Download - Earnings by Source K. Pledge
-
8/4/2019 Earnings by Source K. Pledge
1/173
The Analysis of Insurance Earnings
An Enterprise Approach
-
8/4/2019 Earnings by Source K. Pledge
2/173
-
8/4/2019 Earnings by Source K. Pledge
3/173
John McGarryInsight Decision Solutions Inc.
8920 Woodbine Avenue, Suite 205Markham, ON, L3R 9W9, Canada
Kevin PledgeInsight Decision Solutions Inc.
8920 Woodbine Avenue, Suite 205Markham, ON, L3R 9W9, Canada
The Analysis of Insurance Earnings: An Enterprise Approach
John McGarry, Kevin Pledge
Lulu.com ID: 2568635 (Second Edition) Publish Date 5/26/2008
ISBN: 978-1-4357-1865-4
Insight Decision Solutions Inc.
All rights reserved. This work may not be translated or copied in whole or in part
without the written permission of Insight Decision Solutions (8920 Woodbine
Avenue, Suite 205,Markham, ON, L3R 9W9, Canada), except for brief excerpts in
connection with reviews or scholarly analysis. Use in connection with any form of
information storage and retrieval, electronic adaptation, computer software, or by
similar or dissimilar methodology now known or hereafter developed is forbidden.
www.insightdecision.com
-
8/4/2019 Earnings by Source K. Pledge
4/173
-
8/4/2019 Earnings by Source K. Pledge
5/173
John McGarry
Kevin Pledge
The Analysis ofInsurance Earnings
An Enterprise Approach
www.insightdecision.com
-
8/4/2019 Earnings by Source K. Pledge
6/173
-
8/4/2019 Earnings by Source K. Pledge
7/173
Contents
Preface ....................................................................................................................................................... iIntroduction .......................................................................................................................................... 1
Enterprise Earnings-by-Source Methodology
Earnings By Source Overview.................................................................................................... 7
Enterprise Earnings Analysis .................................................................................................. 13
Derivation of Earnings-by-Source Formula
Principles of Enterprise Earnings Analysis ..................................................................... 31Income Statements ........................................................................................................................ 41
Traditional Life Valuation Sources ....................................................................................... 45
Traditional Life Expected and Margin Sources............................................................. 53
Disability Income Valuation Sources .................................................................................. 59
Disability Income Expected and Margin Sources ........................................................ 73
Universal Life Valuation Sources .......................................................................................... 79Universal Life Expected and Margin Sources ................................................................ 91
Other Considerations ................................................................................................................... 99
Product Examples ....................................................................................................................... 109
Enterprise Earnings Analysis Examples
Traditional Life Example ......................................................................................................... 117
Disability Insurance Example .............................................................................................. 137Conclusion ....................................................................................................................................... 149
Appendices
Terminology ................................................................................................................................... 153
Literature.......................................................................................................................................... 155
Index .................................................................................................................................................... 157
About the Authors ....................................................................................................................... 161
-
8/4/2019 Earnings by Source K. Pledge
8/173
-
8/4/2019 Earnings by Source K. Pledge
9/173
iPREFACE
Preface
Analysis of earnings in most industries consists of a relatively simplebreakdown of revenue and expenses. Insurance business is more complex;
the emergence of profit is determined by pricing assumptions, reserves and
divergences between the assumptions and actual experience over the
lifetime of the business. These complexities have given rise to a process
known as earnings-by-source, sources of earnings or analysis of surplus,
depending on jurisdiction. This process is intended to explain earnings
relative to the underlying sources. Unfortunately in many companies, even
if this process is carried out, the usefulness of it as a management tool is
frequently overlooked. The reasons for this are varied, ranging from
difficulty in explaining results to questions over the validity of the results
themselves.
The content of this book is based on work done for the design of a data
warehouse system that would be used to evaluate strategic decisions. In
order to achieve this it was necessary to go back to first principles and
answer questions as to what would make such a system a usefulmanagement tool.
The resulting approach involves viewing the profit emergence as a
continuous event over the year, rather than a discreet once-a-year event.
Problems with results being tied to the given time period and the
interactions between assumptions over longer periods are removed. At the
same time the results can be demonstrated to be accurate and reconcile
without the need for unexplained balancing items.
This approach has been implemented in the Insight Enterprise system
which, with the ability to slice and drill into a wide range of business
attributes such as location, sales office, product and reinsurer, lives up to its
potential as a powerful management tool.
This work is the culmination of five years research and development since
the publication of the The Analysis of Insurance Earnings (McGarry &
Pledge, 2002) and presented at the Canadian Institute of Actuaries meeting,Halifax, NS, on June 28th 2002. This presentation was referenced in the
Canadian Institute of Actuaries educational note on sources of earnings
(Committe on the Appointed/Valuation Actuary, 2004). While aspects of the
-
8/4/2019 Earnings by Source K. Pledge
10/173
ii THE ANALYSIS OF INSURANCE EARNINGS
derivation and presentation of the approach have evolved and been
generalized and refined, the broad principles remain the same. The
approach has been broadened to include fund based products such asuniversal life, and in addition, it is now tied directly to reported earnings.
We are grateful to many friends, colleagues and especially clients, who have
been associated with the development of this approach. In particular we
would like to express our gratitude to Rick Tse, Lyne Francoeur, Caroline
Rendall and Robert LaLonde.
The authors would appreciated any feedback or comments and can be
contacted at [email protected].
-
8/4/2019 Earnings by Source K. Pledge
11/173
1INTRODUCTION
Introduction
Earnings-by-source is a powerful tool for understanding how earnings arisein a life insurance company. It identifies the impact of new business on
earnings and apportions the remaining earnings amongst the main
insurance variables, e.g. mortality and interest. The financial impact of
divergences from assumptions, particularly over time, is also a useful
indication to the appropriateness of those assumptions.
A perennial issue with the presentation of earnings-by-source is that it is
not accessible to anyone other than actuaries. This is a barrier for its wideruse as a management tool. Generally speaking, management will
understand the actual earnings arising and projected earnings over the
period in the income statement form. The earnings-by-source process is
complex and fragmented, the sources are difficult to reconcile with the
income statement, and there are often large balancing items required in
order to reconcile the sum of the sources to total earnings. It is easy to see
why earnings-by-source may lack credibility and is not more widely used or
appreciated.
The traditional approach taken for earnings-by-source reporting is, by the
nature of its derivation and application, a black-box analysis, divorced
from actual corporate earnings. The formulae are derived by expanding the
reserve increase term of an income statement resulting in a formula of each
source, which are then applied to both actual and expected earnings
components. This is true whether an aggregate formula approach or
seriatim projection approach is taken. Practical issues around the reality ofdata residing in various insurance systems, the complexities of managing
the required extracts, and integrating inconsistent data sources are real
barriers to overcome. Hence the traditional approach involves taking actual
earnings, which are generally understood, together with an implicit set of
projected earnings, and then calculating static sources which bear little
resemblance to the original earnings. Management is expected to jump
from a corporate income statement to a series of sources without any way
to tie the two together.
-
8/4/2019 Earnings by Source K. Pledge
12/173
2 THE ANALYSIS OF INSURANCE EARNINGS
The methodology presented in this guide takes an enterprise approach and
overcomes these limitations by embedding earnings-by-source into a
broader earnings analysis. This involves four key steps:
corporate and projected income are incorporated directly into the
analysis;
earnings-by-source formula is constructed as an explicit
transformation of the income statement;
a notional policy earnings statementis built, reconciling policy
sources with the GL; finally, the valuation and best-estimate analysis is integrated into a
single analysis, instead of being viewed as alternative analyses with
inconsistent, irreconcilable results.
