WPS3926
AN ANALYSIS OF MONEY'S WORTH RATIOS IN CHILE
Craig Thorburn, Roberto Rocha, and Marco Morales1
Abstract
Empirical analyses of annuities markets have been limited to a few developed countries and restricted by
data limitations. Chile provides excellent conditions for research on annuities due to the depth of its market
and the availability of data. The paper utilizes an extensive dataset on individual annuities to examine
econometrically a measure of market performance money's worth ratios (MWRs), or the ratio of the
expected present value of annuity payments to the premium. The results show that annuitants in Chile have
generally got a good deal for their premiums, as indicated by MWRs higher than one and also higher than
those estimated for other countries. The difference between Chile and other countries is striking
considering that annuities in Chile are indexed to prices. The wide range of indexed instruments in Chile,
allowing providers to hedge their risks while extracting higher returns, helps explain the difference. The
high degree of market competition has also contributed to this outcome. Efforts to improve market
transparency through a new electronic quotation system have decreased the dispersion of MWRs. Finally,
MWRs tend to decrease for contracts with longer durations, reflecting pricing for higher longevity and
reinvestment risks. These results are consistent with separate research on the annuity rate, and indicate the
need to ensure competition and market transparency, as well as to develop appropriate financial instruments
for providers in order to ensure good outcomes for annuitants.
World Bank Policy Research Working Paper 3926, May 2006
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the
exchange of ideas about development issues. An objective of the series is to get the findings out quickly,
even if the presentations are less than fully polished. The papers carry the names of the authors and should
be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely
those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors,
or the countries they represent. Policy Research Working Papers are available online at
http://econ.worldbank.org.
1 Craig Thorburn and Roberto Rocha are at the Operations Policy Department of the World Bank and
Marco Morales is at the Diego Portales University in Santiago de Chile. This paper was derived from a
comprehensive report of the Chilean market for retirement products, coordinated by Roberto Rocha and
Craig Thorburn (2006), and part of a broader World Bank project on the payout phase of private pension
systems involving several country studies. The authors are grateful to Gregorio Impavido for valuable
inputs in the early stages of the research. The authors are also grateful to Eduardo Walker, Dimitri Vittas,
Augusto de la Torre, Augusto Iglesias, Guillermo Martinez, Solange Berstein, Guillermo Larrain,
Alejandro Ferreiro, Ernesto Rios, Osvaldo Macias, Richard Hinz, and several industry participants for
comments on earlier versions of the paper.
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1. Introduction
The increased involvement of the private sector in pension provision has led to a
substantial volume of research on the structure, performance, and regulation of private
pension funds, both in developed and emerging countries. However, there are fewer
empirical analyses of the payout phase, which involves the transformation of the final
balance into flows of retirement income through instruments such as annuities and phased
withdrawals (PWs) and a greater role of the insurance sector.
Most empirical studies on the payout phase involve the computation of money's worth
ratios, or the ratio of the expected present value of annuity payouts to the annuity
premium. Money's worth ratios (MWRs) provide a useful measure of the performance of
annuities markets and also allow researchers to investigate the presence of adverse
selection in these markets. However, this empirical research is usually restricted to a
relatively narrow number of developed countries, and based on a relatively limited
number of annuity quotations, which prevents a more in-depth statistical analysis of the
determinants of MWRs.
The absence of more in-depth analyses of the payout phase is cause for concern, as many
countries have implemented pension reforms that have included the introduction of
mandatory private pillars, and will need to face the payout phase in the near future.
Policy-makers in these countries would benefit from analyses that provide more insights
and inputs to the design of a sound regulatory framework for products and intermediaries.
This is particularly the case for annuities, products that involve very long contracts and
complex risks.
Chile provides one of the most relevant experiences for countries that have reformed their
pension systems and that face the challenge of developing markets for annuities and
phased withdrawals. This is due to its well-known pension reform of 1981, which
involved a move from a public pay-as-you-go (PAYG) system to a fully-funded (FF)
system operated by the private sector. At the start of its pension reform in the early
1980s, Chile was a middle-income country without a pension industry, an incipient
insurance sector, little regulatory and supervisory capacity, and undeveloped capital
markets. Twenty-five years later Chile had reasonably developed markets for retirement
products, evidenced by about 320,000 annuity policies and 200,000 PWs, and 17 life
insurance companies providing annuities and managing assets of 20 percent of GDP.
This paper provides a detailed examination of MWRs in Chile, during the 1999-2005
period. The existence of extensive data on individual annuity policies, including
information on individual annuitant characteristics and types of annuities, allows not only
the computation of a large number of MWRs, but also an analysis of their main
determinants. This analysis provides important insights on the performance of the
annuities market and inputs to the formulation of appropriate policies in this area.
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The paper is structured as follows. The second section provides an overview of the
Chilean annuity market. The third section discusses a number of methodological issues
that arise in the computation of MWRs, including formulas, mortality tables and discount
rates. The fourth section examines the data used for the computation of MWRs, stressing
the use of data on actual annuity sales rather than quoted annuities. The fifth section
presents the results, which include an examination of average MWRs across main classes
of annuities, as well as regressions of these ratios against individual annuitant
characteristics such as age, gender, and premiums, as well as types of annuities. The
sixth section compares MWRs for Chile with those produced by other researchers for
Chile and other countries. Finally, the last section summarizes the main findings and
discusses some policy implications.
2. A Brief Overview of the Chilean Annuity Market2
The Chilean annuities market has its origins in the well-known pension reform
implemented in 1981, which entailed the replacement of the PAYG system by an FF
system with individual accounts managed by private pension fund administrators
(Administradoras de Fondos de Pensiones AFPs). The transition from the old to the
new pension system is virtually completed by 2004 nearly 97 percent of contributors
were enrolled in the new pension system. The number of active contributors is 3.5
million workers, or the equivalent to about 55 percent of the labor force. This is a low
coverage ratio by average OECD standards but a high ratio by comparison with middle
income countries in Latin America and other regions.
Workers enrolled in the new pension system can retire at the normal retirement age of 65
and 60 for men and women, respectively. They can also retire earlier if they meet specific
conditions. Until 2004 workers could retire if their accumulated savings could generate a
pension equal to at least 110 percent of the minimum pension guarantee and 50 percent of
their average real wage in the period of 10 years preceding retirement. The government
has discretion over the level of the minimum pension guarantee, but has usually set it
around 25 percent of the average economy-wide wage. A new Pension Law passed by
Congress in 2004 raised these requirements to 150 percent of the minimum pension
guarantee and 70 percent of the average real wage.
At the end of 2004 more than 500,000 workers had retired under the new system, as
shown in Table 1. Since access to lump-sums is restricted, retiring workers can basically
choose between life annuities, phased withdrawals (PWs), or temporary withdrawals
(TWs), which are essentially phased withdrawals combined with a deferred annuity.
The number of retirees choosing annuities has increased considerably in the past 20
years. As shown in Table 1, only 3 percent of the stock of pensioners had chosen
annuities in 1985, while in 2004 this percentage had increased to more than 60 percent.
This number implies one of the highest rates of annuitization in the world.
Annuities in Chile are strictly regulated and until 2004 the range of choices was relatively
limited. All annuities are fixed and indexed to prices. Married males have to buy joint
2 Rocha and Thorburn (2006) provide a detailed analysis of Chile's market for retirement products.
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annuities, thus providing longevity risk insurance to both themselves and their spouses.
A surviving spouse receives 60 per cent of the payment after the death of the main
beneficiary. Retiring workers have the option of buying guaranteed annuities, which start
at a lower level, but maintain payments at this level (i.e., without the 40 percent
reduction) during the guaranteed period, even after their death or the death of their
spouse. This type of annuity has proved very popular in Chile, as it allows more
protection to the spouse and some element of bequest. The new Pension Law passed in
2004 has introduced some additional options, especially variable annuities. The new Law
also introduced an innovative electronic quotation system, designed to enhance market
transparency and reduce the influence of brokers in the selection of retirement products
and intermediaries.
Table 1: Breakdown of Stock of Pensions, by Type of Instrument, 1985-2004
Year Total PWs TWs Annuities
Number % of Total Number % of Total Number % of Total
1985 7,609 7,373 96.8 - 0.0 236 3.2
1990 57,119 36,696 64.2 148 0.3 20,275 35.5
1995 190,400 98,699 51.8 6,803 3.6 84,898 44.6
2000 343,965 147,532 42.9 6,632 1.9 189,801 55.2
2004 520,793 196,242 37.7 6,193 1.2 318,358 61.1
Source: SAFP
Annuity providers in Chile have had access to a wide range of fixed income instruments
with long durations and indexed to prices, including privately-issued instruments offering
higher yields than government bonds. This access has allowed providers to hedge the
complex risks associated with annuities reasonably well. Providers are also allowed to
price annuities freely, and to differentiate risk according to basic annuitant
characteristics, such as age, gender, and income.
