-------~----------------~-
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A f.1hTlli:I1ATICt.L HODZL FOR A
GROUP PSNSION
PROGRAI':
An Honors Thesis (ID 499)
by
Sharon N. O'f.1eara
Thesis Director
John A. Beekman, ASA
Ball State University
Huncie, IN
November 16, 1984
Expected date of graduation (Fall, 1984)
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Table of Contents
Page
I.
Introduction ........................................... 1
II.
Basics of a Pension Plan ••..........•..............•..• 3
III.
Classical Definition of Immunization ••.•••...•••.•••••• 7
IV.
Stochastic
I~1odels
•••••••••••••••••••••••••••••••••••••• 9
V.
Gifford Fong Theory of Immunization ••••••••••••••••••• 11
VI.
Description of the system •.......•.........•.....•.... 14
VII.
The System
A.
Description of Programs
B.
Instructions for Use
C.
Reports
D.
Calculation of Durations
,c,.
List of Programs and Their Functions
F.
Printout of Programs
VIII.
Implications of the Output ............................ 16
IX.
Conclusion ...........•......................•......... 17
x.
Footnotes .•....................................•....•. 13
XI.
Bibliography ••••••••••••••••••••••.••••••••••••••••••• 19
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Introduction
The progressive increase in the number and proportion
of the retired section of the population is of growing concern today.
The probable reduction of an individual's
earning pm"er upon leaving the work force must be planned
for in the earlier stages of one's employment history.
'''hat
resources can be drawn upon to survive once income from work
is discontinued?
In the past many have survived on social
security or private savings.
Drastic decreases in standard
of living have been seen in the life styles of the elderly.
Social Security is cutting back payments as it runs into more
and more difficulties paying the increasing number of elderly.
Economic security is a serious and increasingly important
problem of the United States.
One wayan individual can
ease the worries of income after retirement is to join a
pension program either individually through IRA's or KSOGH's
or through plans offered through the place of employment.
Pension programs have grown significantly since the 1940's;
however, they date back to the 1800's.
This paper outlines
what is necessary for a defined contribution pension plan
to be successful in providing benefit payments at a future
date.
The organization is as follows: A brief outline on
the structure of a pension plan giving rise to the need for
immunization, a definition of classical immunization, followed by a more recent theory of immunization developed by
Gifford Fong.
A model of a specific pension plan will be
2
shown and a description of how to project cashflows '..:ill be
given including a computer system developed to produce the
future cashflow for the product.
Finally, the results will
be shown that are then used by an investment department for
immunization purposes.
3
Basics of Pension Plan
'From the standpoint of the whole system of social
economy, no employer has a right to engage men in any occupation that exhausts the individual's industrial life in
10, 20 or 40 years; and then leave the remnant floating on
society at large as a derelict at sea.,i
This states that
there is an obvious problem of maintaining an adequate standard of living once past the productive, employable years of
life.
There are basically four methods of meeting the pro-
blem of superannu.ated employees.
First, "the employee
could be terminated without any further compensation or any
retirement benefits as soon as the value of the employee's
services is less than the salary being paid. ,,2
This is a
disadvantage to the employee but great financial advantage
for the employer.
Another method of handling the superannuated
employee is to retain the employee at the current level ,.,hile
the company absorbs the cost.
the employer this time.
Another undesirable method to
A third method would be to retain
the employee at a less demanding position.
This being a lit-
tle better than method two because a new, younger employee
can fill the vacancy.
ing the older employee.
This also reduces the cost of maintainHowever, none of these choices seem
to be desirable for the employer or employee.
An alternative
to these methods is to establish a formal pension plan.
A
pension plan is established through employer and employee contributions into a fund throughout the working years of the
employee.
This then accumulates at a predetermined or going
rate of interest until the employee reaches retirement age.
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He will then begin to receive payments from the pension plan
in lieu of his paycheck.
This method has become very popular
in the past forty years.
There are several advantages of pension plans to be considered.
For the employer, the superannuated employee can be
dismissed in a fair, reasonable manner without having to
worry about the cost and inefficiency of retaining him.
The
company will remain desirable for young employees in that advancements can be made.
The cycle vrould flow smoothly with
the older retiring and younger filling their positions.
Also,
the employees will feel more secure knowing provisions have
been made for them upon retirement and hopefully, 'Ilill increase
their morale and productivity.
Another advantage of a pension plan is for tax purposes.
Employer's contributions are tax deductable, a big plus for
the company.
Also, investment income is not taxed until
actually paid out.
