy assume 2% interest, new money interest rates are 9, and the policy loan interest rate is 6%. Suppose further that new money interest rates increase to 10% soon after the policy is issued. The insurer intends to return most of the difference between actual and assumed interest returns through policyholder dividends. If more than 4% of the interest rate differential is returned to an insured who has taken a policy loan of the entire cash value, then the insurer has a negative interest rate margin on the policy.

One solution to this problem is to vary the dividend payments by the extent of the policy loan. The full dividend is paid if the policy cash value remains intact, while a lesser dividend is paid to insureds with policy loans. Critics of this practice argue that obtaining a policy loan is a statutorily guaranteed right, no less than the beneficiary's right to receive the face value uyi)'i death of the insured. The insured's illness does not affect his policyholder dividends, even though it shortens his expected life and therefore reduces the insurer's mortality margin. So also a loan should not affect policyhol?er dividends. For further discussion of this, see R. C. 150

For

Property/Casualty
rates

insurers,

the

risk

is

different. return

When new money exceeds the new money as well, so net

interest

decline,

the portfolio Liability loss

investment cost trends

investment operating

return.

decline

income increases.

When

new

money

interest

rates

rise, return.

the portfolio Liability

investment

return rise

falls above of the

below the new money investment the expected difference duration portfolio, rise. levels,

loss cost trends

so net operating

income decreases.

The magnitude returns

between portfolio of the financial the greater

and new money investment portfolio. The longer

depends upon the of the financial rates

the duration

the reduction

in net operating

income as interest

Interest

rate

changes expose the insurer insolvency, The if the rise of

to two risks. rates bonds on

The first depletes statutory it.

is the risk the insurer's financial After liquid

of statutory surplus. statements assets

in interest long-term

amortization this risk,

reduces

though it

does not eliminate

and short-term
bonds ana

securities realize

are used to pay claims, losses.

the insurer

must sell

long-term

the capital

How likely is this to happen? Many Property/Casualty ------------------__---------------------------------------------------------Winters, "Philosophic Issues in Dividend Distributions," .cOCiety of Actuaries XXX, pp. 125-137. I51

insurers Transactions

do become of the --

insolvent. interest interest longrate rates

The question changes?" will rise

is In

"To what other

degree

are is

insolvencies the

caused

by that

words, that

"What they

probability an insurer

so dramatically

force

to sell

term bonds at capital

losses and become statutorily

insolvent?"

A pension liabilities. expected,

plan

funding

vehicle

can use a segregated participants longer may withdraw

account

to back

its

Fewer non-vested or retirees may live to sell

from employment than The investment account block before manager their

than expected.

may then be forced maturity dates.

assets

from the segregated funds a fixed

The segregated investment cash flows.

account

of liabilities. direction

?t must provide of the insurance

cash flows similar

to and in the opposite

The Property/Casualty long-term

insurer

has a single

asset

account.

The insurer

holds income

bonds to maturity,

and it uses current insurer

premium and investment because

to pay claims. rewons,

Only when the

becomes insolvent

of other

such as inadequate

pricing

or incompetent portfolio rates will

management, does premium with an excessively long

income aq up. duration insurer's itself.

In other words, a financial a rise worth, in interest but they

combined with negative net

may exacerbate rarely cause the

an insolvent insolvency

The investment interest insurer. rate

manager desires changes is not

high

yielding for in short

securities, a stable "duration"

and the

risk

of

significant invest

Property/Casualty cormnon stocks or

But should the insurer bonds?

long duration

152

Risks:

This

question

is

not its

related

to

asset/liability Common stocks

matching. expose

Each type the insurer

of to

security systematic

presents

own risks.

market risks,

such as the market declines

in 1975 and 1987.27

Long-term fluctuating risks

bonds, inflation

if

marked-to-market, rates. portfolio.

expose

an insurer

to

the

risk

of

The investment

manager must balance

these two

in the financial

Conclusion:

In sum, the sensitive.

liability They are

reserves similar

of Property/Casualty to bills. cormron stocks,

insurers other equity

are

inflation

investments, bills are

commercial paper , and Treasury highly for liquid large short-term

Commercial paper and Treasury but their and similar all but the expected yields are

investments, Real estate for

are too low limited by

carriers. and are

investments

regulation managers.

too risky

most experienced investment

investment of choice.

Cormnonstocks,

therefore,

are the apparent

s7 In truth, there was no 'm:::?':zt crash" in 1987, because the market returned about 5% over the year. 'The wression of a crash resulted from the sudden readjustment in October 1987. The 1987 experience differs from a true market collapse in that no econrwL.,: downturn followed October 1987.
1.53

Interest insurers. they offer

rate

changes do not pose a serious corporate yields than

risk

for

stable

Property/Casualty 9n.ismatch," offer. but The

Long-term higher

bonds may entail other fixed

a duration

income securities

actuary

and the investment of the is but

analyst

must be aware of the types and liabilities. The traditional ensuring safety

and inflation

sensitivities matching paramunt: balancing

insurer's

assets

But asset/liability concerns of principal, remain and

one investment expected of each class

concern. returns,

maximizing the risks

of securities.

154