The terminology has been deliberately kept general, as this approach is not
tied to any regulatory jurisdiction. Hence the adjectives expected and
valuation are used for describing the two sets of projection assumptions:
the former best estimate and internal, the latter regulatory and prudent.
Enterprise earnings analysis is not an alternative to earnings-by-source; it
has the traditional sources of earnings embedded into it. However, it allows
much broader earnings analysis across all the components in relation to
actual and projected income.
A simple, robust, practical approach to enterprise earnings analysis is
presented that applies to various types of insurance, and is independent of
local regulatory requirements. This approach will give management andregulators the ability to understand the insurance earnings across product
lines, divisions and companies. While any pan-insurance approach may be
considered too simple for specialists in a given practice area, the approach
can be extended and supplemented.
The proposed approach offers several advantages.
The sources are additive over time, so moving from a yearly to four
quarterly analyses gives consistent results.
The contingency sources (mortality, etc) focus on the immediate
financial impact of the event.
-
8/4/2019 Earnings by Source K. Pledge
13/173
3INTRODUCTION
The approach is general, such that the formula can be tailored to
analyses using either expected or valuation projection assumptions or
both, and also either gross or net premium valuation methods. Henceit is not limited to a single accounting approach.
The approach integrates expectation and valuation projections, giving
a single earnings-by-source satisfying both management and actuarial
requirements in a single, integrated application.
The formulae for the sources are relatively simple and intuitive,
allowing for ease of communication and calculation.
The approach requires no balancing item. The total earnings should be
fully explicable with respect to its sources. Balancing item is used
here in the context of dont know, as opposed to different but
explicable.
As a policy seriatim approach, the analysis can be carried out at any
level, giving insights on earnings by, for example, region, division and
product.
Any earnings-by-source analysis represents an apportionment of total
earnings, requiring some assumptions to hold true and using some level of
approximation. The method used is also a function of the intended purpose
and the availability of the data. There may also be a compromise between
conflicting purposes. Hence, given different approaches, the issue is not
between right and wrong, but between the more appropriate approach
given systems and other constraints.
Emergence of Profit
In order to present enterprise earnings analysis, it is important that the
manner in which earnings arise in an insurance company is understood.
A life insurance policy is a long-term contract for which the beneficiary will
receive a benefit paid on the death of the insured life in return for premiums
paid. The life insurance company will earn interest on the premiums paid,
and incur expenses with regard to the sale and administration of the policy.
Life insurance companies are required to hold a reserve to cover the future
net liabilities (benefits plus expenses less premiums) associated with a
-
8/4/2019 Earnings by Source K. Pledge
14/173
4 THE ANALYSIS OF INSURANCE EARNINGS
policy. The reserve is calculated by accumulating the future net cash flows
over the remaining lifetime of a policy to a lump sum, allowing for interest
earned. This requires a set of projection assumptions for the futurebehavior of the main factors affecting the cash-flows: interest, expenses,
mortality and withdrawals (i.e. surrenders and lapses). The reserve is
calculated with prudence in mind, and this prudence is reflected, explicitly
or implicitly, in the method or assumptions or both.
From an earnings perspective, the full amount of the reserve impacts the
earnings in the year of issue. In subsequent years, it is the change in the
reserve over the year that flows through to earnings. When a policyterminates, the entire reserve is released. For each year of a policy, a profit
or loss may be recognized depending on the interaction of the cash flows
and the change in reserves.
An analysis of earnings by source requires identifying the impact of policies
sold and the variations between the reserve assumptions and actual
experience over the period. The sources of earnings (either positive or
negative) include new business, interest, expenses, mortality and
withdrawals.
-
8/4/2019 Earnings by Source K. Pledge
15/173
5ENTERPRISE EARNINGS-BY-SOURCE METHODOLOGY
Section
1Enterprise Earnings-by-Source Methodology
-
8/4/2019 Earnings by Source K. Pledge
16/173
-
8/4/2019 Earnings by Source K. Pledge
17/173
7EARNINGS BY SOURCE OVERVIEW
Earnings by Source Overview
Earnings-by-source was originally developed as an extension to thevaluation process, resulting in two sets of analysis, based on the same
principles, but producing different results for different purposes. Valuation
earnings-by-source compares actual earnings to those embedded in the
reserves. Expected earnings-by-source compares actual earnings to
earnings projected on a best-estimate or management set of assumptions.
Before discussing these approaches it is worth considering the processes
behind these approaches.
Traditional Processes
Traditionally, earnings-by-source is carried out as part of a
valuation/projection process. This requires bringing the actual data, at
various levels of aggregation, into the projection process, usually by line of
business. While logically, bringing this actual data to the projection systems
should be equivalent to bringing the projections to the actual earnings, in
practice there will be an unavoidable loss of data fidelity and lineage. This
will result in the actual earnings used in the earnings-by-source not being
directly related or reconcilable with reported actual earnings. This effect
will be compounded for multiple lines of business with separate extracts
and requirements.
Another consideration is that at the heart of a valuation/projection system
is a projection model of how policies operate. A projection model is a
simplified version of the reality of policy administration, which will beappropriate for valuation and projection. Bringing actual data into this
projection model will essentially result in another loss of data fidelity and
lineage as unmodeled items are ignored and unmodeled behavior ignored
or smoothed. Again, lines of business with different models are
requirements will only compound these issues from a management
perspective.
This approach reflects the primary purpose of a valuation earnings-by-source which is to use actual data to investigate and support the projection
assumptions and model for each line of business. The purpose of using
earnings-by-source to explain actual earnings arising is secondary. Only
-
8/4/2019 Earnings by Source K. Pledge
18/173
8 THE ANALYSIS OF INSURANCE EARNINGS
modeled actual earnings can be directly explained, while manual
balancing items are required to presented earnings-by-source in the full
context of actual earnings.
Another drawback of earnings-by-source as part of the valuation process is
that only a limited set of policy attributes, usually actuarial in nature, can be
used for analysis. The broad range of policy attributes and relationships
available in the actual data, such as to the agent and agent hierarchy, is lost.
While some of these attributes can be incorporated, these changes are time-
consuming and costly. Hence the potential of using earnings-by-source as a
management tool is limited by the lack of flexibility.
Valuation Sources of Earnings
Earnings-by-source analysis was originally developed as an aggregate
method to understand the change in reserves over a period, and also as an
iterative test of the valuation process by reconciling the reserves at the end
of a period to the reserves at the start of the period using the actual and
expected cash flows over the period.
The analysis entails examining new business (i.e. policies issued in the
period) separate from policies in force at the start of the period. New
business is unexpected as no allowance is made for new business in the
valuation.
Earnings arising on policies in force at the start of the period are compared
to projections embedded in the reserves (based on the valuation
assumptions). This is done by subtracting the gains within the valuationearnings from the actual gains. It is a fundamental identity that a projection
of earnings using the valuation method on the valuation assumptions is
equal to zero. Hence the sources of earnings calculated from actual less
valuation gains is equal to actual earnings.