From the employee's viewpoint, the employer
contributions do not constitute taxable income until actually
received.
At that point it is assumed the employee will be
in a lO\'ler tax bracket.
If a company is to attract new employees, it must offer
some type of retirement benefits.
If it does not, it is at
a strong disadvantage in the labor market.
Hence, pension
plans are a must for a company to survive.
Pensions are also a supplement to income after retirement.
Social Security and individual savings also contribute
to income.
However, neither is adequate to maintain one's
standard of living.
Most individuals need a combination of
'rr""'IIIIp.,. . . . .- - - - - - - - - - - - - - - - - . - . - - . - - -
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5
Social Security, private pensions, and personal savings.
Also, it has been shown that people would rather spend their
money as they earn it rather than put it into savings and
not see it until many years down the road.
Unexpected de-
mands arise where use of the 'savings for retirement' money
is needed immediately.
savings.
A pension plan is a form of forced
This is needed if the individual wishes to maintain
a relatively high standard of living after retirement.
The need for and advantages of pension plans have been
clearly pointed out.
However, the next problem is how is a
company going to provide pension plans for their employees.
Many sources are available to choose from.
Insurance companies,
trust departments of banks, corporate trustees all offer the
service.
The insurance industry first entered into the pension
business with the issuance of the first annuity contract by
Metropolitan Life Insurance Company in 1921.3
The problem of
providing a pension plan is now passed from the company to
the insurance company or other group to handle.
The question
remains as to how is one to guarantee payments upon retirement
and how much will they be; a major concern of the employees.
The company that provides the pension plan creates a
series of long term liabilities representing the obligation
to pay a specific amount of money or provide income for a
certain amount to annuitants.
Investments must be made at
the present time to meet these future demands.
Such invest-
ments are made up of common and preferred stock, bonds, mortgages, real estate, and cash.
All of these have different
rates of return and different levels of risk.
One first must
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analyze the structure of the pension plan and make investments
accordingly.
Liability determinations are based on actuarial
cost estimates. "Good pension administration includes close
monitoring of the estimates and assumptions.
The standard
list of actuarial assumptions include mortality expectation,
... , expected levels
of compensation, administrative costs,
ages of retirement, and finally, anticipated investment earnings.,,4
Until recently, many life insurance companies did not
have investment staffs that would permit them to follow the
total return concept.
A study on investment policies found,
'For most (insurance) companies, the labor, capital, and material resources employed in making investment decisions represent a negligible portion of total resources utilized by the
companies. ,5
New theories have. been developed since the 1940' s
on how to invest to get the·maximum yield and appropriate timing
for pension plans.
7
Classical Defintion of Immunization
'A portfolio of investments in bonds is immunized for
a holding period if its value at the end of the holding
period, regardless of the course of interest rates during
the holding period, must be at least as large as it would
have been had the interest-rate function been constant throughout the holding period. ,,6
Only recently has immunization of
portfolios become a major concern for insurance companies.
The above definition was written in 1971 by La,.,rrence Fisher
and homan L. Weil who then developed what is now known as the
traditional theory of immunization.
Immunization theory is
a key concept of the investment division of insurance companies and, if accomplished
successfull~
can lead to large
profits and a more flexible business.
The Fisher!Weil theory looks at an invester with x dollars now and wants y dollars at some time, t, in the future.
Any deviation from the y dollars at time t is a measure of
risk of the investment.
The Fisherl'lleil theory based their
investment strategy on the duration of an asset.
Duration is
'a number with dimension time attached to a stream of promised payments." 7 I'lathematically:
n
=:2..
j=1
t.P t
J
j
!fp
j=1
t j
-
t
0
D = Duration
Tj = Time
Pt. = Present values at time tj of promised payments.
J
From this they developed the immunization theorem.
They
first assumed interest is to be compounded continuously call this function i(t).
They then assume if interest rates
8
change, all rates change by the same amount.
In other words,
if ia(t) changes to ib(t) then
ib (t) • ia (t) + 1:l
'IIi th
these assumptions made, the immunization theorem states
the portfolio is immunized at to if duration, Dt ' of the
o
promised payments is equal to the desired holding period.
Therefore, an invester who wishes to be immunized from
interest-rate flucuations should have equal durations for
assets and liabilities.
Duration of a portfolio is a linear
combination of the durations of its components.
The invester
can match asset and liability durations by purchasing a singlepayment note whose duration is at least as long as the longest
liability and combining this with assets with shorter durations to come up with the perfect match.