The growth of the number of annuitants has led to a rapid expansion of the insurance
sector, with total insurance assets growing from 5 percent of GDP in the mid-1980s to 20
percent of GDP in 2004. The large volume of pension assets more than 60 percent of
GDP indicates that insurance assets should continue growing strongly in coming years,
as these are pension accounts that will need to be converted into annuities and PWs at
retirement.
The fast increase in the number of annuity contracts attracted new entrants to the life
insurance market, increasing the total number of life insurance companies to 34 by the
late 1990s, 23 of which were providing annuities. As shown in Figure 1 and Figure 2, the
increase in the number of participants in the 1990s led to a continuous decrease in
concentration ratios, quite in contrast with the pension fund sector. The access to a wide
range of financial instruments allowing providers to hedge the risk of their liabilities and
the high degree of competition in the annuities market has generally resulted in good
outcomes for annuitants, as indicated by the high money's worth ratios shown in the
following sections.
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In recent years some life insurance companies have decided to exit the annuities segment
of the life insurance market, discouraged by the very intensive degree of competition, the
thin intermediation spreads and the relatively low returns on equity. These factors have
resulted in some increase in concentration ratios. However, the insurance sector in Chile
remains much more competitive than the pension fund sector, whether measured by the
number of participants or concentration ratios, as shown in Figures 1 and 2.
Figure 1
Number of Life Insurance Companies, Annuity
Providers, and AFPs, 1988-2005
40
35
30
25
20
15
10
5
0
1988 1990 1992 1994 1996 1998 2000 2002 2004
Life Insurance Companies Annuity Providers AFPs
Figure 2
Market Concentration Ratios in Pensions andAnnuities
Herfindahl andShare of Three Largest Firms, 1988-05
2500 100%
90%
oitaRlhadnifr 2000 t
80%
70%
1500 60%
50%
1000 40%
30%
He 500 20% esgarL3foearhS
10%
0 0%
1988 1990 1992 1994 1996 1998 2000 2002 2004
AFP Herfindahl Annuity Herfindahl
AFP 3 Larges t Annuity 3 Larges t
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3. Methodology for Computing MWRs
3.1. MWR Formulas
The money's worth ratio is an indication of the value provided to the customer in an
annuity product. It is defined as the ratio of the expected value of the benefits payable
under the contract to the premium paid. A mortality table and an interest rate yield curve
are required to determine the value of the benefits for this process.
The calculation of the value of the payment streams in Chile requires that the features of
the products be reflected. In particular, it is necessary to allow for the fact that annuities
are issued as either joint or single life, that some are issued with a period of initial
deferment, and that some are issued with the payment guaranteed for a defined period
regardless of survivorship. A small funeral benefit of UF15 is provided as part of the
annuity purchase and is also considered in the calculations. Benefits for dependent
children have not been considered, because it is not possible to identify from the data the
cases where these benefits would be payable. However, the effect of ignoring these
dependent benefits is small, not affecting the conclusions or international comparisons.
As a result of these characteristics, the MWR formula for a single life annuity issued to a
person aged x is as set out in Equation (1):
(1) MWR = 12( -x)
A tpx
t=d +1 (1+ it )t+V
P
where:
MWR is the Money's Worth Ratio;
A is the monthly annuity payment in UF;
W is the ultimate age in the mortality table, the oldest age assumed
where there are not remaining surviving lives;
t x
p is the probability that a life aged x at commencement is still alive at
time t, that is after t months in this case, at age x+(t/12). Note that,
in the case of a guaranteed period then p is set equal to 1 for the
t x
period that the guarantee is in force;
d is the number of months deferment in the case of a deferred annuity;
it is the interest rate used to discount payments at time t, obtained from
the term structure of interest rates;
V is the value of the funeral benefit; and
P is the single premium payment made for the contract.
The first term between parentheses in the numerator is the expected present value of
future annuity payments. The division of this term by the premium is the MWR formula
usually used in empirical research in other countries. Equation (1) also includes the
expected present value of the small funeral benefit V because it is part of the annuity
benefit in the Chilean case.
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The joint life formula contains the reversion of the annuity to the second beneficiary
(typically the spouse) at a lower level (60 percent), and the survivorship of two lives
determining the annuity payment. If the principal beneficiary is noted with symbols as
above, and the reversionary beneficiary is noted with the same symbols but with a `^'
mark and is aged y at commencement of the annuity, then the formula is as set out in
equation (2). Note that the probability term in the numerator would be set to 1 during the
period where annuity payments are guaranteed.
(2) MWR = 12(-x)
A t
t=d +1 px + 0.6((1-t px )t p^ y ) +V
(1+ it )t
P
Note that all annuities in Chile are quoted in Unidades de Fomento (UF), a unit of
account indexed to consumer prices and widely used in financial contracts. In this
analysis all values are expressed in UF and should be interpreted accordingly when
making comparisons with other countries.3
3.2. Mortality Tables
Most empirical studies estimate MWRs with two mortality tables, one reflecting the
mortality of the general population and the other reflecting the mortality of the smaller
annuitant population. These are necessarily cohort tables, constructed either by
incorporating existing projections of future mortality for each cohort, or by estimating
future mortality improvements and applying them to period tables.4 The difference
between the estimated MWRs using the general and the annuitant population assumptions
is frequently interpreted as the effect of adverse selection.
In the case of Chile, there was no mortality table for the population that is updated and
reliable at the time of writing, but three tables have been constructed for the annuities
market. The first of these tables, known as RV-85, is a period table that was developed
when the annuity system started and there were few annuities in force. The table purports
to represent the period experience of annuitant mortality at the time it was developed, but
was partly constructed by making adjustments to mortality data from other countries.
The RV-85 was developed for regulatory purposes, and served until recently as the basis
for the determination of phased withdrawal (PW) payments and the calculation of
technical reserves for annuity providers.
The second table, referred to as RV-98, is a period table based on more extensive Chilean
annuitant mortality data collected between 1995 and 1997. The table represents an
improvement over the RV-85, by including more information on the mortality of the
Chilean annuitant population. However, while the male tables were mostly determined
from the data, the female tables largely impute the observed rate of change between the
3The Pension Law approved in 2004 has allowed other types of annuities, but all the MWRs presented in
this report refer to annuities fixed in UFs, i.e., annuities indexed to prices.
4See, e.g., Brown et al (2001), and James, Song and Vittas (2003).
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RV-85 and RV-98 tables for males, to the RV-85 table for females. As a result, the rate of
mortality improvement is essentially the same for both sexes.
Finally, the third table, referred to as RV-04, is a period table based on Chilean annuitant
mortality data collected between 1995 and 2003. The RV-04 is more representative of
the Chilean annuitant population than its two predecessors and has recently been adopted
for all regulatory purposes. Among several of its positive features, both male and female
tables were developed separately, and the representative version of the table passed all
the standard consistency tests comfortably.5
However, these recently constructed tables still have some shortcomings that need to be
considered. Because there are fewer annuitants at older ages, data was included from the
previous scheme. This implies that the mortality rates at older ages may not be as
representative of annuitants as the earlier ages, and rather reflect the mortality of retirees
under the old system. Rates were updated to 2004 using the national statistical agency's
assumed age-specific improvement rates for the population. The RV-04 table was
selected for the computation of MWRs because it is the most representative of the current
annuity population. The table was adjusted to the relevant year of issue of each annuity
using the same approach adopted in the official table and the same rates.
As shown in Table 2, there are significant differences in the shape of the three mortality
tables. Mortality rates in the RV-98 and RV-04 are systematically and substantially lower
than those in the RV-85. Male mortality rates in the RV-04 are lower than those in RV-
98 for intermediate ages, but higher at some younger and older ages. Female mortality
rates, however, are substantially lower in the RV-04. As noted above, the earlier (RV-85
and RV-98) tables for females are constructed more subjectively than the RV-04 tables
for both sexes and the RV-98 table for males. Whilst the shape and level of the mortality
tables is still a matter for some debate in Chile, the RV-04 table seems to be the most
scientific and robust for both sexes.
Each of these three tables is published as a period table, requiring adjustments in order to
convert them into cohort tables. Cohort results were initially developed using two
alternatives, namely, national population projection rates, and the rates of improvement
between the RV-85 and the RV-04 tables. The first method was ultimately judged as
superior and has been adopted here. The basic reason was the high degree of
arbitrariness involved in the construction of the RV-85 table. In particular, it is clear that
the female improvement rates derived from these tables continue to be open to greater
uncertainty and are well above the observed and assumed population estimates.
5A standard battery of statistical tests is set out in Benjamin and Pollard (2001) and has been applied to the
RV-04 tables separately for male and female tables. In the case of each test, the representative table used in
these calculations is found to pass the test that is, the table reflects the underlying mortality experience.