The sources can be split between operational items such as interest,
premiums and expenses, and contingency items such as mortality and
withdrawal. The sources reflect the appropriateness of the individualassumptions, and the set of assumptions in aggregate. Given that reserve
assumptions contain a margin for prudence, these sources will usually be
-
8/4/2019 Earnings by Source K. Pledge
19/173
9EARNINGS BY SOURCE OVERVIEW
positive. Under a net premium valuation, the difference between the office
and net premium will flow through to the premium source.
A typical valuation source-of-earnings report could be structured as follows,
although some of the sources may not apply depending on the reserving
method:
New Business Strain
Premium Profit
Investment Profit
Mortality Profit
Withdrawal Profit
Expense Profit
The new business strain is the impact of setting up reserves, the premium
profit is the difference between the gross and net premium, usually referred
to as premium load. The interest and mortality profits represent to total
contribution to earnings from these variables.
Valuation source of earnings is used for experience reporting in the US and
to validate reserve changes. It has little value for management reporting, to
address management reporting expected sources of earnings was
developed.
Expected Sources of Earnings
The sources of earnings above are based on the valuation assumptions
where variations between gains under actual experience and the valuation
assumptions are analyzed. This shows how earnings are impacted by the
reserves and gives an indication of the appropriateness of the valuation
assumptions. However, as a management tool, there are shortcomings. The
prudence within the valuation assumption should result in persistent
earnings arising due to the release of margins for prudence, although there
will be fluctuations due to randomness.
The valuation assumptions represent a view of the future required for
calculating reserves. It does not represent the insurers view. The insurer
will have projected income for the following period based on its own view
-
8/4/2019 Earnings by Source K. Pledge
20/173
10 THE ANALYSIS OF INSURANCE EARNINGS
of future events, including new business. Such projections may be based on
best-estimate assumptions where there is a 50% probability of the actual
outcome being higher (or lower) than the assumption. However, in theabsence of detailed monitoring it is likely that the corporate assumptions
are either aggressive or conservative: the nature of corporate projections is
that new business and withdrawal assumptions are likely to be aggressive.
Irrespective of this, the corporate projections are used to manage the
business, and hence understanding earnings with regard to these
projections is critical. More generally, we will refer to expected
assumptions, which may or may not be a best estimate of future events.
Sources of earnings calculated on expected assumptions (assumed here to
be best-estimate) changes the nature of the analyses. Firstly, the difference
between gains calculated from actual experience and the expected
assumptions should average to zero over time as variations should be due
only to randomness. Hence this represents a performance test for the
sources, and a test of reliability of the expected assumptions. The sum of
these experience sources will not equal actual earnings; expected earnings
must be included as a source for this to occur. Also, there will be expectedearnings for new business as this will certainly not be unexpected under the
corporate earnings projections. An expected earnings-by-source raises the
analysis from a comprehension-and-reconciliation tool to a management
tool, although this still represents two alternative analyses.
A typical risk sources-of-earnings report could be structured as follows:
Expected Profit (including both inforce and new business)
New Business Profit
Inforce Profit
Premium Profit
Investment Profit
Mortality Profit
Withdrawal Profit
Expense Profit
-
8/4/2019 Earnings by Source K. Pledge
21/173
11EARNINGS BY SOURCE OVERVIEW
The expected sources-of-earnings analysis is well established: (Collins &
Keeler, 1993) outline the approach in the context of business plans and
embedded value, while (Farmer, 1997) outlines the approach in the contextof best estimate analysis. It was introduced as a Canadian reporting
requirement in 2004, and is also a South African requirement.
The Canadian regulatory framework incorporates the concepts outlined
above, using a PPM (Policy Premium Method) valuation method (1992)
with explicit best estimate (unmadded) and valuation (madded)
assumptions, together with dynamic financial analysis requiring a base,
best-estimate, projection over the medium term. This was originallyintroduced as DST (dynamic solvency testing) in 1992, later become DCAT
(dynamic capital adequacy testing) in 1998. Finally source-of-earnings
reporting was introduced in 2004. The report structure required for
reporting is reproduced below. The relationship with the above report is
presented below, for simplicity it is assumed that there are no best estimate
new business assumptions.
Expected Profit on Inforce Operations (Expected Profit)
Impact of New Business (New Business Profit)
Experience Gains & Losses (Inforce Profit)
Changes in Best Estimate Assumptions and Other Changes
Earnings on Operations Before Taxes
Earnings on Surplus
Net Income Before Taxes
The assumption change and surplus items have not been included here for
simplicity, but will be addressed in the main body.
Enterprise Sources of Earnings
There are several limitations of the valuation and expected sources of
earnings:
Firstly, being developed from the valuation process, results presented
are geared towards the actuarial objectives of reconciling and
explaining changes in reserves.
-
8/4/2019 Earnings by Source K. Pledge
22/173
12 THE ANALYSIS OF INSURANCE EARNINGS
Secondly, there is a disconnect between actual reported earnings and
the calculated sources.
Last but not least, these analyses are effectively developed
independent of each other.
To overcome the first limitation, the earnings-by-source process needs to be
viewed independent of the valuation process. This, not only provides an
independent check on the valuation process, but can also provide integrated
presentation to multiple audiences, including Management, Finance and
other departments. The natural platform for such enterprise analysis is a
data warehouse, fed with the raw data and capable of executing the
calculations at the most granular level. It is important to make the
distinction between a platform designed for this purpose and one that
would be fed the results of earnings-by-source analysis and merely presents
them as the latter would be restrictive and limited as a management tool.
The last two limitations listed above are addressed by an integrated
sources-of-earnings analysis approach. This is described in the next section.
-
8/4/2019 Earnings by Source K. Pledge
23/173
13ENTERPRISE EARNINGS ANALYSIS
Enterprise Earnings Analysis
As described in the previous section, one of the main limitations of thevaluation and expected source of earnings approaches is that these analyses
are effectively independent of each other, and independent of the reported
earnings. To overcome this, an integrated sources-of-earnings analysis is
proposed incorporating both valuation and expected sources. Explicit
policy earnings are introduced, together with the concept of a gain
statement, to link this to reported earnings and enable clear steps through
the process.
The integrated approach is referred to here as the Expected-Margin sources
of earnings. It has the expected sources explicitly embedded, with the
valuation sources as the sum of the expected and margin sources. The
margin sources allow expected profit to be analyzed by source, and are the
bridge between the valuation and expected sources. While the method
allows actual earnings to be analyzed against expected and valuation
assumptions simultaneously, this does not preclude using the method solely
on the valuation or expected assumptions. With the full Expected-Marginsources of earnings, the valuation sources of earnings report is simply a
report on the more detailed results and not a separate method. Similarly for
expected sources-of-earnings report.
The source-of-earnings reports are available from the full Expected-Margin
sources of earnings analysis is shown on the next page.
The methodology and formula will be developed first for the Valuation
source of earnings as this reflects the standard approach and illustrates the
method and formulae, and then for full Expected-Margin sources of
earnings. A separate development of the stand-alone Expected sources of
earnings is not presented here there is a direct parallel with the Valuation
method and formula.
-
8/4/2019 Earnings by Source K. Pledge
24/173
14 THE ANALYSIS OF INSURANCE EARNINGS
Report Description
Valuation In-force sources derived from the difference
between actual experience and the valuation
assumptions. New business source from actual
impact. For reconciling and validating reserves,
and understanding the impact of prudent
valuation assumptions.
