or How it Works and How it’s Done!
the Society announced that it was reducing the payments to With-Profits
Annuitants (WPAs) by 20%, it was decided to collect data from annuitants
to study the impact and try and identify any patterns. A computer model
was developed initially to predict what the reduction might be, but
later on to understand the likely future impact on annuitants’ pension
were asked to send the following details about their annuities:
annuitants have provided all this information. The data was initially
stored in a spreadsheet as set out in the diagram below. This enabled
basic cross checking of the totals, the derivation certain ratios and
percentages, validated that the numbers supplied were correct
arithmetically, that they were internally consistent and that as far as
possible what has been sent has been accurately reported and
transmitted. For example, the % Change for the Basic Annuity should be
constant, except for 2002, and it should match the Anticipated Bonus
Rate chosen by the annuitant.
The Equitable Life Annuity
The initial annuity is
derived from the consideration money supplied by the annuitant and other
factors such as gender, age, joint or single life, annuity rates in
general, etc, etc. In the case of ELAS, there is a significant
complication since the annuities being reviewed are called With-Profits
Annuities. As one ELAS representative said, “Why would you want to
take a Fixed Annuity, when you can take a With-Profits Annuity that will
start at the same level as those offered by other Pension companies
except that ours (ELAS’) will grow at least in line with inflation?”
The Equitable Life
Assurance Society (ELAS) produces With-Profits Annuity - Annual
Statements every year for each annuitant and which contain the following
Guaranteed Annuity (BGA)
Bonus Annuity (DBA)
Bonus Annuity (FBA)
Gross Annuity (TGA)
Society also produced another document somewhat confusingly called the
Bonus Declaration for the Year Ending 31 December 19NN, which contained
references, amongst other things, to:
Bonus Rate (ABR)
Rate of Return (ORR)
Bonus Rate (DBR)
N.B. In the footnote to
each page is a summary of all the abbreviations used in each section as
an aid to understanding.
So far as is known, the
last Annual Statement that was issued is dated March 2000, announced the
ORR and DBR for 1999, which became effective on 1st April
2000 which, in the example illustrated, as the annuity started on 28th
of February, means that it became effective on 1st March
2001. This is confusing enough, but the Society uses a concept known as
the Interim Rate. In the year in question it was set at 9%, which the
Society then used to compute the annuity payment, though the actual rate
turned out to be 10%.
4.4) The Method
A model/simulation of
the Society’s system was developed for analysing annuities initially
to 'forecast' future results but subsequently was extended to evaluate:
The consequences of decisions made by annuitants
The strategy and tactics used by the Society to manage the
With-Profits Annuities and their payments.
It is based, using
M/soft Excel, on the detailed analysis of 72 annuity annuities supplied
by 51 annuitants as evidently some have multiple concurrent annuities.
These are linked to a summary page for statistical analysis and
graphical output, which in turn is linked to a M/soft Word document. So
far as can be judged, it is statistically valid though evidently the
sample being self selected is not truly random in the accepted sense of
the term. The data includes annuities from the late 80's through to 2000
and include all types, sizes, options, etc.
The average annuity on
the database is £8,620 compared to a claimed average by the Society of
approximately £6,000. There are 17 annuities with annual payments in
excess of £10,000 p.a. but these have not been removed to see the
effect of the change, as it is not believed it would be significant. In
any event, as annuitants’ details have been added, the “average
values” that have been derived from the data have not varied
significantly so that it is reasonably certain that the analysis is
based on a valid data sample.
In the absence of
direct access to the Society’s computer systems and internal records,
it is not known if this is the method used by the Society but since this
model gives results that correspond to reality then it is:
4.5) The Model
The data supplied by
the annuitants, as illustrated above, is put into a second spreadsheet,
as shown in EXAMPLE 1 below. There is one spreadsheet for each annuity
and these are then summarised automatically for statistical analysis and
generate the charts displayed in Section 2.
The model of the system used by the Society is in itself of interest as it throws up a number of points that are not immediately visible from the documentation given to annuitants. Regrettably in order to illustrate these points it is necessary to enter into some technical detail. However if there is to be any true understanding of the issues involved, the effort is essential
1 includes all the changes to the ORR, DBR & TRL made by the Society
plus the various uplifts and reductions imposed by the Society in recent
As will be immediately
obvious, in addition to the abbreviations mentioned earlier there are
several others that must be added to the menagerie. These are as
Guaranteed Annuity (NGA)
Declared Bonus Annuity (NBA)
Return for a Level Annuity (TRL)
The last complexity is
that in this section, some of these abbreviations will have some
extensions such as:
“.ly” for Last Year, “.ty” for this year or
“.01” for 2001, “.99” for 1999, etc
At the outset of the
annuity, the annuitant transfers a sum of money, the consideration,
in exchange for a regular payment, the annuity. The annuitant
agrees with the Society in advance an Anticipated Bonus Rate (ABR).