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Table 2: Levels and Changes in Mortality Rates
Male Female
Period Tables Improvement Rates Period Tables Improvement Rates
Age for Cohort Tables for Cohort Tables
RV85 RV98 RV04 Pop. RV04/ RV85 RV98 RV04 Pop. RV04/
unbiased Projection RV85 unbiased Projection RV85
50 0.0054 0.0044 0.0044 1.40% 1.44% 0.0027 0.0022 0.0015 1.40% 3.91%
55 0.0082 0.0059 0.0058 1.40% 2.39% 0.0042 0.0030 0.0024 1.50% 4.04%
60 0.0124 0.0089 0.0091 1.50% 2.23% 0.0066 0.0047 0.0035 1.40% 4.46%
65 0.0189 0.0146 0.0139 1.50% 2.16% 0.0104 0.0080 0.0049 1.40% 5.22%
70 0.0288 0.0239 0.0219 1.50% 1.94% 0.0165 0.0137 0.0072 1.50% 5.76%
75 0.0447 0.0384 0.0356 1.50% 1.61% 0.0272 0.0237 0.0127 1.30% 5.30%
80 0.0693 0.0624 0.0593 1.40% 1.11% 0.0451 0.0401 0.0261 1.20% 3.84%
85 0.1070 0.0963 0.0971 1.20% 0.69% 0.0750 0.0680 0.0523 1.20% 2.54%
90 0.1636 0.1472 0.1511 1.20% 0.56% 0.1238 0.1115 0.0942 1.20% 1.94%
95 0.2459 0.2213 0.2219 1.20% 0.73% 0.2013 0.1812 0.1527 1.20% 1.95%
100 0.3600 0.3240 0.3097 1.20% 1.07% 0.3180 0.2862 0.2283 1.20% 2.34%
105 0.5064 0.4557 0.4261 1.20% 1.23% 0.4792 0.4313 0.3328 1.20% 2.57%
110 1.0000 1.0000 1.0000 1.20% 0.00% 1.0000 1.0000 1.0000 1.20% 0.00%
Source: SVS and Staff Calculations
Note: The values for the RV-04 tables shown here are not updated to any particular year, i.e., are
representative of mortality centered around 1999.
3.3. Discount Rates
In line with most other studies, the computation of MWRs is performed with two
alternative discount rates, the interest rate on government or central bank bonds and the
interest rate on corporate bonds. The MWR computed with the first rate is frequently
considered to be the most meaningful to the average customer, as it excludes risk and
reflects its opportunity cost more accurately. It is also used to facilitate comparisons
across countries. The alternative discount rate is also computed, as it may reflect more
appropriately the opportunity cost for some consumers, and because it is more relevant
from the point of view of the provider.
The risk-free discount rates were obtained by the yield curve of 20 year indexed central
bank bonds (the PRC-20) in March of 1999, 2002, 2003, 2004 and 2005 as indicated
below, the annuity sample consists of all annuities sold in those five months.6 The yield
curve for those five months was provided by the Central Bank of Chile, consisting of
daily estimates of the zero coupon yield curve for maturities ranging from one month to
20 years. These curves were originally generated using interpolation and smoothing
approaches developed by the RiskAmerica company, drawing on what is usually a
limited number of trades on any given day in the PRC-20. The Central Bank of Chile
makes some additional adjustments, based on the transactions of similar debt instruments.
6March was the month selected to allow comparisons with estimates of MWRs by other researchers.
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The yield curve utilized in the MWR computations was the average of the daily yield
curves in March of each of those five years.7
The second technical limitation that had to be addressed was the absence of debt
instruments with sufficiently long duration. Although Chile has had more success in
lengthening the maturities of debt instruments than most other emerging countries, the
yield curve still does not cover the possible life of annuity payments. Consistent with the
approach taken by James, Iglesias, and Martinez (2005), the yield curve was assumed to
be flat after 20 years. This solution seems reasonable, as the yield curve in the months
examined is essentially flat in the durations from 15 to 20 years. Finally, the alternative
discount rate was constructed by adding the actual spread of corporate bonds over the
PRC-20 for each of the periods 2002 - 2004. In March of 2002, 2003 and 2004, these
spreads were 1.7, 2.5 and 1.4 percent, respectively.
4. The Data
Most empirical studies generally involve the collection of several annuity quotations, the
computation of averages for different categories, and the calculation of MWRs for these
categories (e.g., single annuities by sex and age, joint annuities, guaranteed annuities).
The high level of disclosure in Chile includes information on every individual annuity
sold. As a result, it is possible to compute MWRs for all these categories using actual
sales.
The access to actual annuity sales represents a significant improvement over other
studies, because the computed MWRs are more consistent with the value actually
provided to customers. Another advantage of the study is the much larger size of the
sample and the wider range of data points generated. This allows more robust estimates
of the averages of different categories, the econometric analysis of some of the main
determinants of MWRs, and a more robust analysis of dispersion of annuity prices and
transparency of the annuities market.
At the same time, it is important to recognize the possible problems of comparability with
other studies. The use of actual annuity sales may lead to higher MWRs than those
computed with quotations, even in cases where there are no real differences. This is
because customers receive a number of quotes and typically exercise preference for one
of the better quotes. Therefore, data based on actual annuity sales will typically capture
the better quotes, while data based on quotations will typically reflect the average of
several quotes. As a result, MWRs produced with actual sales will tend to be higher.8
The much larger sample used in this study may also be a source of differences. If the
quotations collected in other studies are not representative of the universe of annuity
sales, the results and comparisons may be biased.
7The authors are grateful to the assistance provided by Messrs. Klaus Schmidt-Hebel and Jorge Perez, of
the Central Bank of Chile. The Central Bank adjustments result in higher yields than those generated by
the direct application of the RiskAmerica software.
8This problem is recognized by Cannon and Tonks (2004).
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The dataset used in this study comprises 937 annuities issued in March of 1999, 1,517
annuities issued in March of 2002, 1,193 annuities issued in March of 2003, 1,490
annuities issued in March of 2004, and 1,391 annuities issued in March of 2005. These
5,137 annuities only include normal old age retirement and early retirement annuities,
and exclude disability and survivorship annuities. Table 3 provides summary statistics
for the whole dataset, while Table 4 provides information for separate subgroups.
As shown in Table 3, until 2004 the average age of retiring males and females was about
58 and 56, respectively, well below the normal retirement age of 65 and 60, and
reflecting the large numbers of early retirees. The average age of retirement increased
significantly in 2005, reflecting the introduction of stricter rules for early retirement. The
share of deferred annuities (i.e., TWs) increased from 20 to 30 percent of the total, but the
period of deferment remained short roughly 80 percent of deferred annuities were only
deferred for a year, and only 3 percent or less were deferred for 3 years or more. These
patterns of selection reflect at least to some extent the influence of annuity brokers
since commissions are determined by the size of the annuity premium, brokers do not
have incentives to recommend TWs paired with long periods of deferment.
While only 30 percent of annuities issued were deferred, close to 80 percent had
payments guaranteed for a certain period of time independent of survivorship. The length
of the guaranteed period is also relatively high roughly 60 percent of all guaranteed
annuities had a 10-year guarantee, and 90 percent were guaranteed for 10 or 15 years.
The choice of guaranteed versus non-guaranteed annuities is not prescribed or influenced
by broker activity, as the commission does not depend on whether the annuity is
guaranteed or not. The preference for guaranteed payments probably reflects a decision
to smooth retirement income within the family unit, as well as a bequest motive.
Table 3: Summary Statistics of the Dataset
1999 2002 2003 2004 2005
All Cases
Number 937 1,517 1,193 1,490 1,391
Average Age of Males 57.83 56.98 57.77 57.70 59.46
Average Age of Females 55.76 54.85 55.55 56.02 58.46
Average Purchase Price (UF) 1,971.66 1,859.65 2,116.94 2,098.79 2,454.9
Number of cases with 199 331 307 409 419
deferment (21.2%) (21.8%) (25.7%) (27.5%) (30.1%)
Of which:
- 12 months 164 275 238 322 315
- 24 months 32 54 60 75 91
- 36 months 2 2 8 10 9
- 48 months 1 0 1 2 3
Number of cases with 708 1,191 948 1,153 1,093
a guaranteed term (75.6%) (78.5%) (79.5%) (77.4%) (78.6%)
Of which:
- 5 years 11 19 17 18 23
- 10 years 422 701 511 636 559
- 15 years 244 387 335 380 353
- 20 years 18 64 63 93 124
- other 13 20 22 26 34
Source: SVS and Staff Analysis
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Table 4 provides more detailed information, showing that joint life annuities accounted
for approximately 70 percent of all annuities issued in the sample months. Single female
and single male annuities accounted for around 20 and 10 percent of the total,
respectively. The large share of joint annuities is an important feature of the Chilean
pension system, as it ensures retirement income for surviving spouses and helps prevent a
large number of old people (mostly women) falling into poverty, or having to access the
minimum pension guarantee. The large share of joint annuities is to a large extent due to
product regulation retiring married males can only buy joint annuities. However, the
large share of guaranteed joint annuities reveals an element of voluntary transfers within
the family unit as mentioned before, the main beneficiary accepts voluntarily a
discounted annuity in exchange for a higher annuity for his spouse during the guaranteed
period (higher than the standard 60 percent reversionary payment), in the event of his
death during this period.
The high share of guaranteed annuities in the case of single male and single female
annuities reflects primarily a bequest motive, with the main beneficiary accepting a
discount in exchange for the guarantee of some value to his/her heirs in the event of
his/her death. The increase in the share of TWs and deferred annuities reveals the
consumers' preference for larger payments in the early phases of retirement and may
reflect the use of TWs and deferments as a substitute for the loss of access to lump-sums.