Expected In-force sources derived from the difference
between actual experience and expected
assumptions, together with expected profit. New
business source may include expected
assumption. For explaining impact of policies and
reserves on earnings to management.
Margin In-force sources derived from the difference
between expected and valuation assumptions,
For explaining expected profit as release of
margins due to the prudence in the valuationassumptions and method.
Expected-
Margin
The full analysis combining valuation, expected
and margin sources.
Expected-Margin Analysis
The expected sources discussed in the previous section have a completely
different interpretation from the valuation sources. The expected approach
breaks the link with the explicit valuation assumptions which are now
embedded in the expected profit source. Hence the expected approach lacks
the explanation and validation of reserves through the reserve roll-forward.
The question then arises as to whether these two approaches can be
integrated to give a single, consistent source analysis incorporating bothvaluation and risk sources. The valuation analysis considers actual earnings
less valuation earnings, while the expected sources examine actual earnings
less expected earnings. To integrate these two approaches, expected
-
8/4/2019 Earnings by Source K. Pledge
25/173
15ENTERPRISE EARNINGS ANALYSIS
earnings can be considered the bridge between actual and valuation
earnings. This requires consideration of actual less expected earnings
separate from the expected less valuation earnings: the expected andmargin sources of earnings respectively. The expected sources have
already been discussed. For the margin sources, given that valuation
earnings are identically zero, as already discussed, total margin sources
equal expected earnings and the individual margin sources are equal to the
impact of the difference between the expected and valuation assumptions
(and methods).
The earnings by source analysis incorporating expected, valuation andmargin sources will be referred to as Expected-Margin earnings-by-source.
An Expected-Margin earnings-by-source report could be structured as
follows:
Sources Expected Margin
New Business X X
Inforce Business
Premium X X
Investment X X
Mortality X X
Withdrawal X X
Survival X X
Expense X X
TotalActl Expd
Earnings
Expected
Earnings
The first item to note is the new survival source that is not present in
traditional sources of earnings. The survival source represents the
residual reserve increase on policies not terminating due to mortality or
withdrawal. This source is not apparent in the traditional sources of
earnings due to the assumptions used to develop the formulae or it is
-
8/4/2019 Earnings by Source K. Pledge
26/173
16 THE ANALYSIS OF INSURANCE EARNINGS
allocated to other sources. For traditional products the source is not
expected to be material except for policy alterations and possibly where
there are errors or approximations in the reserving process. Valuationsources are the sum of the Expected and Margin sources; in total this is
equal to actual earnings.
The sum of the margin sources is equal to expected earnings, where each
source (except new business) identifies the impact of the margins for
prudence or convenience within the valuation assumptions or method.
Finally the sum of the expected sources represents the performance of
actual experience against the expected assumptions (and vice versa).
The above report clearly incorporates both the valuation and expected
earnings-by-source analysis. It allows management to assess performance
against reasonable projections, while allowing actuaries to understand and
validate the valuation and in addition to test the appropriateness of the best
estimate assumptions and the magnitude of the margins in the assumptions
or method.
Reported and Policy Earnings
The Expected-Margin sources report includes actual earnings as the sum of
expected and margin sources, and expected earnings as the sum of the
margin sources. While this report allows actuarial and management
requirements to be resolved in a single analysis, it does not relate the
sources to the income statement.
The aim of relating sources to the income statement is a central propositionwhich has an impact on how the formulae are developed. Relegating it to an
after-thought will largely result in failure in both immediate aim and the
larger objective of developing an enterprise earnings analysis.
There is a technical issue to be resolved before embedding sources of
earnings into the income statement. Reporting earnings exist in the general
ledger which is independent of, but related to, the policy data. Premiums,
claims and reserves are fed from the policy systems, but with only limitedpolicy attributes. Expenses and investment income are not policy-related
data, and need to be unitized to allow policy analysis. For expenses,
acquisition and maintenance expenses are not defined in the general ledger,
-
8/4/2019 Earnings by Source K. Pledge
27/173
17ENTERPRISE EARNINGS ANALYSIS
and need to be calculated in an expense study. To overcome these
constraints, policy earnings need to be constructed using premiums,
claims and reserves already on the policy side, together with unitizedexpenses and investment income. Ideally the difference between reported
and policy earnings will be earnings on surplus. In reality, reported earnings
will contain non-policy policy amounts, e.g. aggregate reserve
adjustments, and income taxes. Hence the difference between reported and
policy earnings will be surplus plus other amounts. In order to investigate
these other amounts, it is important that the policy earnings contain the
account and product information as reported earnings.
Hence policy earnings are used as the actual earnings for policy sources of
earnings, with the difference between reported and policy earnings
identifying primarily the surplus source of earnings. In the subsequent
discussion, actual earnings are referring to policy earnings.
Income and Gain Statements
The Expected-Margin sources report above contains the differencesbetween the three types of earnings involved in the sources calculation:
actual, expected and valuation.
The report format below presents the income statements for actual,
expected and valuation earnings.
Income Actl Expd Valn
Premium X X X
Investment X X X
Claims X X X
Reserve Increase X X X
Expenses X X X
Total X X X
-
8/4/2019 Earnings by Source K. Pledge
28/173
18 THE ANALYSIS OF INSURANCE EARNINGS
Now consider the similar report for the actual, expected and valuation
sources, showing the underlying actual, expected and valuation earnings
used to calculate the sources.
Gain Actl Expd Valn
Premium X X X
Investment X X X
Mortality X X X
Withdrawal X X X
Survival X X X
Expenses X X X
Total X X X
This form of earnings will be referred to here as a gain statement, as the
source components are often referred to as gains or strains (e.g. actual
death strain less expected death strain). The convention of referring to the
terms as gain or strain depending on their usual sign will be ignored here
for simplicity.
The relationship between these separate income and gain statement
reports is clear and unambiguous. Total actual, expected and valuation
earnings should be identical under either report. In order to explain sources
in terms of the income statement, it is necessary to derive the gains
statement formulae as transformations of the income statement. Note that
the gain statement transformation is independent of the type of earnings
(actual, expected or valuation). That is, the same structural transformation
should be used, although with differences reflecting discrete and
probabilistic events.
The new business source does not appear in the gain statement. A policytransitions from new business to inforce depending on the new business
definition. Hence new business earnings need to be identified by a policy
status which can then be brought into the income, or equivalent gain,
-
8/4/2019 Earnings by Source K. Pledge
29/173
19ENTERPRISE EARNINGS ANALYSIS
statements. The income statements below illustrate the split between
inforce and new business earnings for the income statement report. The
total actual new-business earnings are referred to as new business strain.There are no new business earnings for the valuation earnings.
Income Actual Expected Valuation
Inforce NB Inforce NB Inforce
Premium X X X X X
Investment X X X X X
Claims X X X X X
Reserve Increase X X X X X
Expenses X X X X X
Total X X X X X
An integrated, enterprise approach to earnings analysis brings together
reported earnings and both valuation and risk sources.
Statement Structure:
Earnings Statement (standard income statement, based on particular
source / set of assumptions),
Sources Statement (statement structured based on the differencesbetween the earnings types),
Earnings-by-Source Statement (typically items from Sources
Statement by Gain plus surplus).
Line Items:
Traditional layout with change in reserves are referred to as Income
Lines,
Rearrangement based on contingent events are referred to as Gain
Lines.