This theorem should
lead the investor to at least break even if all assumptions
hold.
This theory has been developed with much more
theories now taking its place.
po~erful
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II
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Stochastic vs Deterministic J.1odels
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The classical definition used a deterministic model when
discussing the term structure of interest rates. liThe term
structure of interest rates exhibits the relationship among
the yields on default free debt instruments of different
maturities. IIS
This deterministic model, however, is inc on-
sistent vri th the treatment of assets where the prices are
determined under the assumption that returns on the assets
are random variables, i.e. not deterministic.
Phelim Boyle
summarizes two methods to determine the price of
Fi
pure dis-
count bond at time t with maturity time s and spot rate r.
Both of these methods follow a stochastic or random model.
It should be clear that a stochastic model is better suited
to determine spot interest rates because one, it is consistent with the method used in determining returns on assets
and two, it is a natural process assuming the market is
efficient and investors act rationally.
Furthermore, a
stochastic process is "a mathematical model used to describe
a natural process. ,,9
The two methods developed in Boyle's paper are by Vasicek
ambyC~
Ingersole and Ross.
Both assume the spot rate fol-
lows a Markov or continuous process.
The Cox, Ingersole and
Ross method also eliminates the possibility of negative interest rates.
It is very important to utilize a realistic
model in determining the maturity structure of liabilities so
the appropriate assets may be selected.
This matching of the
term of the assets in relation to the term of the liabilities
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so as to reduce the possibility of loss due to change in interest rates is of the greatest importance because, "it is
one of the three main factors within (the company's) control
which can endanger the solvancy of an office.,,10
The results of the Vasicek and Cox, Ingersole and Ross
methods make it possible to achieve immunization under the
classical definition.
There are differences in the mean
terms in the deterministic and stochastic models.
In the
deterministic model, the mean term is equal to maturity
date T.
The Vasicek model shows the mean term is less than
T but is bounded by T as T ~
term is always less than T.
the riskiness of the bend.
O{).
In the last model, the mean
Remember, the mean term measures
Hence, the stochastic models
give rise to larger investments in longer term bonds because
of the lower risk or less dramatic effect of an interest rate
change.
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11
Gifford Fong Theory of Immunization
Immunization involves the matching of the first
of asset and liability cashflow.
~oments
This protects against
parallel movements in interest rates.
Also, investment flex-
ibility is provided in that cashflo", matching is not required.
However, a problem encountered \vi th this technique is that
non-paralled shifts in interest rates are not protected
against.
A new risk management strategy was developed by
Gifford Fong and Oldrich Vasicek that addressed the risk of
non-parallel, movements in interest rates.
This is a little
more complicated than classical immunization since the second
moment as well as the first moment is involved.
The Gifford
Fong Str.ategy aims for an optimal tradeoff between risk and
return rather than minimizing the portfolio's immunization
risk.
Fong purposes to achieve this optimal tradeoff between
risk and return by maximizing the lower bound on the portfolio return.
The lower bound is a confidence interval on
the realized return for a given probability level.
The first condition necessary in the Gifford Fong strategy
is the traditional matching of durations.
Duration is the
weighted average time of all the portfolio payments, the weights
being the present values of the payment amounts.
Hathematically:
12
m = number of portfolio payments
Ci = Amount of payment due at time ti
poet) = Discount function
10 = Initial portfolio value or the sum of '
the present value of the payments.
11
Another condition that must be met is the i1ean Absolute
Deviation Constraints.
This says that the asset cash-flows
must be more dispersed than the liability cash-flO\'IS.
These
two constraints will subject the portfolio to immunization
risk from arbitrary or non-parallel shifts of interest rates.
A measure of immunization risk is denoted M2.
Mathe-
matically:
jvJ2 =
m
H = investment horizon
This is simply the second moment of future cash-flows or the
',.,eighted variance of times to payment around the horizon date. 12
For a portfolio that adheres to the above two conditions:
2
m
2t
m
2t
M =
(ti-D) V At (t. - D) V Lt
i=1
i=1
1.
D = Duration
VT = Present value
AT = Assets
LT = Liabilities
or the difference of the future cash-flows of assets and liabilities.
Traditionally jvJ2, immunization risk, is minimized.
Fong optimizes the riSk/return trade-off by maximizing the
lower bound of a rate of return confidence interval.
Define
Ds as a random variable representing an arbitrary change of
13
interest rate.