5. Analysis of Money's Worth Ratios
As mentioned before, most empirical studies present estimates of MWRs computed with
two mortality tables (the annuitant and the population tables) and with two discount rates
(the government and the corporate bond rate). Moreover, these four estimates are
presented separately for single male, single female and joint annuities. Some studies
present MWRs of guaranteed annuities, whenever such information is available. In the
very few countries that offer indexed annuities, such estimates are presented as well.
The lack of a reliable and updated population table for Chile reduces the value of the
traditional exercise of comparing MWRs with population and annuitant tables to estimate
the impact of adverse selection. Moreover, even if a reliable and current mortality table
for the population was available, the exercise would still have limited value, as only 60
percent of the Chilean population is on average covered by the pension system, a much
lower coverage ratio than the ratios of OECD countries for which MWRs have been
computed. The uncovered segment of the population is the segment with the lowest
incomes and probably the lowest life expectancies. Therefore, an exercise of this type
would produce exaggerated measures of adverse selection in the Chilean case.
On the other hand, the availability of a larger dataset of individual annuities in the
Chilean case allows a much more detailed examination of MWRs across different types
of annuitants. This section analyzes in detail the MWRs computed with the risk-free rate
and the cohortized RV-04 table, considered the most relevant in the Chilean case. The
analysis includes the examination of the MWRs for the main classes of annuities, an
econometric investigation of the individual MWRs against individual annuitant
- 13 -
characteristics, and an analysis of dispersion of MWRs. The next section compares
MWRs for annuitants in Chile with those estimated for annuitants in other countries,
computed both with the risk-free rate and a higher discount rate.
Table 4: Summary Statistics of Dataset by Subgroups
1999 2002 2003 2004 2005
Single Life Males
Number 82 139 114 144 108
Average Age of Males 59.22 57.49 57.81 58.13 59.74
Average Purchase Price (UF) 1,475.85 1678.00 1,544.60 1,631.88 1973.34
Number of cases with deferment 7 22 14 22 25
(8.5%) (15.8%) (12.3%) (15.3%) (23.1%)
O/w: - 12 months 6 16 12 17 22
- 24 months 1 6 1 5 2
- 36 months and longer 0 0 1 0 1
Number of cases with a guaranteed term 52 102 85 101 75
(63.4%) (73.4%) (74.6%) (70.1%) (69.4%)
O/w: - 5 years 0 5 4 7 7
- 10 years 39 68 56 52 41
- 15 years 10 19 18 27 17
- 20 years and longer 1 10 7 15 8
Single Life Females
Number 185 309 256 373 520
Average Age of Females 57.89 56.46 57.51 58.66 60.99
Average Purchase Price (UF) 1,779.28 1,619.47 1,984.87 2,007.26 2,187.79
Number of cases with deferment 44 69 71 113 175
(23.8%) (22.3%) (27.7%) (30.3%) (33.7%)
O/w: - 12 months 37 57 56 81 132
- 24 months 7 12 12 27 38
- 36 months and longer 0 0 3 5 5
Number of cases with a guaranteed term 151 250 208 310 416
(81.6%) (80.9%) (81.3%) (83.1%) (80.0%)
O/w: - 5 years 1 3 2 5 8
- 10 years 89 149 120 175 217
- 15 years 53 82 70 104 138
- 20 years and longer 5 16 16 26 41
Joint Life
Number 670 1,069 823 973 763
Average Age of Males 57.66 56.92 57.77 57.64 59.42
Average Age of Females 55.17 54.39 54.94 55.01 56.73
Average Age difference (male age less 2.49 2.53 2.83 2.62 2.69
female age) in years
Average Purchase Price (UF) 2,085.47 1952.69 2237.30 2202.07 2705.19
Number of cases with deferment 148 240 222 274 219
(22.1%) (22.5%) (27.0%) (28.2%) (28.7%)
O/w: - 12 months 121 202 170 224 161
- 24 months 24 36 47 43 51
- 36 months and longer 3 2 5 7 7
Number of cases with a guaranteed term 504 839 655 742 602
(75.2%) (78.4%) (79.6%) (76.3%) (78.9%)
O/w: - 5 years 9 11 11 6 8
- 10 years 293 484 335 409 301
- 15 years 181 286 247 249 198
- 20 years and longer 14 58 62 78 75
Source: SVS and Staff Analysis
- 14 -
5.1 An Overview of the Results
Table 5 presents estimates of MWRs for March of 1999, 2002, 2003, 2004 and 2005,
using the cohortized version of the most updated mortality table for the annuitant
population (the RV-04), and the risk-free yield curve.9 The table shows the overall
averages for each of the five years, the maximum and the minimum, and the averages for
well defined categories, including type, age, gender, size of the premium, and the
presence of guaranteed and deferred periods. It must be emphasized that these are
MWRs computed for indexed annuities.
Table 5: Money's Worth Ratios in March of 1999, 2002, 2003, 2004 and 2005
Computed with the Risk Free Rate and an Update Cohort Annuitant Table
March March March March March
1999 2002 2003 2004 2005
All cases 0.978 1.079 1.036 1.064 1.062
- maximum 1.148 1.222 1.181 1.276 1.223
- minimum 0.755 0.872 0.872 0.876 0.706
Male Single Life 0.987 1.086 1.044 1.061 1.054
Female Single Life 1.009 1.111 1.063 1.097 1.086
Joint Life 0.968 1.070 1.026 1.052 1.046
Male Single Life age 55 0.981 1.075 1.034 1.049 1.042
Male Single Life age 65 0.996 1.117 1.069 1.086 1.067
Female Single Life age 55 0.994 1.101 1.049 1.076 1.064
Female Single Life age 60 1.021 1.131 1.077 1.105 1.083
Joint Life Male 65 and Female 60 0.998 1.083 1.050 1.078 1.069
Purchase Price up to UF 1,000 0.980 1.078 1.045 1.068 1.067
Purchase Price above UF 3,000 0.997 1.099 1.047 1.075 1.071
Without guaranteed term 0.990 1.092 1.045 1.071 1.073
With guaranteed term 0.974 1.076 1.033 1.062 1.059
Without deferment 0.979 1.079 1.035 1.063 1.061
With deferment 0.974 1.080 1.036 1.067 1.064
The first thing to note is that the average MWR in 1999 is slightly lower than one, a value
that is usually taken to indicate a fairly priced annuity. In 2002 and the following years
average MWRs are all higher than one, and also higher than MWRs estimated for other
countries. As shown in more detail in the next section, MWRs of nominal annuities
estimated with similar assumptions usually range from 0.9 to levels slightly above 1 and
are much lower in the case of indexed annuities.
Second, there is a significant variation in individual MWRs, as indicated by the wide
difference between maximum and minimum values. Maximum values range roughly
from 1.15 to 1.25 and minimum values range from 0.75 to 0.85. These variations reflect
to a good extent price differentiation by providers based on the individual characteristics
of annuitants, but they may also reflect inefficiencies, as discussed below.
9As mentioned before, the month of March was selected simply to allow comparisons with previous
estimates made by other researchers. These comparisons are provided below.
- 15 -
Third, the MWRs of joint annuities are lower than those of single annuities, and the
MWRs of single male annuities are lower than those of females. One possible
explanation for the lower MWRs of joint annuities (the bulk of the annuities market) is
their longer expected duration and consequent greater mortality and reinvestment risk
relative to single life annuities. Greater risk would justify an increase in premiums for a
given value of benefits, and therefore a lower MWR. However, the same argument
would apply to single female annuities relative to males, and yet the MWRs of females
turn out to be higher. A possible further explanation is the larger average premium of
single female annuitants relative to single male annuitants (Table 4) but it is also
recognized that the number of single life male cases is small. The relationship between
MWRs and premiums will be discussed further below.
Fourth, MWRs of older annuitants are systematically higher than those of younger
annuitants, regardless of gender. This positive relationship between MWRs and age can
be explained by the greater mortality and reinvestment uncertainty associated with
annuities issued to younger ages, and the inclusion of a risk premium (a smaller annuity
relative to the premium) by the provider. This result contrasts with those produced by
Mitchell et al (2001) and Brown et al (2001) for the US and the UK, respectively, but is
consistent with those reported by James, Iglesias and Martinez (2005) for Chile.
Fifth, there is a positive relationship between MWRs and the size of the premium. This
result could be due to the lower unit costs and higher profit margins associated with
larger premiums insurance companies may pay better rates for larger annuity premiums
just like banks pay higher interest rates for larger deposits. The positive association
could also reflect the more sophisticated market search by educated consumers with
higher incomes and larger premiums. These two effects probably offset the longevity
effect, which would produce a negative relationship retirees with higher incomes and
larger premiums tend to have higher life expectancies and expose providers to greater
risks due to the longer expected duration of their annuities.
Sixth, MWRs of guaranteed annuities are smaller than those of non-guaranteed annuities.