Prior to 1997, the
Society offered a facility called a GIR, Guaranteed Interest Rate, which
was set at 3.5% above the anticipated rate of return. There may have
been other rates but annuitants have not sent any. The TRL for GIR
annuities is the ABR * 1.035. The TRL for non-GIR annuities is the same
as the ABR. EXAMPLE 1 illustrates a non-GIR annuity.
For the reasons
explained below and which relate to how the Society computes the TGA,
the model does not precisely calculate the value of the TGA. The
difference is not large, between ½ and 1%, is NOT cumulative and is
ONLY significant when the model comes to forecast the exact reduction of
an annuitant’s annuity before their renewal date. A request for a
detailed explanation has been sent to the Society but there has been no
response so far.
only to the difference above, the model computes exactly all the values
of the BGA, DBA, FBA & TGA for all years from three basic sets of
Self evidently, the
model also uses the various bonus rates issued by the Society, as
described above, but they apply to all annuitants though they are
different for GIR and non GIR annuities.
In EXAMPLE 2 the
starting Guaranteed Basic Annuity has been rounded for purposes of
clarity and will be used as the basis for illustration in this section.
The actual calculations
may be a little esoteric but there are two reasons why the underlying
logic may be worth absorbing:
Many annuitants have stated they do not understand how their
annuities are calculated and they would like to know, as is surely their
Understanding the Society’s calculations, will lead to a better
understanding of what the Society is doing or not doing on behalf of its
members, the WPAs.
model data displayed in EXAMPLE 2 should be used to follow these
The Basic Guaranteed Annuity (BGA)
is computed as follows, after the first year:
= BGA.ly / ABR or
9,346 = 10,000 / 1.07
is repeated each year, so that the BGA always declines at a constant
rate, save in the most exceptional
circumstances as in 2002 described below. Any variation must be approved
by a majority of members and by the Court. Any further variation in BGA
or DBA seems very unlikely.
The Declared Bonus Annuity (DBA)
is computed as follows:
In the first year, the New Declared Bonus Annuity (NBA) is
derived first as follows:
x DBR x No of days between the start date and year end / 365 (In the
example, the start date was 28th February)
10,000 x 0.065 x 306 / 365 = 545
value is not added to this year’s annuity but carried forward to the
DBA for the first year is always zero.
Most annuitants do not
know that the start date of the annuity is not the date of the first
payment, but appears to be the date when the annuity was processed,
which is not necessarily the same The start date of the annuity in
theory can be easily derived by backwards iteration and most times is
easily computed but in practice turns out to be another source of error.
For a small percentage of annuities, the value for the initial DBA is
not immediately computable by this method and which leads to the
conclusion that the data was entered into the system incorrectly as no
other explanation seems logical. This has no long-term significance
partly as the difference is only a few pennies and the method used by
the Society is to some extent self correcting, since any error here is
compensated by the way Final Bonus Annuity is calculated.
In the second year, the Declared Bonus Annuity is computed as
= DBA.ly + NBA.ly / ABR
or (0 + 545) / 1.07 =
is computed as follows in two steps:
NGA.ty = BGA.ty + DBA.ty or
(9,346 + 509) = 9,855
NBA.ty = NGA.ty x DBR.ty or
(9,855 x 0.065) = 641
This step is then
repeated for each year in succession.
the 2002, the Society increased the GBA and DBA by 4% for all annuitants
(0.5% for GIR’s) as part of the Compromise Deal and that calculation
is as follows:
= BGA.ly / ABR x 1.04
or 7,629 / 1.07 x 1.04 = 7,415
= DBA.ly / DBR.ty x 1.04
or 1,817 /1.07 x 1.04 =
There is one other
feature of the DBA that must be mentioned. In EXAMPLE 2, the DBR for
1997 has been set at 6.50%, mainly to illustrate the basis of the
calculation. In the process of analysing all the data, it was obvious
that certain annuitants, where the start date of their annuity lies
between January 1st and March 30th were not
treated the same way as other annuities. In the first year their DBR was
always set to zero. The Society states that this is because in that
period, just as with the ORR, the DBR cannot be known and rather than
use the previous year’s DBR, surely the most logical thing to do, it
decided to set it at zero.