-
8/4/2019 Earnings by Source K. Pledge
30/173
20 THE ANALYSIS OF INSURANCE EARNINGS
Report layouts and transition between these reports is illustrated on the
following pages.
The abbreviations used in the following illustrations are:
P Premium
I Investment Income
C Claims
R Change in Reserves
M Mortality
W Withdrawal
S Survival
E Expenses
-
8/4/2019 Earnings by Source K. Pledge
31/173
21ENTERPRISE EARNINGS ANALYSIS
Valuation Analysis
Earnings Statement
Income GL Act Val
P x x x
I x x x
C x x x
R x x x
E x x x
Tot x x x
Gain Act Val
P x x
I x x
M x x
W x x
S x x
E x x
Tot x x
Sources Statement
Income Val
P x
I x
C x
R x
E x
Tot x
Gain Val
P x
I x
M x
W x
S x
E x
Tot x
Earnings-by-Source Statement
SOE
NB x
S1 x
S2 x
S3 x
etc x
Tot x
Surplus x
-
8/4/2019 Earnings by Source K. Pledge
32/173
22 THE ANALYSIS OF INSURANCE EARNINGS
Expected-Margin Analysis
Earnings Statement
Income GL Act Exp Val
P x x x x
I x x x x
C x x x x
R x x x x
E x x x x
Tot x x x x
Gain Act Exp Val
P x x x
I x x x
M x x x
W x x x
S x x x
E x x x
Tot x x x
Sources Statement
Income Exp Mar
P x x
I x xC x x
R x x
E x x
Tot x x
Gain Exp Mar
P x x
I x x
M x x
W x x
S x x
E x x
Tot x x
Earnings-by-Source Statement
SOE
NB x
Expd x
S1 x
S2 x
etc x
Tot x
Surplus x
-
8/4/2019 Earnings by Source K. Pledge
33/173
23ENTERPRISE EARNINGS ANALYSIS
The critical difference between the two approaches can be seen in the
Earnings-by-Source statement. Under the Valuation Method, there are no
expected earnings and the sources are different from the sources under theExpected-Margin Method.
The Valuation Method is principally a tool used by actuaries for experience
reporting and as an independent validation of reserves. Hence the income
sources will often be skipped.
The Expected-Margin Method is likely to present expected (and margin)
income sources to show the difference between actual and expected (and
expected and valuation) statements.
It should also be clear from the above diagrams that Valuation Sources are
also available from the Expected-Margin method by summing the Expected
and Margin sources.
Source Analysis
The sources above represent summary measures quantifying impact onearnings, but certainly could not be used to manage the associated areas.
Consider some of the sources in detail.
New business summarizes the impact on earnings of the following
fundamental drivers:
The number of producing agents,
The number of appointments per week,
The appointment-application conversion ratio, and
The application-inforce conversion ratio.
Investment summarizes the impact on earnings on the various asset classes
held and relative volumes.
Expenses summarizes the expenses arising from the various front-line
departments and areas, such as sales, new business and underwriting,
administration etc.
Clearly these three areas will not be directly managed by sources presented
in the earnings analysis. Where best estimate assumptions can be derived in
-
8/4/2019 Earnings by Source K. Pledge
34/173
24 THE ANALYSIS OF INSURANCE EARNINGS
a manner consistent with the metrics used to manage the area, the
enterprise earnings analysis brings these disparate areas together. This
allows management to understand earnings arising with regard to thecorporate business plan, as well as to interpret and judge the impact of
actions across the various departments and areas.
Continuous Earnings Analysis
For earnings analysis to be used as a management tool, it needs to be a
continuous, ongoing process, such that trends and current impacts can be
assessed as they arise in the context of longer term analysis. This allows theresults to become actionable. For insurance, a monthly process is the
practical equivalent of continuous.
There are several advantages to a monthly process:
It allows the current position to be known immediately, allowing effective
action to be taken where required.
It allows results to be viewed over any time period and givesconsistent results at any date level.
Events, such as issue and termination, are recognized as they occur,
with the amounts at occurrence, instead of an arbitrary point of time
in the future (for issues) or the past (for terminations).
It simplifies the projection formula required as second order effects
can be ignored.
A monthly earnings analysis effectively tests the underlying rates
which are the true drivers, and not amounts which are affected by
volume issues.
It is not intended to present a short-term, monthly process as an alternative
to medium term, yearly planning. However, it can be argued that a short
term process is as important. Companies are managed using annual
planning cycles, but the full impacts of actual experience over the year with
regard to the projected plans may not be known until mid way through thefollowing year, a full year past the mid-point of the projection period. In
addition, changes may arise during the projection period invalidating the
-
8/4/2019 Earnings by Source K. Pledge
35/173
25ENTERPRISE EARNINGS ANALYSIS
original projection, such that analyzing performance against the original
plan is an academic exercise.
The relationship between short and medium term assessment can be
characterized as either strategy is important but can only be flawed
without tactical assessment, or if you dont know where you are, how can
you know where you are going.
Monthly projections over longer periods are effectively projected earnings
on actual experience over the period. For a given year, the monthly
projections can be compared to the initial annual projection. Assuming no
changes in assumptions, the difference between the two will identify second
order effects. It should be noted that in traditional earnings-by-source,
second order effects are arbitrarily distributed amongst the sources.
Arbitrary as used here does not imply random, but the fact that any two
actuaries may allocate the second order effects differently.
Monthly earnings analyses will have varying degree of volatility. For
meaningful benchmarks, the monthly sources will need to be summed (or
averaged) over longer periods. The monthly trends within those periodsmay indicate where action could be taken, or that the expected assumptions
are no longer appropriate and need to be revised. It may be possible to
manage the volatility itself in order to give more stable earnings.
This is particularly true for sources that are (partially) manageable, namely
interest, expenses and withdrawals. Either the targets are inappropriate
and need to be revised, resulting in a basis change, or corrective action
needs to be set out, with no change in basis. This assumes that the expectedassumptions are indicative of performance targets set by management.
One reason for analyzing sources of earnings is to test the appropriateness
of the reserve assumptions by attaching a financial impact to the variation.
While the financial impact quantifies the variation, it is the rates, and not
amounts, that are being tested. It should be remembered that these
amounts depend on the method of calculation, the approximations used,
and the order in which the variations are calculated. However, ultimately,
these sources are an apportionment of the total earnings. Given a consistent,
robust approach, the financial impact, and trends arising will be a very
useful guide in understanding earnings.
-
8/4/2019 Earnings by Source K. Pledge
36/173
26 THE ANALYSIS OF INSURANCE EARNINGS
Enterprise Gains and Sources
The term sources of earnings is used broadly across industries, and within
various departments of an insurance company. Even between actuarial
departments in different companies and different jurisdictions, there are
variations in interpretation. Add to this the generally interchangeable use of
terms like earnings, income, profit, gains. Clearly, enterprise earnings
analysis requires an a priori definition of these terms.
The terminology adopted here to consider a source to be a difference
between two earnings (e.g. actual and expected) while a gain is a
transformation of the income items (e.g. mortality is the death claims less
reserves released on death). Hence the gain mortality has a risk source,
margin source and valuation source.
When looking to develop an enterprise earnings analysis, it is important to
consider the level of detail at which sources are analyzed. Specialists in
particular areas may consider certain detail important, which at any
enterprise level may distract from overall analysis. For example, rate and
volume analyses can be carried out on investment income and even newbusiness. Auditors may not be happy with a simple actual-to-expected for
expenses and wish to see the components of the expenses.