The interpretation of this result is confused by the fact that the guarantee can alter the
duration, and therefore the reinvestment risk, positively or negatively depending on the
length of the guarantee relative to the life expectancy of the annuitant. Long periods of
guarantee tend to increase duration, especially at older ages. Finkelstein and Poterba
(1999) obtain exactly opposite results for the UK, and interpret these results as evidence
of adverse selection in the UK annuity market. According to the argument, individuals
who expect to be longer-lived would self-select into non-guaranteed annuities, while
individuals who are concerned about the potential for early death would self-select into
guaranteed annuities (to leave a bequest or guarantee larger payments for the surviving
spouse). If this interpretation is correct, the results in Table 5 would suggest the absence
of adverse selection in Chile.
Finally, deferment periods seem to make little difference in the value offered to the
customer. However, this result may be simply due to the preponderance of very short
deferments in the Chilean market.
- 16 -
5.2. Econometric Analysis of MWRs
Most empirical studies examine the differences of MWRs across different classes of
annuities without testing whether these differences are significant. The large dataset of
individual annuities in Chile enables a more formal examination of the main determinants
of MWRs, and the testing of whether the relationships identified above are significant.
For this purpose we specify the MWR as a function of individual annuitant
characteristics, as in equation (3):
(3) MWRi,t = f (genderi,t, agei,t , premiumi,t , guaranteei,t , defermenti,t)
Where MWRi is the money's worth ratio of the annuity bought by individual i at time t,
regressed against the gender and age of the individual annuitant, the size of the annuity
premium expressed in logs, and the guaranteed and deferment periods. Since the bulk of
the market is constituted by joint annuities, the equation was estimated using this type of
annuity as the base variable and dummies included for single male and single female
annuities. Likewise, 1999 was considered as the base year and dummies were included
for 2002, 2003, 2004, and 2005. Table 6 shows the results obtained through least squares
with robust standard errors. This specification was selected after conducting a number of
specification tests, including the White test for heteroskedasticity of the residuals.
Table 6: Main Determinants of MWRs
Dependent Variable: 100*MWR; Least Squares with Robust Standard Errors
Pooled Data for 1999, 2002, 2003, 2004, and 2005; Observations: 6526
Variable Coefficient Std. Error t-Statistic Prob.
C 62.39024 0.722912 86.30404 0.0000
AGE 0.410145 0.008974 45.70317 0.0000
LOG(PREMIUM) 1.618070 0.073313 22.07059 0.0000
GUARANTEE -0.134448 0.008383 -16.03824 0.0000
DEFERMENT 0.016582 0.007399 2.241063 0.0251
Male 1.345882 0.206458 6.518928 0.0000
Female 4.023704 0.089566 44.92436 0.0000
2002 10.66352 0.149209 71.46677 0.0000
2003 5.699579 0.152080 37.47739 0.0000
2004 8.253581 0.150549 54.82318 0.0000
2005 6.507061 0.156551 41.56508 0.0000
R-squared 0.639507 Mean dependent var 104.9609
Adjusted R-squared 0.638954 S.D. dependent var 5.600486
S.E. of regression 3.365172 Akaike info criterion 5.266519
Sum squared resid 73778.36 Schwarz criterion 5.277954
Log likelihood -17173.65 F-statistic 1155.747
Durbin-Watson stat 1.754037 Prob(F-statistic) 0.000000
Source: Authors' estimations on SVS data.
- 17 -
Equation (3) explains about 65 percent of the variations of MWRs within the pooled
sample, and the results confirm the signs and significance of all the relationships
examined above. MWRs are positively and significantly related to age, in contrast with
the results of other researchers for the UK and the US, indicating that the risk associated
with younger ages and longer durations is an important factor in annuity pricing in Chile.
MWRs are also positively and significantly related to the size of the premium, indicating
that the cost and market search effects offset the longevity effect. MWRs are negatively
associated with longer periods of guarantee, again providing support to the hypothesis
that longer durations imply greater risk for the provider and have a negative impact on
MWRs.
As mentioned before, the negative coefficient for the guarantee variable could reveal the
absence of adverse selection effects in the Chilean annuities market. Alternatively, it
could reflect the net result of two different effects. Maybe higher income members with
longer life expectancies self-select into non-guaranteed annuities and members with
shorter life expectancies self-select into guaranteed ones, but the longevity risk is
outweighed by the reinvestment risk. James, Iglesias and Martinez (2005) examine
actual/expected death ratios of guaranteed and non-guaranteed annuitants and show lower
ratios for members with non-guaranteed annuities, indicating that individuals with longer
life expectancies self-select into these annuities. Although their results are overestimated
by the use of outdated mortality tables (the RV-85 and the RV-98), this is a more direct
test of self-selection and provides evidence of some adverse selection in the Chilean
annuities market. Therefore, the coefficient of the guarantee variable may not provide a
robust test for adverse selection.
The positive and significant coefficient for the deferment variable is perhaps surprising,
although this result should not be emphasized, given the very short length of deferments
in Chile. Moreover, this was the only variable that proved non-significant at the 5
percent level when the equation was estimated separately for each year (these results are
shown below). Finally, the signs of the male an female dummy variables are consistent
with the relationships among the average MWRs for joint, single male and single female
annuities, although the sign of the female dummy coefficient does not have an obvious
explanation.
Overall, the major conclusions to be drawn from this analysis is that, in Chile, there is
evidence that annuities with longer expected durations get lower MWRs than annuities
with shorter durations, and that larger premiums get better value on average than smaller
ones. This is consistent with the view that insurers are concerned with the higher
reinvestment and mortality risks presented by long durations and, in the case of size, the
effect of fixed expense loadings is more significant in the Chilean market than attempts to
differentiate mortality between annuitants of different income levels. An additional
factor, the relevance of niche marketing and more sophisticated and price sensitive
customers at higher premiums, may also be an explanation.
Additional insights on individual annuity pricing can also be gained by examining the
pairs of correlation coefficients across these variables. As shown in Table 7, the
- 18 -
relationship between premium size and age is positive but not statistically significant. A
positive correlation would be expected, as older retirees would have more time to
accumulate a higher balance. However, this positive association is weakened by the
strong association between annuitization and early retirement in Chile, caused in good
part by early retirement rules that facilitate retirement by higher income workers with
larger premiums, and also the influence of brokers, that induce early retirement.
The relationship between deferment and age is negative, suggesting that older retirees are
less likely to opt for TWs than younger retirees. Given the relatively small volume of
such cases, however, and the rational desire for flexibility for younger retirees, this is
understandable. The negative and significant relationship between guarantee periods and
age suggests a strong reaction by early retirees to the risk of reduction on reversion after
the first death, or a stronger bequest motive among early retirees. The positive
association between premiums and the length of guarantee periods indicates that higher
income annuitants are more willing and capable of buying the guarantee, i.e., accepting a
discount in the early payments relative to the premium in exchange for larger payments
for the surviving spouse.
Tables 8 through 12 present the results obtained for individual years, showing that
equation (3) explains 40-50 percent of the variations in MWRs in each year. The
coefficients have the same signs as those obtained in the pooled sample and are
significant, except for the deferment variable, which proved non-significant at the 5
percent level in all individual years.
Table 7: Variable Correlation Matrix
MWR Age Premium Deferment Guarantee
MWR 1
Age 0.4626* 1
Premium 0.1744* 0.0297 1
Deferment Period 0.0277 -0.0490* 0.0729* 1
Guaranteed Period -0.1713* -0.1455* 0.2077* 0.0962* 1
- 19 -
Table 8: Main Determinants of MWRs
Dependent Variable: 100*MWR; Least Squares with Robust Standard Errors
YEAR=1999; Observations: 937
Variable Coefficient Std. Error t-Statistic Prob.
C 60.86516 2.100710 28.97362 0.0000
AGE 0.406372 0.023248 17.47959 0.0000
LOG(PREMIUM) 1.854153 0.227955 8.133850 0.0000
GUARANTEE -0.136101 0.023538 -5.782169 0.0000
DEFERMENT -0.006032 0.022320 -0.270278 0.7870
Male 1.639658 0.522999 3.135107 0.0018
Female 4.316622 0.286877 15.04697 0.0000
R-squared 0.407434 Mean dependent var 97.81531
Adjusted R-squared 0.403611 S.D. dependent var 4.899386
S.E. of regression 3.783611 Akaike info criterion 5.506677
Sum squared resid 13313.61 Schwarz criterion 5.542855
Log likelihood -2572.878 F-statistic 106.5742
Durbin-Watson stat 1.903532 Prob(F-statistic) 0.000000
Table 9: Main Determinants of MWRs
Dependent Variable: 100*MWR; Least Squares with Robust Standard Errors
YEAR=2002; Observations: 1,517
Variable Coefficient Std. Error t-Statistic Prob.