Now it is important to
be clear that this has no effect on the Total Gross Annuity, at least
not until the 20% reduction is applied, (See below) but it does have the
effect of reducing the DBA, which is guaranteed, and increasing the FBA,
which is not guaranteed and thus can be removed by the Society. The
significance is that, using EXAMPLE 1, after the 20% reduction had been
applied, the TGA in 2003 would have been approximately £300 higher that
that actually paid.
The Final Bonus Annuity (FBA) is computed as follows:
= TGA – NGA
or 11,683 – 9,181 = 2,502
is the normal calculation, but in 2003 the Society introduced a 20%
reduction to the Final Bonus Annuity. (FBA) For many annuitants the
above calculation would have meant the FBA would have become negative,
which is obviously not permissible because
it would break the contractual terms of the annuities.
Under these conditions the FBA is computed as follows:
TGA.03 – NGA.03 is greater than zero,
THEN FBA.03 = TGA.03 –NGA.03
TGA.03 – NGA.03 is less than or equal to zero,
THEN FBA.03 = 0
since this results in an unequal reduction for different annuities and
annuitants, it would have been more logical to permit the FBA to go
negative so that all annuitants received the same percentage reduction
on their TGA. However,
as stated above, this would have been a breach of contract.
The Total Gross Annuity
is the most contentious of all the elements that go to make up the
annuity for the WPAs – not least since how this is calculated directly
affects how much the annuitant receives. As noted above, the formula has
never been explained in any detail and even where it has the results of
the formula do not appear to work. What is known is that the Society
decided that, as it could not know the true ORR in the early part of the
year, it would use a so called Interim rate for the first part of the
year and after April 1st the ORR as announced by the Society.
is not appropriate to comment on this issue in this section other than
to say, there are easier ways that deliver results that very closely
match those derived by the Society and it is those that will be
model uses this simplified version, which produces perfectly adequate
values for the purposes of this analysis and is as follows:
= TGA.ly / TRL x ORR
10,857 = 10,561 / 1.07 x 1.10
noted above, in 2003, the Society introduced a 20% reduction that was
imposed on all WPAs. The computational logic of the Total Gross Annuity
and the FBA in 2003, which was a little more complex, is as follows:
(TGA.03 -TGA.02 *0.2)
is less than TGA.fy,
TGA.03 = TGA.fy
TGA.03 = TGA.03- TGA.02 *0.2 and
= TGA.03 - TGA.03
11,448 - (12,216 * 0.2) = 9,005 which is greater than 8,754 so
= 9,005 and FBA = 9,005-8,754 or 251
is no pretence that the formula described above gives an exact
duplication of the FBA, although the difference is relatively small,
typically less than 0.5% or approximately £500 in an annuity of £10,000
p.a. The model continuously adjusts for the error so that the overall
results remain in line with the numbers given by the annuitants. The key
point is that the underlying logic of the process by which the Society
derives the annuities is not obscured and it is that issue that is being
recent years there have been other alterations as follows:
Following the House of Lords ruling the ORR was reduced by 1% in
2001 and 2002 and by 1.5% in 2003 and 2004.
As part of the Compromise deal the TGA was increased by 2.5% in
changes come into force on the anniversary of the annuity though they
are not based on a calendar year, but on the Society’s year, which
appears to run from April to March.
General Rules about the ELAS With-Profits Annuities
a result of the analysis, it appears that the following logic applies to
all With-Profits Annuities with Equitable Life Assurance Society:
A) Overall Rate of
Return (ORR) in relation to the Total Return for a Level Annuity (TRL)
the TRL is the ABR increased by a factor of 1.035
the TRL is the ABR and is NOT increased
B) Anticipated Bonus
Rate (ABR) in relation to the Declared Bonus Rate (DBR)
If the ABR = DBR
If the ABR > DBR
If the ABR < DBR
Note: In all
conditions, the relationship between the ABR and DBR has no effect on
the TGA and FBA
logic is normally obscured since the ORR & DBR change each year and
is ONLY evident when the values are set at a constant level over a
period of time that the validity of these logic statements become clear.
In EXAMPLE 3 below, with the same starting point, but setting the Declared Bonus Rate at zero, there is no change to the Total Gross Annuity, though as the Declared Bonus Annuity is now zero the Final Bonus Annuity increases to compensate.
illustrates two very important points:
The values of the BGA and DBA combined are independent of the
value of the Total Gross Annuity.
The Final Bonus Annuity is simply the difference between the two
there are two independent series, one, which determines the values of
the BGA and DBA and the other, which determines the TGA.
EXAMPLE 4, the TRL has been set to equal the ORR. It is self evident
that in this situation, the annuity remains level as it expected and
advised by the Society.