Another consideration is consistency between the actual and projected
amounts. Detail may be available at one either side, but not available (or
meaningful) for both. The level of detail available in sources often reflects
the perspective of the person designing or driving the development of the
analysis. An accountant may want to see more expense detail, while anactuarial modeler may want to see more projection detail.
Hence individual sources should be developed to explain the impact of the
fundamental drivers to management, recognizing that for each source a
separate, more detailed analysis may be required in order to explain these
bottom line sources.
Within an insurance company, there may be fundamentally different
product lines: traditional life, universal life, disability, investments etc.These various product lines present a related challenge. The variation in
methods applied, level of detail required and terminology used can make
-
8/4/2019 Earnings by Source K. Pledge
37/173
27ENTERPRISE EARNINGS ANALYSIS
the task of integrating the results at enterprise level in a meaningful manner
insurmountable.
The enterprise earnings analysis presented here has been developed to
overcome the issues outlined above. Consider the gains items developed for
the policy status movement method (discussed later):
Gain Definition
Premium Earnings arising due to premiums paid and
premiums embedded in the reserve
Investment Earnings arising due to investment income from
assets backing reserves and the interest
assumption used in the reserves.
Payment Earnings arising from amounts paid on inforce
policies compared to those embedded in the
reserves. Payments include dividends, disability
benefits, and annuity payments.
Mortality Earnings arising due to death claims in excess of
reserves released and those embedded in the
reserves.
Withdrawal Earnings arising due to reserves released in excess
of cash values paid and those embedded in the
reserves.
Survival Earnings arising due to the increase of reserves on
inforce policies and those embedded in the
reserves.
Expense Earnings arising due to expenses incurred and
expenses embedded in the reserves.
Commission Earnings arising due to commissions paid and
commission embedded in the reserves.
-
8/4/2019 Earnings by Source K. Pledge
38/173
28 THE ANALYSIS OF INSURANCE EARNINGS
Two sources not included in the above list are new business and surplus:
The new business source is derived from a policy stage, summing over
all the income components.
Surplus consists of investment income on assets not allocated to
reserves less any corporate expenses. Hence the surplus source can be
modeled in the above gain items.
The development and interpretation of these gain items are set out below.
Many gain items will be familiar, although the terminology used here may
vary from the normal practice. Developing a method to satisfy all types ofinsurance, across different jurisdictions and valuation methods requires
finding a balance in both gain items and terminology.
-
8/4/2019 Earnings by Source K. Pledge
39/173
29DERIVATION OF EARNINGS-BY-SOURCE FORMULA
Section
2Derivation of Earnings-by-Source Formula
-
8/4/2019 Earnings by Source K. Pledge
40/173
-
8/4/2019 Earnings by Source K. Pledge
41/173
31PRINCIPLES OF ENTERPRISE EARNINGS ANALYSIS
Principles of Enterprise Earnings Analysis
Summary
The approach introduces a number of refinements to the standard
earnings-by-source method:
It is embedded in the corporate income statement, bringing together
general ledger and policy data. Actual gains are calculated directly
from the income statement. That is, the aim is to explain the actual
corporate earnings. Differences between the corporate liability income and policy
income can be quantified. These differences may arise due to
aggregate adjustments or cash-flows not available at policy level.
While such amounts should be known, where unexpected amounts
arise, it is possible to investigate the cause. Where the corporate
income is compared directly to policy projected amounts, any such
discrepancies would be unquantified, and may lead to a material lack
of correspondence between actual and expected. The difference
between corporate liability and policy income may be crudely
considered a balancing item, but as investigation can shed light onto to
the causes, it is not an unknowable balancing item. Such differences
can be treated in one of three ways: as a separate non-policy or
unmodeled source, added to actual earnings, or added to expected
earnings.
The method focuses on the total actual, expected and valuationearnings, rather than individual sources. This approach ensures that
on summing the sources, balancing items are not required to reconcile
with income. Individual sources are then calculated by differencing
the appropriate components between actual, expected and valuation
earnings as required.
The method requires seriatim policy admin, valuation and projection
data, together with the general ledger data. The fundamental nature ofthe different type of data within systems is recognized and
accommodated in the formulae used.
-
8/4/2019 Earnings by Source K. Pledge
42/173
32 THE ANALYSIS OF INSURANCE EARNINGS
It analyzes profit monthly, which is effectively continuously.
New business is not defined as a source as such but a policy stage.
That is, policies issued in the period are identified as such. This gives
flexibility in defining the new business periods as well as analyzing
over longer periods where a policy changes from contributing to new
business strain to inforce experience.
Two gain methods are required: status movement for traditional
products and fund movement for fund-based products. The status
movement method includes a base policy status movement method
together with a benefit status extension. The policy status movement
is effectively the traditional method, while the benefit status
movement is required mainly for disability income, but can be applied
more generally where there is a material impact on reserves.
Income Statement Transformations
The concept of a "gain statement" is introduced where the gain items are
calculated as a transformation of the income statement. This has the
following consequences:
The gain statement fully reconciles with the income statement
Starting reserves are released on exit, and not the ending reserves as
theoretically required by formulaically expanding the increase in
reserves. In practical terms, the current reserve held is the last one
calculated and companies may not generally calculate reserves on
terminated policies.
A survival source is introduced. This is essentially the increase in
reserves on policies in force throughout the period. No attempt is
made to attribute the survival source into mortality and withdrawal
sources. This is theoretically possible when calculating expected gains
but not practicable, or indeed meaningful, when calculating actual
gains.
The same transformation is applied to both actual and projected
income statements. With the projected amounts derived from a
-
8/4/2019 Earnings by Source K. Pledge
43/173
33PRINCIPLES OF ENTERPRISE EARNINGS ANALYSIS
generic income projection, the projection process does not become
overwhelming and confusing.
Data
The method assumes the following data sources are available.
Monthly general ledger income statements.
Monthly policy administration system contract snapshots including
benefit, cash value and fund value amounts, as well as reinsurance
contract snapshots.
Monthly policy transactions: premiums, claims, commissions, direct
and ceded
Unitized general ledger amounts (expenses, investment income) are
required to bring "non-policy" amounts into the policy analysis.
Monthly policy reserve snapshots
Monthly policy projection data
Where data is not available monthly, the monthly formulae can still be
applied, although the degree of approximation will be increased.
Monthly Profit Arising
There are many theoretical and practical advantages to analyzing earnings
effectively continuously on a monthly basis.
It allows analyses to be carried out over any time period.
New business strain is recognized in the month of issue, instead of at
an arbitrary point sometime within the first policy year. In addition, its
experience after the month of issue is included in the experience gains
and losses.
Deaths and withdrawals are recognized in the month of exit, using the
amounts applicable to that month, instead of having to use startingyear amounts.
-
8/4/2019 Earnings by Source K. Pledge
44/173
34 THE ANALYSIS OF INSURANCE EARNINGS
The monthly assumption eliminates (actually minimizes) secondary
terms and second order interactions which arise in an annual analysis.
Secondary terms include premiums lost and expense saved afterdeath. Such terms are often included in any exposition, complicating
the formulae, but ignored in practice. Second order interactions make
the approach dependent on the order of calculation, which is an
impediment to standardizing the approach. With a monthly
assumption, second order interactions and hence order dependence
are minimized.