C 65.91515 1.296474 50.84185 0.0000
AGE 0.499496 0.016820 29.69642 0.0000
LOG(PREMIUM) 1.862513 0.144434 12.89526 0.0000
GUARANTEE -0.118013 0.016261 -7.257291 0.0000
DEFERMENT 0.025761 0.015423 1.670247 0.0951
Male 1.352054 0.394186 3.429992 0.0006
Female 4.419103 0.179380 24.63540 0.0000
R-squared 0.536716 Mean dependent var 107.9591
Adjusted R-squared 0.534875 S.D. dependent var 4.709875
S.E. of regression 3.212139 Akaike info criterion 5.176355
Sum squared resid 15579.93 Schwarz criterion 5.200924
Log likelihood -3919.265 F-statistic 291.5563
Durbin-Watson stat 1.614660 Prob(F-statistic) 0.000000
- 20 -
Table 10: Main Determinants of MWRs
Dependent Variable: 100*MWR; Least Squares with Robust Standard Errors
YEAR=2003; Observations: 1,191
Variable Coefficient Std. Error t-Statistic Prob.
C 70.19722 1.505577 46.62479 0.0000
AGE 0.406500 0.018254 22.26915 0.0000
LOG(PREMIUM) 1.356398 0.142582 9.513102 0.0000
GUARANTEE -0.133558 0.016452 -8.117811 0.0000
DEFERMENT 0.020258 0.013499 1.500708 0.1337
Male 2.042872 0.376537 5.425418 0.0000
Female 3.864239 0.220587 17.51798 0.0000
R-squared 0.478898 Mean dependent var 103.5660
Adjusted R-squared 0.476257 S.D. dependent var 4.219287
S.E. of regression 3.053501 Akaike info criterion 5.076315
Sum squared resid 11039.46 Schwarz criterion 5.106187
Log likelihood -3015.945 F-statistic 181.3513
Durbin-Watson stat 1.269357 Prob(F-statistic) 0.000000
Table 11: Main Determinants of MWRs
Dependent Variable: 100*MWR; Least Squares with Robust Standard Errors
YEAR=2004; Observations: 1,490
Variable Coefficient Std. Error t-Statistic Prob.
C 74.47563 1.466312 50.79111 0.0000
AGE 0.380927 0.018095 21.05134 0.0000
LOG(PREMIUM) 1.335759 0.146455 9.120596 0.0000
GUARANTEE -0.141260 0.017002 -8.308617 0.0000
DEFERMENT 0.018659 0.014863 1.255400 0.2095
Male 0.896550 0.455371 1.968831 0.0492
Female 4.289322 0.172651 24.84389 0.0000
R-squared 0.465397 Mean dependent var 106.3872
Adjusted R-squared 0.463234 S.D. dependent var 4.509411
S.E. of regression 3.303790 Akaike info criterion 5.232704
Sum squared resid 16186.98 Schwarz criterion 5.257634
Log likelihood -3891.365 F-statistic 215.1699
Durbin-Watson stat 1.798048 Prob(F-statistic) 0.000000
- 21 -
Table 12: Main Determinants of MWRs
Dependent Variable: 100*MWR; Least Squares with Robust Standard Errors
YEAR=2005; Observations: 1,391
Variable Coefficient Std. Error t-Statistic Prob.
C 72.51743 1.879981 38.57349 0.0000
AGE 0.347256 0.024670 14.07629 0.0000
LOG(PREMIUM) 1.667719 0.165144 10.09859 0.0000
GUARANTEE -0.137314 0.019536 -7.028687 0.0000
DEFERMENT 0.017231 0.016807 1.025200 0.3054
Male 0.847786 0.554230 1.529663 0.1263
Female 3.600156 0.184605 19.50199 0.0000
R-squared 0.407568 Mean dependent var 106.1712
Adjusted R-squared 0.405000 S.D. dependent var 4.506864
S.E. of regression 3.476427 Akaike info criterion 5.334907
Sum squared resid 16726.39 Schwarz criterion 5.361265
Log likelihood -3703.427 F-statistic 158.6889
Durbin-Watson stat 2.027204 Prob(F-statistic) 0.000000
5.3 Analysis of Dispersion of MWRs
An efficient and transparent annuities market should produce similar prices (or MWRs)
for customers with similar characteristics. The results above indicate that annuity pricing
is influenced by the characteristics of the annuitant such as age and gender, but the
regression does not explain a relatively large share of the variations of MWRs across
individual annuitants and over time. The unexplained variations in MWRs could be
simply due to the absence of key explanatory variables, such as the level of education of
individual annuitants and their geographical location, as well as variables capturing
provider characteristics. These limitations could not be overcome, as the dataset on
individual annuities used to compute MWRs does not provide information on providers
or further information on the characteristics of annuitants, beyond those explored above.
The dispersion of MWRs could also be due to institutional and regulatory inefficiencies,
such as the lack of a transparent pricing system and the excessive influence of brokers.
The influence of these factors may be examined, because during this period there were
substantial efforts to improve market transparency. As mentioned before, a major
development in the annuities market was the passage of a new Pensions Law in 2004 that,
among other factors, introduced a cap on broker's commissions and an electronic
quotation system that allows easy and transparent comparisons of annuity and PW prices.
The draft of the Pensions Law was first submitted to Congress in 2000, and it is possible
that the market started changing behavior in anticipation of the Law's approval. Such
- 22 -
change in behavior was observed in the sharp reduction in broker's commissions, from 6
percent of the premium in 1999 to 2.5 percent before approval of the Law in 2004.10 If
annuity rates became the main element of price competition, as opposed to other sales
tactics that included cash rebates to annuitants, it would be reasonable to expect less
dispersion of MWRs.
As shown in Table 13, there was indeed a significant reduction in the dispersion of
MWRs after 1999, measured by the decline in the coefficient of variation. Moreover, the
reduction in dispersion was more pronounced in the bottom third of the market, i.e., for
annuitants with lower premiums and incomes. The decline in the coefficient of variation
was not continuous over the whole period (it was lowest in 2002 for the bottom third and
lowest in 2003 for the whole market), but this is probably due to the fact that MWRs
were computed only for the months of March of each year, and not for the whole year,
and there were probably specific factors affecting MWRs in those particular months.
The reduction in the dispersion of MWRs after 1999 is also illustrated in Figure 3, which
shows the residuals around a simple regression of MWRs against individual premiums in
1999 and 2005. It is also apparent in Figure 3 that the reduction in the dispersion of
MWRs was stronger at the lower end of the market. Overall, these results are consistent
with the sharp decline in broker's commissions after 1999 and probably also reflect a
change in the behavior of market participants after the submission of the new Pensions
Law to Congress in 2000.11 The fact that the reduction in the dispersion of MWRs was
more pronounced for lower premiums is a positive development, as these MWRs are
generally related to lower income annuitants without complementary sources of
retirement income.
Table 13
Mean, Standard Deviation and Coefficient of Variation of MWRs in Different Years
March 1999 March 2002 March 2003 March 2004 March 2005
Bottom All Bottom All Bottom All Bottom All Bottom All
Third MWRs Third MWRs Third MWRs Third MWRs Third MWRs
Mean 0.980 0.980 1.077 1.080 1.034 1.036 1.060 1.064 1.055 1.062
Std. Dev. 0.049 0.049 0.041 0.047 0.043 0.042 0.042 0.045 0.041 0.045
Coef. Var. 4.956 5.009 3.807 4.363 4.137 4.074 3.942 4.239 3.928 4.245
Source of raw data: SVS
Whereas the dispersion of MWRs declined after the submission of the draft Pensions
Law to Congress in 2000, the effects of the actual approval and implementation of the
Law in 2004 are less clear. As shown in Table 13, the coefficient of variation declined
further in the bottom third of the market in March of 2005, relative to March 2004, but
increased slightly for the whole market in the same period. This is somewhat surprising,
as the actual implementation of the Law in mid-2004 seems to have generated further
efficiency gains, as indicated by a further decline in broker's commissions from 2.5 to 2
10See Walker (2005) and Rocha and Thorburn (2006).
11Walker (2005) and Rocha, Morales and Thorburn (2006) provide econometric analyses of the annuity
rate with company data and show that there were structural shifts in the annuities market after submission
of the draft Pensions Law to Congress in 2000.
- 23 -
percent between 2004 and 2005, and evidence that annuity pricing has been based on the
best quotes produced by the new quotation system.12 Therefore, it would be reasonable
to expect a further reduction in the dispersion of MWRs in 2005.
Figure 3: MWRs and Premiums in 1999 and 2005
MWRs and Premiums in 1999
1.2
1.1
1
R
MW
0.9
0.8
0.7
0 2000 4000 6000 8000 10000 12000
Premium(UF)
MWRs and Premiums in 2005
1.2
1.1
R 1
MW
0.9
0.8
0.7
0 2000 4000 6000 8000 10000 12000
Premium(UF)
12Rocha and Thorburn (2006) provide more detailed information on the new quotation system.