Therefore the change in value of the port-
folio assets and liabilities is _M2Ds'
The rate of return of
the asset portfolio is
R = "R - aM 2 Os
R = Rate of return random variable
1\
R = Target (expected) rate of return
a = Constant varying by duration of the asset
portfolio
The confidence interval for R can be represented as:
1\
R=R+k\r R
R = Confidence level.
Fang suggests maximizing the lower bound of this confidence
interval also written as
~
- k
a M2'\) s
"
Maximizing this is the same as minimizing M2 - )..P.
The use of linear programming and the duality theory will
accomplish the task of immunization.
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Desription of the System
It is necessary to give a simple example on how to
project cashflows and describe what implications can be
made from the output.
I have chosen to use a group pension
plan called the Growth
Gua~
project cashflo\vs.
Contract (GGC) for which to
The structure of the GGC is as follows:
X denotes the deposit period
for a group, usually 12 months.
Y denotes the holding period.
The company holds the money
Y months at a guaranteed interest rate. Y usually ranges
from two to five years.
Z denotes the disbursement period
of the money back to the insured.
Zxpenses can either be deducted from the account, credited,
or separately billed.
Benefit payments can be made throughout
the X-Y-Z periods, prorata,
or not
paid at all, LIFO.
There
are four combinations of billing/benefit payout options.
are accounted for in the system.
All
The system contains a main
program to project the cashflows, many subroutines used by
the main program, a database of all sales made from July, 1983
to the present, and several matrices containing fund balances,
deposits, disbursements, and interest earned.
It is of vital importance to keep the system updated each
month with all of the new sales, fund balances etc. to receive
an accurate cashflow projection.
invalid conclusions may result.
If this is not properly done,
To keep it current, user-
friendly programs are included to add new sales, insert fund
balances, and make adjustments.
--------~--.-------.--
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15
Several assumptions must be made before the cashflow
can be projected.
First is the amount of monthly deposit
expected in future months.
divided by the X period.
~ust
This is simply the total sale
If a policy is prorata, an assumption
be made as to how much the monthly benefit ?ayments sre
expected to be.
This is calculated by the underwriting
department based in past experience.
The deposits and bene-
fit payments should be monitored to see if they are deviating
from the original assumption.
~ade
If so, an adjustment should be
through the ADJUSTMENTS program.
This step is as im-
portant as keeping the database updated if accurate cashflows
are to be projected.
The main program ',viII take the sale from the database
and project a ten year cashflmv for each one.
accumulated to produce the final reports.
Totals are
From the results
the investment department can easily see the total dollar
amount 0::' inflows that are expected and how and when disbursements from benefit payments and maturities are made.
Also, the present value of the inflows and outflows, 1'1 ( 0) ,
the first and second moments, and D1- and D2, duration, are
shown for each case and in total.
Ultimately, matching of
the second derivatives (D2) is desired.
Following is a
printout of the system and brief explanations where needed.
GGC CASHFLOW PROJECTIONS
August, 1984
Introduction:
This system is designed to project the cash flows for the GGC sales
since July, 1983. The cash flows are projected ten years into the
future. Each sale is processed individually while the sum is accumulated.
A projection consists of three streams:
1).
2).
3).
inflows consisting of deposits only.
outflows consisting of expenses, benefit payments and
maturities.
an accumulation of the fund balance.
The final report contains an i ,flow monitor, out flow monitor, total
projection and, if opted, projections for each individual record.
One may request the projection from any point in time from July of
1983 to ten years past the current month. Any projection made starting
Detween July, 1983 and the current month uses the final balances as of
the projection date. If a projection is requested for a future date, the
most current fund balance is used to start the cashflow streams. Only
sales existing at the projection date are used to produce the streams.
Uhderwriter Responsibilities
For this system to be accurate, the Underwriters must be sure to
update it each month. Their primary responsibilities are to add the new
sales each month, add fund balances for the existing records, ,md make
adjustments that are necessary.
There are eleven possible adjustments, two of which require
monitoring the benefit payments and deposits. The changes would be made
to the benefit payment assumption field and expected monthly deposit
field if they consistently vary from the original assumptions.
All adjustments can easily be made using the "Adjustments" program
and new sales are entered using the "Newsales" program. Both are user
friendly.
Using the System
The system must be run on an IBM PC equipped with an APL chip. To
begin, insert an APL disk in disk drive A and hit control, Alt, Delete at
the same time. Next, clear the workspace by typing) )CLEAR. Take out
the APL disk and insert the cash flow disk. Load the program by typing
)eOPY CASHFLOW. It will take a minute or two to complete this step. A
final important step that must be done before running any of the programs
is to tie the files so they can be accessed. This requi res two commands
as follows:
'DATA' 11 (QUAD)
'NAMES' n, (QUAD)
.,
FTIE 100
FTIE 200
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The quote is the uppercase k and the quad is the upper case 1.
system is now ready to run any program.