The monthly approach allows one further assumption whicheliminates the second order interactions and order dependence: that
interest is not earned on cash-flows arising in the month. Effectively
earnings are transferred to surplus at the end of the month and will
accrue interest in surplus. On the liability side, interest will only accrue
on the assets backing the reserves. From a practical perspective this
assumption will not have a material impact on the analysis as it is
more a case of allocation than exclusion, for both the actual experience
and expected assumptions. From a formula perspective, it simplifiessources and removes interdependence between the sources, giving
rise to simplicity, robustness and transparency in the method.
The formulae can still be applied on a quarterly or annual basis. It just
needs to be recognized that this is a practical approximation.
The projected profit arising is based on a monthly projection. Hence
over longer periods, the projected profit can be viewed as projected
profit on actual experience arising over the period. It can be viewed
that the expected rates are being tested against actual experience. The
annual sum of monthly projected profit would not reconcile with
profit projected annually. Companies often focus on medium term
projections, say one to three years, for business plans, and may not
welcome the difference. However there are several advantages to the
monthly approach.
For medium term projections, there may be significant changes inbusiness practice mid-way through the period, invalidating the
original projection, and making any reconciliation an academic
exercise.
-
8/4/2019 Earnings by Source K. Pledge
45/173
35PRINCIPLES OF ENTERPRISE EARNINGS ANALYSIS
While there is a place for medium term projections, these are often
carried out without a full understanding of the current position. This
can only undermine the validity of any such projections at outset.
There is an increasing funnel of uncertainty as projections get longer.
This arises due to second order interactions between the assumptions.
Testing actual experience against such projections becoming
increasingly unreliable as actual experience diverges from the
projections assumptions.
As discussed above, a longer term projection can be utilized in this method,
although adjustments may be required. In fact longer term projections can
be used in conjunction with the monthly projections, allowing second order
interactions and impacts of business changes to be identified.
Analyzing Earnings over different Periods
Many companies still carry out analyses on an annual basis; it is therefore
worth examining the implications of analyzing earnings by source at yearly,
quarterly or monthly intervals in more detail.
Yearly vs. Quarterly
Depending on how frequently a company calculates reserves, earnings are
usually analyzed over a calendar year or quarter.
Earnings are analyzed over a given period by first splitting the policies in
force at the end of the period between those policies active that the start of
the period and those policies issued over the period. For policies in force at
the start of the period, the actual experience is compared with the projected
earnings implicit in the reserve held at the start of the period. Hence
analyzing earnings over a year will give a different result from analyzing
earnings over the four quarters of the year and then aggregating the results.
In the analysis over the year,
policies issued over the year are kept separate throughout the year reserves released on exit are calculated at the start of the year
projected earnings are set at the start of the year
-
8/4/2019 Earnings by Source K. Pledge
46/173
36 THE ANALYSIS OF INSURANCE EARNINGS
In accumulating earnings analyzed on a quarterly basis,
policies issued over a quarter are kept separate throughout the
quarter
policies are treated as in force in the quarters following issue
reserves released on exit are calculated at the start of each quarter
the actual experience of previous quarters is recognized, and the
projected earnings are revised with the recalculation of reserves at the
end of each quarter
The quarterly analysis may be considered preferable to the yearly analysis
as
Policies issued over the year are moved into inforce experience
analysis
Reserves released on exit are calculated closer to the exit date and are
a more reliable estimate for the liability
By recognizing experience, and revising the projected earnings eachquarter, the experience variation is tested over a shorter period, and
hence distortions due to compounding and the interaction between
sources are reduced
Carrying out the yearly analysis using reserves calculated at the start
and end of the year effectively ignores reserves and related
information actually known during the year.
Any approximations regarding cash-flow timing will be more accurate
over a shorter period.
Monthly Analysis
The above argument that a shortened analysis period improves accuracy
can be extended to argue for a monthly analysis. There are several
additional benefits that monthly analyses have over longer time periods.
The calendar month can be considered an effective unit of time for lifeinsurance, e.g. premiums are largely paid monthly, among other things. This
allows for simple assumptions regarding cash flow timing. Assume that
premiums are paid, and expenses are incurred, at the start of the month,
-
8/4/2019 Earnings by Source K. Pledge
47/173
37PRINCIPLES OF ENTERPRISE EARNINGS ANALYSIS
and claims paid at the end of the month. These assumptions result in a
simplification of the formulae for sources.
The main impact is on the contingency sources: mortality and withdrawal.
The formula focuses on the benefit paid and reserves released in the month
of exit. That is, the source is concerned with the immediate consequences of
the event. Where formulae are derived over longer periods, there is a
theoretical allowance for premium lost and expenses saved, although these
items are usually ignored. For an annual study, a January lapse requires
eleven lost premiums, while a December lapses needs no premium
adjustment.
New business is only treated as such in the month of issue, and for the
remaining months of the year, such policies are included in the inforce
block. This approach has two benefits. The first is that the impact on
earnings of setting up reserves is limited to the initial reserve, without an
arbitrary roll-forward to the end of the year. The second is that after the
month of issue, the margins released and experience variations are
captured with the experience analysis, and not isolated until the end of the
year.
Methods and Product Types
Sources of earnings analysis identify the impact on earnings of reserves
being set up and released due to a change in policy status. When a policy is
issued a reserve is set up, while on termination, the reserve is released and
there also be a benefit payment. As well as these policy status movements,
over the policy lifetime events may also occur which also results in reserves
being set up and released, and hence have an impact on earnings. Consider a
disability policy, with a benefit status which can be either healthy or
disabled, where claim reserves are held on disabled policies. A change in
benefit status results the set up or release of the claim reserve.
For fund based products, the fund mechanism must be brought into the
earnings analysis. There are several aspects of the fund mechanism which
need to be taken into account:
Deposits, surrenders and changes in fund value do not impact
earnings
-
8/4/2019 Earnings by Source K. Pledge
48/173
38 THE ANALYSIS OF INSURANCE EARNINGS
Charges deducted from the fund constitute revenue
The reserve includes the fund value and may also include an
additional reserve in excess of the fund value
The fund mechanism is continuous such that the discrete nature of the
status movements does not capture the fund movements.
Hence for fund-based products, the policy status movements described
above continue to impact earnings, although through reserves and benefits
in excess of the fund value, and in addition, net charges from the fund
constitute revenue.These can be presented as three separate methods for earnings-by-source:
Policy Status Movement: the traditional earnings-by-source method
Policy/Benefit Status Movement: for disability income and other
products where a benefit status change has a material impact on
reserves and hence earnings. The policy status movement can be
considered a special case of this method.
Policy Status/Fund Movement: for fund-based products, both
universal life and investments.
Given that the policy status movement is just a special case of the
policy/benefit status movement; these can be combined into a single status
movement method. For fund movements, the additional sources and
varying presentation of income warrant this being considered a separate
method. Hence two methods for earnings by source can be presented.
Status Movement: sources of earnings are driven by policy status
movements (issues and terminations) and where required benefit
status movements.
Fund Movement: sources of earnings are driven by policy status
movements together with fund movements. For simplicity, fund
movement is used instead of policy status/fund movement, such
that policy status movements are implicit in the method.
Earnings by source is primarily intended to explain the impact of long-term
reserves on earnings through the cash-flows embedded in the reserves.