- 24 -
It is possible that the lack of clear evidence on the reduced dispersion of MWRs in 2005
is simply due to the limited amount of information, based only on one month. Moreover,
the coefficient of variation is a limited statistic, as it does not control for changes in the
individual determinants of MWRs. The White test for heterokedasticity of the residuals
controls for such changes and provides some evidence, albeit limited, that dispersion
declined in 2005. As shown in Table 14, the coefficients of the year dummies were all
negative and significant, except for 2002, indicating that the dispersion of MWRs
declined relative to 1999, the base year. Moreover, the coefficient of the 2005 dummy is
higher than the 2004 dummy in absolute value, indicating that the dispersion of MWRs
declined from 2004 to 2005, after controlling for changes in the determinants of MWRs,
albeit by a limited amount.
Table 14: White Heteroskedasticity Test
Obs*R-squared 241.1479 Probability 0.000000
Test Equation
Dependent Variable: RESID^2; Least Squares
Pooled Data for 1999, 2002, 2003, 2004, and 2005; Observations: 6526
Variable Coefficient Std. Error t-Statistic Prob.
C 141.1213 79.19219 1.782010 0.0748
AGE -7.339350 1.377755 -5.327035 0.0000
AGE^2 0.069465 0.011813 5.880583 0.0000
LOG(PREMIUM) 17.71593 17.36348 1.020298 0.3076
(LOG(PREMIUM))^2 -1.177378 1.138494 -1.034154 0.3011
GUARANTEE -1.416413 0.228646 -6.194797 0.0000
GUARANTEE^2 0.068083 0.012801 5.318755 0.0000
DEFERMENT 0.243182 0.151408 1.606134 0.1083
DEFERMENT^2 0.008477 0.006064 1.398003 0.1622
Male 11.85092 1.736567 6.824335 0.0000
Female -2.340857 1.155242 -2.026291 0.0428
2002 -2.758191 1.621989 -1.700499 0.0891
2003 -4.945800 1.704210 -2.902108 0.0037
2004 -3.741583 1.629701 -2.295870 0.0217
2005 -3.841310 1.688727 -2.274677 0.0230
R-squared 0.036952 Mean dependent var 11.30530
Adjusted R-squared 0.034881 S.D. dependent var 39.62918
S.E. of regression 38.93189 Akaike info criterion 10.16380
Sum squared resid 9868670. Schwarz criterion 10.17939
Log likelihood -33149.48 F-statistic 17.84465
Durbin-Watson stat 1.947129 Prob(F-statistic) 0.000000
- 25 -
More research on MWRs is merited, because price dispersion in March of 2005 still
seemed significant, and a closer inspection of the sample revealed several cases where the
annuitants' age, gender, premium, and terms of the annuity purchased were similar, but
MWRs were different. As mentioned before, there is separate evidence that the new
quotation system has enhanced the transparency of the Chilean annuities market and has
ensured that pricing is effectively based on the best quotes. The systematic computation
of MWRs would provide further evidence as to whether the new quotation system is
indeed eliminating market inefficiencies and reducing differences that cannot be
explained by individual risk characteristics.
6. Comparisons with Other Empirical Studies
6.1. Comparisons with MWR Estimates for Other Countries
Comparing MWRs in Chile with those estimated by other researchers for other countries
provides many additional insights into the performance of the Chilean annuities market.
Such a comparison is done in two steps. The first involves a comparison of MWRs
calculated with cohort annuitant tables and the risk-free rate. As mentioned before, this is
the measure that reflects most accurately the value of the annuity to the average consumer
(the annuitant), and the one most commonly used for international comparisons. The
second step involves a comparison of MWRs also calculated with the cohort annuitant
table, but discounted with the corporate bond rate. This measure captures more
accurately the cost of the annuity to providers.
Table 15 shows a selected number of MWRs in Chile, estimated for annuities issued in
March 2004. The MWRs are computed with the most updated cohort annuitant table (the
cohortized RV-04) and two discount rates the risk-free rate and the corporate bond
rate.13 Tables 16 and 17 summarize the results obtained for other countries by other
researchers, using similar parameters. Most MWRs computed for other countries are
nominal, i.e., they related to nominal annuities. This reflects the absence of indexed
annuities in most countries the UK is the only country in this sample that has developed
indexed annuities as well. Table 16 also shows indexed MWRs for the US, based on
quotations of indexed annuities by a life insurance company (ILONA). These annuities
have not been sold in the US market, but are also shown for purposes of illustration.
As shown in Tables 15 and 16, the average MWRs estimated for Chile are higher than the
average nominal MWRs estimated for all other countries, across all classes of annuitants.
The differences between the Chilean MWRs and the MWRs of indexed annuities in the
UK and the US are striking, amounting to 20 percent. The average MWRs in the US and
UK decline with age, unlike in the Chilean case. The MWRs for males and females tend
to be very similar in other countries, unlike in the Chilean case. MWRs of joint annuities
are very similar or lower than single annuities, more similar to the pattern in Chile.
13The year 2004 was chosen because it was the last year for which MWRs were computed both with the
risk-free rate and the higher corporate bond rate.
- 26 -
The first conclusion from a comparison of Tables 15 and 16 is that Chilean annuitants
have got a better deal than annuitants in other countries, especially considering that
Chilean annuities are indexed. Buyers of indexed annuities in the UK get a much lower
annuity value of 86 percent of the premium, and pay a charge of about 5 percent of the
premium to obtain inflation protection. The cost of inflation protection in the US is even
higher, amounting to more than 20 percent of the premium. This result is in part
explained by the large supply of indexed instruments in the Chilean case unlike their
British and American counterparts, Chilean providers have access not only to indexed
Government bonds, but also to other higher yield instruments indexed to inflation, and
that allows them to hedge inflation risk while obtaining more attractive returns.
Table 15: Money's Worth Ratios in Chile, March 2004
Computed with Cohort Annuitant Tables and Alternative Discount Rates
Risk-Free Rate Corporate Bond Rate
All cases 1.064 0.904
- maximum 1.276 1.146
- minimum 0.876 0.740
Male, Age 55 1.049 0.897
Male, Age 65 1.086 0.955
Female, Age 55 1.076 0.905
Female, Age 65 1.105 0.971
Joint (65-60) 1.078 0.892
Table 16: Money's Worth Ratios in Selected Countries
Computed with Cohort Annuitant Table and Risk-Free Rate
Australia Canada Switzerl. UK 1 UK UK 2 US 3
(James) (James) (James) (Cannon) (James) (Brown) (Brown)
Nominal Annuities
Male, Age 55 - - - - - 0.921 0.934
Male, Age 65 1.013 0.981 1.046 - 0.977 0.908 0.927
Female, Age 55 - - - - - 0.928 0.937
Female, Age 65 1.002 0.976 1.036 - 0.979 0.907 0.927
Joint 0.988 0.980 0.985 0.981 0.987 - 0.929
Indexed Annuities
Male, Age 55 - - - - - 0.867 -
Male, Age 65 - - - - 0.887 0.854 0.822
Female, Age 55 - - - - - 0.876 -
Female, Age 65 - - - - 0.877 0.857 0.782
Joint - - - - 0.880 - -
Notes: (1) Cannon and Tonks' estimate is the overall average; (2) For males 60 and 65 and females 60 and
65; (3) MWR for indexed annuities in the US relate to annuities offered by Irish Life of North America
(ILONA), which have never been sold.
Sources: Brown et al (2002), James et al (2003), Cannon and Tonk (2004)
Workers who retire early get lower MWRs in Chile. As mentioned before, this result is
explained by the higher reinvestment and mortality risks associated with annuities with
longer expected duration. The opposite result in the UK and the US cannot be easily
interpreted. Longer expected duration also explains the lower MWRs of joint annuities in
Chile, and it is noteworthy that joint annuities have similar or lower MWRs in other
- 27 -
countries as well. On the other hand, the differences between MWRs of single male and
single female annuities in Chile cannot be easily explained. The larger premiums in the
case of single females partly explain the higher MWRs, but even controlling for this
factor, MWRs of single female annuities remain higher than those of males, as noted
above. It is possible that these results are due to the small number of single male
annuities.
Table 17: Average Money's Worth Ratios in Selected Countries
Computed with Cohort Annuitant Table and Corporate Bond Rate
Australia Canada Switzerl. UK 1 UK UK 2 US 3
(James) (James) (James) (Cannon) (James) (Brown) (Brown)
Nominal Annuities
Male, Age 55 - - - - - - 0.840
Male, Age 65 0.896 0.879 0.944 - 0.879 - 0.853
Female, Age 55 - - - - - - 0.838
Female, Age 65 0.865 0.864 0.916 - 0.860 - 0.847
Joint 0.846 0.868 0.875 - 0.873 - 0.841
Indexed Annuities
Male, Age 55 - - - - - - -
Male, Age 65 - - - - 0.784 - -
Female, Age 55 - - - - - - -
Female, Age 65 - - - - 0.747 - -
Joint - - - - - - -
Notes and sources: Table 13
An important question that arises in the Chilean case is whether these high MWRs are
sustainable. The increase in MWRs to levels higher than one has been accompanied by
negative spreads vis-à-vis the risk free rate, raising the issue as to whether providers are
able to generate profits in the annuity business. As shown in Figure 4, the average
annuity rate reported by providers was lower than the average risk-free rate in 1999, but
since the early 2000s the average annuity rate has exceeded the risk-free rate, a result
which is unusual by international comparison. For example, Brown et al (2001) compute
the internal rates of return on US annuities and obtains rates ranging from 5.9 to 6.5
percent p.a., lower than the yields of 10 and 30-year Treasury bonds, which were 7.1 and
7.3 percent p.a. in the same period. James, Song and Vittas (2003) perform the same
exercise for several countries and obtain similar results.14
Annuity providers can still achieve positive financial spreads and generate profits
investing in higher yield paper, which is exactly what providers have been doing the
share of lower yield Government and Central bank bonds declined from 40 to 15 percent
14The annuity rate here is defined as the internal rate of return on the annuity contract, thus comparable
with the results in Brown et al, and with the yield on financial instruments. Other researchers (Orszag
(2001), Cannon and Tonks (2004)) define the annuity rate as the ratio of the annuity payment over the
premium. This indicator is much higher than the internal rate of return on annuities in Chile this indicator
exceeds the annuity rate by more than 200 basis points. It is a useful indicator that can be easily computed
and used to track the annuity rate (the two series are highly correlated), but is not directly comparable to the
yield of financial instruments. The ratio of payments to the principal is only equal to the internal rate of
return in the case of perpetuities or consols.