The
The options are:
Newsales - to add new sales
- to enter monthly fund balance
Adjustments - to adjust existing records
Program - to project the cash flows
New~al
Newsales and newbal should be run together monthly. 'Program' may be
run at any time. Adjustments are stored for one period only.
**All adjustments for one month should be made at one time to prevent
losing ,ny of the net changes.
Records in Database
1983:
Policy if!
Company Name
Carpenter's Severence & Annuity
Frisch's Restaurant (12.55%)
Total Petroleum
Hanna Mining
Michigan Consolidated Gas
GWL Savings (12.56%)
GWL Savings (12.69%)
Tab Merchandising
8oscov's Department Store
Hydrotex
Rexham Corp.
Cassentino
Mobile Home
Anaheim Union H.S.
Pepsi-Cola
Oakland Unified School
Nabors Alaska
Cameo
American Petroleum
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Records in Database
1984:
Policy II
Company Name
Hudson Screw
Housing Authority of st. Louis
General Hospital of Everett
Robert C. Wilson
Schweiger Industries
City of Springfield
Sherwood Enterprises
Electro Corp.
Pool Arctic Alaska
KLA Instruments
Boscnv'.s Department Store (12.85%)
First Michigan Cap. Corp.
Frisch's Restaurants (13.15%)
Harrison & Crossfield
Whiting Corp.
Georgia Kraft
Fieldale Corp.
National Asbestos
Tandin
St. Judes (13.85%)
St. Judes (13.9%)
Cleveland Newspaper Pub.
Harrison & Crossfield (14.07%)
Intercity Transit
Washington Forge
Manville (14.41%)
Accent Displays Inc.
American Petroleum
Panhandle Motor Services
Pro jection :
AJRPOSE:
CALCULATION OF
DISBURSEMENTS:
CALCULATION OF
FUND BALANCES:
CALCULATION OF
DURATION:
To project casn flow streams for each sale and
accumulate totals for all sales since July, 1983.
User may choose any date to make the projection.
Any date prior to 7/83 will give all zeros. Any
date past the date the 1st fund balances will start
at the date of the most current fund balance.
Durations can be calculated if user desires. The
floating point arithmetic required for these
calculations slows down the system considerably.
Be prepared to spend an afternoon running
"Projection".
1.
Benefit = LIFO, Expenses = BILL
Disbursement vector =
2.
Benefits = LIFO, Expenses = DEBIT
Max (.15, .00038 X FB)
.00038 X 2000 + .0003 (FB-2000)
3.
Benefits = PRORATA, Expenses
Ben % assumption X FB
4.
Benefits
2+3
°
= PRORATA,
FB
FB
2,000
2,000
= BILL
Expenses - DEBIT
FB (X+l) = FB(X) + Dep (X+l) - Disb (X+l) +
[FB(X) + Dep (X+l) - Disb (X+l)] X (Int/12)
(Y\
DO
=
L.
~t.
1;)1:
t.=o
01
=
'"
~
-t.;o
02
=
t
t v
A. t
."'-
L
-1..=0
1.."" \Jc
1\ to
~t.. ~
C"'-"'''- ~
PURPOSE:
Same as setproj except fund balances for current
month have been entered and are used as beginning
fund balances.
Mjustments:
PURPOSE:
To change a factor of a record in the database.
Changes can be made to:
-
Policy number
-
Company name
-
Policy type
-
X-Y-Z period
Interest rate
-
Effective date
-
Expense payment
-
Annual benefit percent assumptions
-
Expected monthly deposits
FUNCTI ONS CALLED:
V-period, 2-period, Interest, Expenses
START
Type ADJUSTMENTS
PROGRAM:
-6-
Projection
Variable Table and Their Function
Accumulators:
INt
SP
NOEP, NDIS8, NF8
DEP, OISB, FBV, INT, MAT
ROEP, ROIS8, RFB
Interest
Single premiums
Deposits, Disbursement, Fund balance of new sales
Deposits, disbursements, fund balance, interest and
maturities for current sale
Deposits, Disbursements, fund balance of renewal sales
TOTDEP, TOTDISB
TOTFB, TOTINT,
TOT:-tAT
Accumulate total
SORTPOL
DRTD, DRTl, DRT2
MORTO, MDRTl, MDRT2
AORTO, ADRTl, ADRT2
ARORTO, AMDRTl, AMDRT2
t-blds policy numbers as they are read from "DATA"
DO, 01, 02 for outflows at credited interest rate
DO, 01, 02 for outflows at market interest rate
DO, 0, 02 for inflows at credited interest rate
DO, 01, 02 for inflows at market interest rate
DURO, DURl, DUR2,
~RO, MDURl, MDUR2,
ADURO , ADUR l, ADUR2,
AMOURO, AMDURl, AMDUR2
Temporary variables to accumulate durations as they are
being calculated. Assigned a position in above vectors.