It may not be
obvious, but in order to achieve the same level of growth for a GIR
annuity that a non-GIR annuity achieved, that is the TGA in 2003 would
be £11,322, the TRL would be 11.0745 (10.7 *1.035), the ORR would need
to be in excess of 13% each and every year! That is not possible in
today’s economic reality, which may be an explanation of why the GIR
annuity was withdrawn in 1996.
addition, the model has identified some anomalies between what is normal
and/ or what was stated or implied by ELAS in its documentation. In some
cases this appears to be arithmetic errors on behalf of the Society,
which implies that there is clerical intervention in the calculations of
annuities. Quite why there should be these errors in what one would
assume to be a highly automated, system driven methodology is not
of the consequences of the actions of the Society has been to remove a
substantial amount of money from the WPAs for the remainder of their
lives. For example, if an annuity is reduced by £3,000 p.a., the
annuitant has not just had a reduction of £3,000 but £3,000 p.a. for
the rest of his or her life. A new base level has been set, so that even
if the annuity increases in the future it is from the new lower level.
If the annuitant lived another 17 years, then whatever happens in the
future, the annuitant has lost £51,000 income.
follows therefore that one of the key numbers is how to determine the
life expectancy of the ‘typical’ annuitant. The method chosen is to
compute the number of years between the annuitants’ age at July 30th,
2003 and the remaining ‘actuarial’ life expectancy of the annuitant.
the life expectancy of the Society’s annuitants is a very specialised
area of research and statistical study and lies outside the area of this
analysis but the following has been extracted from various sources on
the Internet and which are pertinent to this report.
There is a BBC document that reports increasing life expectancy
up by 5 years for men and 4 for women in the period 1980 to 2000. Thus
it follows that by today, life expectancy has increased again.
expectancy was 75.2 for men and 80.1 for women in 1999.
and posted on the Internet, retrieved by a search using Google and
“Life Expectancy” )
expectancy is heavily weighted in favour of the social classes I, II
& IIIN, the classes most likely to buy private pension funds. In
1996, the life expectancy for these classes is approximately 75.8 for
men and 81.1 for women compared to the average across all classes of
73.9 and 79.3 respectively.
from www.bris.ac.uk/poverty/wales/NHS-RAR_1.pdf and posted on the
Internet, retrieved by a search using Google and “Life Expectancy”)
implies the following that in 1999 the life expectancy for these social
classes will be
/ 73.9 * 75.8 = 77.1 for men
/ 79.3 * 81.1 = 81.9 for women
expectancy is increasing steadily so that by 2003 it would be reasonable
to expect a life expectancy of 78.6 for men and 83.5 for women. The
actuarial age of death of 80 was selected as being a reasonable median
age for the purposes of the model and this report.
is worth noting that if the life expectancy is reduced by 1 year, the
percentage reduction in the amount of money removed by the Society is
approximately 1.25% p.a. In other words, even if the selected age of 80
is overly optimistic, the effect on the reduction over the lifetime of
the WPAs is quite inconsequential!
method used by the Society to compute the annuities is very subtle and
as the variables vary each year more or less independently of each
other, it is not possible to see what the effect of each change might be
unless each variable is isolated from the others. This section has been
devoted to an attempt to explain how each variable works.
It is clear that the relationship between the ABR and DBR
determines which part of and how much of the annuity, is in the terms of
the Society guaranteed.
It is clear that the relationship between the ORR and TRL
determines the overall size of the annuity.
The difference between these two arithmetic series defines the
TGA. It is this part of the annuity that is completely un-guaranteed by
The critical decision therefore is to choose the Anticipated Bonus Rate (ABR) that in the annuitant’s judgement best suits his or her needs. However:
two objectives are in mutual contradiction.
the other sections, how these inter-relationships work in real life,
will be explored and various contentious issues exposed.
The data sample is small and not truly random and the numbers and values
used in the preparation this report are based on the data supplied by
annuitants. It is possible that there are statistical anomalies or
errors that have not been detected and that may result in some of the
numbers used in this report being less accurate than they otherwise
might have been. However, it is very unlikely that the conclusions,
deductions and inferences that have been made have been materially
affected by any such errors.
Your with-profits annuity - planned
reduction to income payments
am very sorry to let you know that we will need to make changes to your
with-profits annuity, which will significantly reduce your income
payments. This letter gives
you some warning, before your next review date.
have done our best to protect you, as far as possible, from the major
setbacks we have recently experienced.