- 28 -
of the portfolio in the past 10 years while the share of mortgage and corporate bonds
increased commensurately. Figure 4 indicates that a portfolio of corporate bonds would
have generated returns exceeding the annuity rate by 100-120 basis points in 2002-2005.
However, this strategy implies excessive concentration of risks in one asset class.
Moreover, providers also have to pay for brokers' commissions, cover their operating
costs, make an allowance for several risks such a default risk, and generate an adequate
return on equity. Therefore, both the MWRs and the spreads estimated for recent years
indicate a situation that may not be sustainable.
An international comparison of MWRs estimated with a higher discount rate yields
similar conclusions. As shown in Table 15, the average MWR for 2004 drops from 1.06
to 0.9 when it is computed with the corporate bond rate. However, MWRs for
representative classes of annuities in Chile remain significantly higher than the
corresponding averages for other countries, as shown in table 17. This suggests thin
margins for Chilean providers on a present value basis, possibly making some providers
unable to cover all costs and risks and still generate a positive profit margin. It is
possible that the high MWRs observed in recent years reflect aggressive pricing strategies
by some providers and that MWRs computed with the risk-free rate will eventually
decline to levels closer to one with the ongoing industry consolidation.
Figure 4
Annuity Rate and Interest Rates on Central Bank Bonds
and Corporate Bonds (% p.a.), 1993-2005
10%
9%
8%
7%
6%
5%
4%
3%
2%
1993 1995 1997 1999 2001 2003 2005
Annuity Rate (RV-04) Central Bank Bonds Corporate Bonds
6.2. Comparisons with Other Estimates for Chile
This section compares the MWRs estimated in this study with those estimated by James,
Iglesias and Martinez (2005), who compute MWRs using data on quoted annuities from 4
insurance companies in March 1999 and March 2003. The MWRs are calculated using 3
alternative mortality tables, 2 different discount rates, and 2 different premium levels.
- 29 -
The mortality tables are the RV-85 and the RV-98 in period form, and the RV-98 in a
cohort form using rates of mortality improvement from the Canadian Institute of
Actuaries. The two discount rates used are the risk-free rate and the corporate bond rate.
The MWRs are estimated for premiums of UF 1,000 and UF 4,000. Table 18 reproduces
their MWRs for 1999 and 2003 while Table 19 reproduces our estimates for the same
years to facilitate comparisons.
As shown in Tables 18 and 19, our MWRs computed with the risk-free rate for 1999 are
roughly equal to those presented by James et al for joint annuities, only slightly higher in
the case of single males age 65, and higher in the case of single females age 60. The
results are somewhat surprising, especially for single male and joint annuities, because
the differences between the period RV-98 and the cohort RV-04 should lead to larger
differences between MWRs. Moreover, our MWRs are estimated from the total universe
of actual sales, while James, Iglesias and Martinez use a sample of quoted annuities from
4 companies. Since annuity sales tend to reflect the best quotes, MWRs based on sales
should be higher than those estimated from quotes.
Table 18
Money's Worth Ratios for Chile Estimated by James et al for 1999 and 2003
March 1999 March 2003
RV-98 Period RV-98 Period RV-98 Cohort RV-98 cohort RV-98 Cohort
Risk-free rate Risk-free rate Risk-free rate Risk-free rate Corp. bond rate
UF1,000 UF1,000 UF1,000 UF4,000 UF1,000
Premium Premium Premium Premium Premium
Male, 65 0.979 0.981 1.012 1.013 0.905
Male, 55 - 0.941 0.976 0.999 0.879
Female, 60 0.963 0.925 0.958 0.992 0.845
Female, 55 - 0.899 0.929 0.977 0.810
Joint 1.000 0.977 1.008 1.025 0.883
Source: James, Iglesias and Martinez (2005)
Table 19
Money's Worth Ratios for Chile Estimated by this Report, 1999 and 2003
March 1999 March 2003
RV-04 Cohort RV-04 Cohort RV-04 Cohort
Risk-free rate Risk-free rate Corporate bond rate
Average Average Average
Male, 65 0.996 1.069 0.955
Male, 55 0.981 1.049 0.897
Female, 60 1.021 1.077 0.971
Female, 55 0.994 1.049 0.905
Joint 0.998 1.050 0.892
Source: Table 4
Our MWRs computed with the risk-free rate for 2003 are higher than those presented by
James, Iglesias and Martinez for the same year, with the differences ranging from 3 to 10
percent. Again, the differences are larger in the case of females. These differences are
more consistent with the differences between the mortality tables, especially regarding
- 30 -
female mortality rates, as well as the differences between annuity sales and annuity
quotes. However, it is noteworthy that our MWRs increase between 1999 and 2003
while the MWRs estimated by James, Iglesias and Martinez remain stable or even
decrease. This stability of MWRs is at odds with the behavior of the risk-free rate
annuity rate differential in the same period. As shown in Figure 4, the relation between
the risk-free rate and the annuity rate would only be consistent with MWRs lower than
one in 1999 and higher than one in subsequent years, including 2003.
The main conclusion of James, Iglesias and Martinez, that Chilean MWRs are high by
international comparison and that Chilean annuitants have got a good deal for their
money is the same as the one reached here, but their numbers probably underestimate the
true MWRs in March 2003. In addition to the use of an outdated mortality table, it is
possible that their results are also being affected by a small and non-representative
sample of annuity quotes. The risk-free yield curve used for discounting is probably
different and may be also contributing to the different results.
7. Conclusions
On any measure, the results in Chile indicate good value for consumers. In part, this can
be explained by the larger supply of assets indexed to consumer prices in Chile, including
higher yield indexed instruments such as mortgage, corporate, and infrastructure bonds.
Rocha, Morales and Thorburn (2006) provide separate evidence that the annuity rate is
positively correlated with the share of higher yield assets in the portfolios of providers,
suggesting that MWRs are also positively affected by this factor. In other countries,
providers are either exposed to inflation risk, due to the absence of indexed instruments,
or can only access lower yield indexed instruments such as indexed government bonds.
The high MWRs may also reflect aggressive pricing behavior in a very competitive
annuities market. It is interesting to note that the structure of MWRs suggests efficient
risk differentiation MWRs are higher for customers that present relatively lower
reinvestment and mortality risk to the provider. That is, annuities with a shorter expected
duration tend to have higher ratios than those with a longer duration. However, the
overall levels of MWRs seem excessive, suggesting that providers may be either counting
on future increases in interest rates, or deliberately accepting temporary losses to drive
competitors out of the market and gain market share. Rocha, Morales and Thorburn
(2006) provide separate evidence that the annuity rate increases with the level of
competition, and decreases for larger firms with established market share, suggesting that
the high degree of competition also explain the high MWRs.
The MWRs of the recent years probably cannot be sustained for a longer period,
however, as they indicate very low spreads and profit margins and possibly losses in the
annuity business for at least some companies in this period. The industry could absorb
these losses, because of the strong capital buffer accumulated in the 1990s, and which
was due to the introduction of a strict capital regulation early in that decade (Rocha and
Thorburn (2006)). However, the continuation of aggressive pricing strategies could lead
- 31 -
to further erosion of capital. Therefore, some market adjustments should be expected,
leading to some decline in money's worth ratios.
Although individual annuitant characteristics explain a significant share of variations in
MWRs, a large share of these variations remains unexplained. The dispersion of MWRs
has decreased since March 1999, reflecting the threat imposed by the submission of the
draft Pension Law to Congress. There is evidence, albeit limited, that dispersion of
MWRs declined further in March 2005, possibly reflecting the approval and
implementation of the Pensions Law in 2004, especially the new electronic quotation
system. More research on MWRs is merited, to confirm whether the new quotation
system has indeed resulted in the elimination of price inefficiencies and a reduction in
price dispersion. More generally, the new system is an important and welcome
innovation, and its outcomes should be closely and frequently monitored by regulators in
Chile and other countries.
- 32 -
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