DURANS
MKTINT
PRANS
Answer if want to calculate duration
If calculating duration, holds market interest rate
Answer if print each sale
SIZE
Size of database
counter for files, general
J,I
FLAG
Used in calculating remaining time i.e. projection date
- effective date
T
Time
Ramaining time of policy
Remaining time from 7/83 i.e. projection date - 7/83
Sale information read from "DATA"
INFO
x, y,Z
Nl
N
·ZTYPE
Zl
OZ
Q
Count
X,Y,Z periods
Total time of policy - X+Y+Z
Remaining time of policy
Type of dibursement for Z period
Number of quarterly deposits
Original Z period
Month starting disbursement period i.e. (X+Y+l)
Counter used to determine when to make quarterly
dibursement
INSlRUCTIONS TU USE GGC
CASHFLO~
Starting the system:
C!1Jy IBM PC's with an APL chip can run the system. One is located outside of
Luke Girard's office, one Is on lOth floor by David Wolpo, and one on 6th
floor by Paul Er ickson' s 0 f f ice.
To begin insert the APL disk in drive A. This should be located right next to
the PC. Boot up the system by hitting CTRL, ALT, DEL at the same time. About
45 seconcs later a message "see describe" will ClPppt'r. ('1 ear the screen by
typing )Clear- )1s the uppercase semi colon. Remove the APL disk and insert
the GGCCF APL disk. Loao new workspace by typing )LOAD CASHFLOI'I. If
"workspace not compatible" appears type )COPY CASHFLOW. This takes about two
minutes. Next insert the MATRICES Disk in drive A ana type )COP\ MATRICES.
All information is now loaded. Reinsert the GGCCF APL disk in drive A.
The sy~.tem is now ready to run. Type INSTRUCTIONS for general instructions on
how to enter information. There are several options available.
All APL characters are founa on a STSC APL sheet located near the P.C.
IMPORTANT
Before starting two commands must be typed!
'DATA'
'NAMES'
OFTIE1OO
C FTIE 200
'is uppercase k
o is uppercase
L
This rust be done to be able to access the files.
~tion
1:
Add new sales. Type NEWSALES to begin. The user is prompted to
enter all of the pertinent information fur each sale. If a mistake
was entered several things can be don~ to correct it. If it
occurred before the 'Is this a new or rpre~~l ~ale?' question hit
CTRL ESC. This exits from the program. To re-enter simply re-type
NEI'ISALES. If the error occurs after that question the followin\,i
must be typed.
1.
OFDROP
100
-1
2.
OFDROP
200
-1
is uppercase L
is uppercase 2
3.
is uppercase )
[ is i key
a number will appear - say X
4.
F~~TRIX
FBMAlRIX [100il)
[100;
l)~X-l
(one less the number shown above)
A new sale can now be entered.
---~---------------------
----------------------
Optlon 2:
Make adjustments to existinG sales. Type ADJUSlMENlS to begin.
The user is given eleven options on different adjustments to make.
Several may take a couple of minutes to complete. The adjustment
Is complete when the questions, '00 you want to make another
adjustment?' appears. The best way to corr~rt pn error is to make
a negative adjustment or re-enter the ~riginal assumption. This
should zero out any changes that were made.
Option 3:
Enter new fund balance. Type NEWBAL to begin. This program enters
fund balances, deposits, cisbursements, and interest into different
matrices. The matrices are FBMATRIX, DEPMATRIX, BENMATRIX,
l~lMA1RIX.
If error occurs, the appropriate matrix entry must be
found to search for policy number which is the first column of all
matrices. Type FBMAlRIX [(0 + 100);5lJ ~is the uppercase I.