However, unfortunately, to be fair to all our other
policyholders, we must now begin to make these changes.
which have taken place so far on with-profits annuities
20 July 2000, our decisions on bonuses have been particularly affected
increases in the money we set aside for potential claims for
the House of Lords' decision in July 2000, we had to reduce the value of
with-profits annuities. We
did this, other than for with-profits annuities, by reducing the policy
value by 5% at that time. We
made significant further reductions in July 2001, April 2002 and July
2002. This means, allowing
for bonuses, our other with-profits policyholders have suffered an
overall reduction of about 20%.
far we have largely protected you from these falls. In fact, you and
other with-profits annuitants have generally received a positive
investment return of about 14% over the same period.
we have said, most other with-profits policyholders have suffered
significant reductions in the value of their annuities, whereas those
who have with-profits annuities have not.
We were able to do this because if you have a with-profits
annuity, you cannot withdraw your funds.
It was possible for us to phase the cuts to with-profits
annuities in the hope of improved financial conditions.
Unfortunately, because conditions have not improved we can no
longer keep doing this.
basically means that with-profits annuities, like yours, are now out of
line by about 30%.
Action we need to take now
now need to bring with-profits annuities back into fine with other
policyholders and we plan to do this over two years.
We will be putting in place the following changes.
also review the amount of your income payments each year at the
anniversary of the date your with-profits annuity policy started.
That review reflects the gap between the expected bonus rate you
chose and the bonus rate which applies.
This then sets the level of income payments you will receive for
the following year.
The reductions quoted above will apply to the amount of annuity
after this review.
would like to emphasise that you will not receive less than the
guaranteed payments under
the annuity (known as the 'basic annuity' and 'declared bonus
annuity') and this may reduce the effect of these reductions.
do we need to change now?
originally decided to spread the reductions over the term of
with-profits annuity policies because we hoped that poor investment
conditions would recover reasonably quickly.
However, we are now in one of the longest periods of poor
stock-market performance for many years.
And, like most other companies, we have suffered heavy investment
We have reduced our investments in stocks and shares to very low
levels in order to secure and stabilise the With-Profits fund.
Unfortunately, because of our circumstances now - highlighted in the
Interim Report that you should have received - we can no longer afford
to phase these reductions in.
am very sorry that we have had to take this decision.
We carried out a great deal of work to look for alternatives that
would avoid reducing incomes in this way.
We had hoped to continue to reduce your income in a phased way
over the term of your annuity.
However, our changing circumstances and the growing gap between
with-profits annuities and other policies meant that it would have been
very unfair to other policyholders to continue to act in this way.
We must balance the interests of all continuing policyholders and
it is no longer fair to delay the reduction in values that our other
policyholders have recently suffered.
we cannot set final bonuses in advance, it is not possible to provide
individual calculations before the anniversary date.
However, 1 hope that the details set out above, together with the
enclosures with this letter, will give you a reasonably clear idea of
how much the reduction in your income next year will be.
You will, of course, receive a statement at your anniversary date
in the usual way.
(This is an undated document but received early November 2002, with the reference number 02/00000427/8926A/10v1. Copyright is acknowledged.)
3 of the Document entitled “How your with-profits annuity works”
issued with the November 2000 circular. This document has no date or
reference number but copyright is acknowledged.
Can you give me an
idea of how my income payment
will be affected by the final bonus rates
Unfortunately, we cannot give precise percentages of the levels of reduction in income before the change comes into force because:
rates are not guaranteed in future; and
there is a wide range of policies available.
we have produced some examples in the table opposite, which we hope will
use the table opposite you need to know the date your policy started and
also the anticipated bonus rate (ABR) you chose when you took your
policy out. You can find both of these in your original policy documents.
your start date in the first column and then look for the ABR that is
equal to or is closest to the ABR, which applies to your policy.
Then run along the row for the start date and down the column for
the ABR. The percentage
range is a guide to the approximate reduction to your gross income,
which will apply from the first policy anniversary on or after 1
example, Mr Smith began his policy on 15 April 1997 with an ABR of 4.5%
(please see shaded box). His
current annual gross annuity is £4800, which means he receives a gross
income of £400 on the first of each month.
On 1 May 2003, the first payment date after the next policy
anniversary, we will reduce his income by between 21% and 25%.
This would mean his new monthly gross income would be between £316
(£400 less 21 %) and £300 (£400 less 25%).
The anticipated bonus rate is the rate you chose before the annuity
started. We describe this reduction in your policy document.
We will always pay, at least, the guaranteed benefits under the policy
(the basic and declared bonus annuity).
For that reason, the reductions shown in the table for policies,
which began in 2000 are significantly lower than the changes shown for
The reductions shown are not the largest or smallest which could arise
as the range depends on future bonus rates.
N/A stands for not applicable or does not apply.