Locate correct policy and count which entry is X. Type FBMATRIX [X
(from above step); j to locate the incorrect entry. Count its
position, say y. To correct the entry type FBMATRIX [X; YJ ~pew
entry~ lhis must be oone for all matrices that may have receiveo
the incorrect answer. Also, if a deposit was entered wrong and a
was or single premium salE, SPMATRIX must be correcteG in a similar
fashion.
Option 4:
Pro,iect cashtlows. Type PROGRAM to begin. A series of questions
follows. Once the answers are entered the projection begins. It
may take an afternoon to run. All reports are produced after the
projection is complete. I suggest beginning it in the morning. If
for any reason it must be stopped hit CTRL BREAK (Upper right
corner). This interrupts the program. Corrections can be made to
the programs. Type ~ t) LC to continue ~ is the J key, (lis
uppercase L. Be sure not to change any variables like X, Y, Z, J,
or totals. If PROGRAM is stopped and restsrttd by typing PROGRAM,
the whole process is started over. If )RESET is typed the position
is lost.
~ D lC does not work.
---------------~-----~---
-------~-----------
Reports Generated from Projection
Illustration:
Inflow Monitor
1. Outstanding future deposits at beginning of period $5,000
2.
3.
4.
5.
6.
New sales in month
Renewed sales
Adjustments
Expected in-month deposits
outstanding future deposits at end of period
1,000
2,000
500
(1,500)
7,000
Illustration:
Outflow Monitor
Cash Items
Actual
1. Funds at beginning
$25,000
2. Single premiums
2,000
3. Annual premiums
1,700
4. Disbursements
(300)
5. Maturities
(1,000)
6. Interest credits
3,000
7. Funds at end of period $30,400
Projected
~25,000
o
1,500
(350)
(900)
2,900
$28, 150
Disbursement
Cashflow
Movement
~
a
2,000
200
50
( 100)
100
$2,250
Non-cash Items (excludes single premiums)
8.Newsales
9. Renewal sales
10. Adjustments
$1,000
2,000
500
11. Total movement
$5,750
-
------~
-------------------------
-
-------
----------
-
-----------
The inflow monitor will show what the forward commitment position ought to be (7,000) and hm'l it changed.
The
outflOl'l monitor will show how much the company should have
invested and disbursed (30,400) and how it changed.
It will
also show why the future disbursement cashflows have changed
since the beginning of the period.
These monitors, however,
do not show changes due to changes in disbursement assumptions.
To keep track of adjustments, in adjustment report can
be produced.
only.
This will show the adjustments for that month
It is displayed for 120 time periods to show the net
monthly change.
Adjustments are broken down into changes due
to adjustment in:
X period - total deposits expected
Benefits - total benefit payments made
Interest - change in interest rates
Expenses - How expenses paid
Y period - Holding period
Z period - Disbursement period
Calculation of Durations
DO =
~
vt
n
D1 = £.
t=O
D2
=
n= number of months remaining
in contract
At=Assets
At
t=O
tvt A
t
~
t=O
111 = D1 .;. DO
112 = D2 .;. DO
Zero, first, and second moments, Duration 1, and Duration
were calculated for assets and liabilities. They were also
calculated at the interest rate stated in the contract as well
as a common market rate for all contracts. The user determines this rate. They are displayed as follows:
2
Outflows
Credo Int.
DO
D1
D2
111
112
Market
Inflows
Crect. Int.
Market
- - -
--~~--
-----
-----~---
Program
Function
System translation
APL keyboard
Turnprinter
start printer on/off
Start
start printer
stop
stop printer
Printrep
Displays cashflo\\' for each sale
Duration
Prints durations, DO, D1, D2,
M1, M2, for each sale
Totals
Prints final totals for all sales
In monitor
Inflow report
Out monitor
Outflow report
Adjrep
Displays total adjustments
made to database and the net
change in position
Instructions
General instructions to
use system
Program
Core program to project cashflows and make adjustments
Projection
Projects cashflow for each
sale 10 years into the future
Totsp
Stores totals for single
Newsp
premium sales
Rensp
separately
X1
Determines remaining time
X2
X3
Y1
Y2
13
from projection date to end
of contract.
Sets x, y, z
to appropriate lengths.
---------~~-~----~~---
-------------- -----
Program
Function
Adj:.lstments
Allows changes to be
made in database
Y period
r1akes adjustments to
Z period
specific items.
Interest
Expenses
New sales
Add sales each month
Ne'tlbal
Updates fund balance each
J
month
Set proj
Set proj 1
Determines which fund balance
Set up of database
How records are stored
to use to start projection
Data
Contains numerical information
Names
Contains company names
FB matrix
Matrix of all sale fund
balances.
Size 100 x 50
Similar matrices for deposits, disbursements, interest, adjustments, single premium deposits
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16
Implication of the Output
This program takes one line of business from a medium
sized company and calculates the first and second moments.
This analysis can then be sent to the investment department,
so they can invest in the appropriate length assets to
guarantee the money will be available when needed.
If this
is done for all possible lines of business the result will
be a smooth cycle with final payments being made with the
corresponding deposited money.
Having the first moments
of assets and liabilities match is the first task.
''lords, the Dean durations should be equal.
In other
In the classical
case, the second moment of the assets should be greater than
. the second moment of the liabilities.
In other theories,
mainly the Gifford Fong Theory, the goal is to maximize the
lower limit of the confidence interval.
In either case, the
output can guide the investment division as to what investments
to make.
:. f
! '
17
Conclusion
The solubility of an insurance company is greatly
affected by the actions of the investment department.
If
they do not invest properly, reserves may have to be dipped
into weakening the financial standing of the company.
Im-
munization has recently been developed to help companies
steer away from the misforturne of making inadequate investments.
As the name suggests, immunization is a process to
acquire a high degree of resistance or security against outside threats of danger.
In the insurance industry, the company wants to be
immune from shifts, parallel as well as non-parallel, in
interest rates of their investments.
This can be accomplished
through many different techniques of immunization.
The aid
of high powered computers and different hardware packages
can make immunization a relatively easy process that can be
accomplished by any size company.
to be blazed.
The trail has just begun
Many new avenues are yet to be pursued in the
development of immunization theory.
18
Footnotes
1Lee ·,ve lling Squier, Old Bge De'Oendency in the United
States (New York: MacMillan 0., 1§12), p. ~2.
2Everett Allen, Joseph Helone, Jerry Rosenbloom, Pension
Planning (Illinois: Richard D. Irwin, Inc., 1981), p.8.
3Kenneth Black Jr., Group Annuities (Philadelphia: University of Pennsylvania Press, 1955), p. 9.
4'llilliam C. Greenough, Francis P. King, Pension Plans and
Public Policy (New York: Columbia University Press, 197b):-P.192.
5Lawrence D. Jones, Investment Policies of Life Insurance
Companies (Boston: Harvard Univeristy, 1968~' P:-;37.
6Lawrence Fisher and Roman L. 'lleil, Coping with the Risk
of Interest Rate Fluctuation. Journal of Business, 44, p. 11.5.
7 Ibid •
8Boyle, Phe[m, Immunization Under Stochastic Models of the
Term Structure, Journal of the Institute of Actuaries, 105
(1978), 177.
-- ---9Beekman, John A., "What on Earth is a Stochastic Process?,"
October, 1970, p.2.
10Redington, F.M., Review of the Principles of Life Office
Valuations, Journal £! the Institute £! Actuaries, 78(1952), 289.
11Gifford Fong and Oldrich Vasicek, The Tradeoff Between Return and Risk in Immunized Portfolios," Financial Analyst
Journal (1983), 4.
12 Ibid ., p. 5.
19
Bibliography
Allen, Everett, Joseph Melone, and Jerry Rosenbloom. Pension
Planning. Illonois: Richard D. Irwin, Inc., 1981.
Beekman, John A. '.lhat on Earth is a Stochastic Process?
ber, 1970.
Black, Kenneth. Group Annuities.
of Pennsylvania Press, 1955.
Octo-
Philadelphia: University
Boyle, Phelim P. Immunization Under Stochastic Models of the
Term Structure. Journal £f ~ Institute £f Actuaries, 1978,
105, 177-187.
Fisher, La'.'Irence, and Roman L. '.veil. Coping with the Risk of
Interest Rate Flucuations. Journal £f Business, 1971, 44,
408-431.
Fong, Gifford, and Oldrich Vasicek. The Tradeoff Between
Return and Risk in Immunized Portfolios. Financial Analyst
Journal, 1983, 1-8.
Greenbough, 'ililliam C., and Francis P. King. Pension Plans
and Public Policy. New York: Columbia University Press,
~6.
Jones, Lawrence D. Investment Policies of Life Insurance Companies. Boston: Harvard University, 1965:----Redington, F .M. Revie'" of the Principles of Life Office Valuations. Journal of the Institute of Actuaries, 1952, 78,
286-340.
- Squier, Lee ;'1. Old Age Dependency in the United States.
York: l1acMillan Co., 1912.
New