However, not all insurance products require long-term reserves to be held
-
8/4/2019 Earnings by Source K. Pledge
49/173
39PRINCIPLES OF ENTERPRISE EARNINGS ANALYSIS
on policies, specifically health products and separate funds. The methods
used for such products can be shown to be special cases of the above
methods. There are clear benefits for using a consistent method across alllines of business.
-
8/4/2019 Earnings by Source K. Pledge
50/173
-
8/4/2019 Earnings by Source K. Pledge
51/173
41INCOME STATEMENTS
Income Statements
Corporate Income Statement
Before addressing the sources of earnings in detail, it is worth reviewing the
income statement, as this is the object of analysis, and using this to
introducing the formula notation to be used throughout.
Consider a company that sells life contracts with a benefit payable on death
or surrender.
The corporate income statement can be written as
CashflowCashflow
CashflowCashflowCashflowCashflowCashflow
C
CMIE
RIWCQCIIPP
Where
C Corporate earnings
Cashflow
indicates sum over transactions records in the period.
PP Premium paid over the period
II Investment income over the period
QC Death claims over the period
WC Withdrawal (surrender) claims over the period
RI Reserve increase over the period
IE Incurred expenses over the period
CM Commissions earned, i.e. sales remuneration, over the period
Corporate earnings can be split between earnings on surplus and earnings
on liabilities. That is
LSC
such that
-
8/4/2019 Earnings by Source K. Pledge
52/173
42 THE ANALYSIS OF INSURANCE EARNINGS
CashflowCashflow
S SIESII
and
CashflowCashflow
CashflowCashflowCashflowCashflowCashflow
L
CMLIE
RIWCQCLIIPP
The new terms introduced here are
S Earnings on surplus
SII Investment income on surplus assets over the period
SIE Incurred expenses allocated to surplus over the period
L Earnings on liabilities
LII Investment income allocated to assets backing reserves over the
period
LIE Incurred expenses allocated to liabilities over the period
Policy Income Statement
Now consider an income statement generated from the policy
administration and valuation system data, together with unitized expenses
and investment income.
CashflowStart
StartEndCashflowCashflowStartCashflow
CMUE
RRWCQCiRPP010
Where new terms are defined below.
Policy earnings over the period.
Start
Sum of policies in force at the start of the period
-
8/4/2019 Earnings by Source K. Pledge
53/173
43INCOME STATEMENTS
End
Sum of policies in force at the end of the period
i Investment return
0R Reserve calculated at start of period
1R Reserve calculated at end of period
UE Unit expenses
The liability investment income and expenses are assumed to be unitized on
policy reserves and counts respectively.
StartCashflow
iRLII0
StartCashflow
UELIE
In an ideal world, it would be reasonable to assume that corporate liability
earnings equal policy earnings. However in real life, this is not the case.Claims may be posted directly into the general ledger, and aggregate
reserve adjustments are often held. The exact treatment of such non-policy
amounts depends on the materiality of the amounts involved and the effort
required to allocate to policy.
Valuation Income Statement
The valuation income statement contains valuation cash-flows projectedover the period using valuation (i.e. reserving assumptions). A valuation
income statement, where cash-flows match the assumptions used to
calculate reserves should identically equal to zero. That is,
0v
To derive these valuation cash flows, consider the iterative reserve formula
which relates the reserves held at two points in time. The formula below
uses the formula convention and assumptions already outlined. For
simplicity of notation, explicit population assumptions have been included,
-
8/4/2019 Earnings by Source K. Pledge
54/173
44 THE ANALYSIS OF INSURANCE EARNINGS
whereas the assumptions for cash-flow amounts such as premiums have
not been made explicit.
Start
v
Start
v
Start
v
Start
v
Start
v
Start
vv
Start
v
CMUE
PPWBwQBqRpiR10
1
Where the new terms as defined as:
vSuperscript indicates valuation assumptions
In addition, the population probability terms are defined as
q projected number of deaths over period
w projected number of withdrawals over period
p project number of survivors at end of period ( wq 1 )
This is a general reserve formula including all income terms, some of which
may not apply depending on the valuation method used.
Rearranging the iterative reserve formula into income terms gives the
valuation income statement.
Start
v
Start
v
Start
vv
Start
v
Start
v
Start
v
Start
vv
CMUE
RRpWBwQBqiRPP010
The valuation income statement contains cash-flows projected over theperiod using valuation (i.e. reserving) assumptions. The structure of the
formula matches the policy income statement formula above, with discrete
events replaced by probabilistic ones calculated on initial policy exposures.
-
8/4/2019 Earnings by Source K. Pledge
55/173
45TRADITIONAL LIFE VALUATION SOURCES
Traditional Life Valuation Sources
Traditional life business is used to develop the policy status movementmethod. This method is recognizable as the standard earnings-by-source
analysis. It can be applied to traditional life and payout annuities policies,
although the derivation below focuses on traditional.
Policy Gains Statement
The policy income statement above can be transformed into a gains
statement by decomposing the starting policies into the sum of end policiesand policies exiting due to the death and withdrawal. In addition the policy
amounts released on death and withdrawal, specifically the death and
withdrawal benefits are also brought in.
The formula for transforming the starting policy summation is given by
WdrwlsDeathsEndStart
where
Deaths
sum over policies terminating due to death in the period
Wdrwls
sum over policies terminating due to withdrawal in the period
Now consider that when a policy terminates there is a notional amount on
the policy associated with the termination reason: the death benefit andcash value. The amounts released on termination will not exactly match the
associated claim amounts due to timing and small adjustments such as
interest and premiums returned. However it is these policy amounts that
will be used in any projection for calculating expected amounts. Bringing in
these policy amounts will allow the actual to expected termination gains to
be compared on a consistent basis without any distortions arising due to
timing and adjustments.
Defining the death and withdrawal benefits as
QBDeath benefit
-
8/4/2019 Earnings by Source K. Pledge
56/173
46 THE ANALYSIS OF INSURANCE EARNINGS
WB Withdrawal benefit
These can be brought into the income statement using the following
identities.
DeathDeath
QBQB0
WdrwlWdrwl
WBWB0
The gain statement can be developed by introducing the above terms into
the income statement with some rearrangement.
CashflowStartEnd
WdrwlCashflowWdrwl
DeathCashflowDeath
StartCashflow
CMUERR
WBRWCWB
QBRQCQB
iRPP
10
0
0
0
Where is the policy or actual gain.
Valuation Gains Statement
The valuation gains statement is derived from the valuation income formula
by applying the identity that the expectation of survival, death and
withdrawal must sum to one. That is,
vvv wqp 1
The valuation gains statement is therefore.
-
8/4/2019 Earnings by Source K. Pledge
57/173
47TRADITIONAL LIFE VALUATION SOURCES
Start Start
v
Start
vvv
Start
v
Start
v
Start
v
Start
vv
CMUERRp
WBRwQBRq
iRPP
10
00
0
The valuation gain statement is identically equal to zero, just as for the
valuation income statement. That is,
0v
Earnings by Gain
The actual and valuation gains statements are now presented together for
each source. The earnings for each source is the difference between the
actual and valuation gain term.
Gain Actual Earnings Valuation Earnings
Premium
Cashflow
PP
Start
vPP
InvestmentStart
iR0
ar t
viR0
Mortality Claim
CashflowDeath
QCQB
Mortality Gain Death
QBR0
Start
vQBRq
0
WithdrawalClaim CashflowWdrwl
WCWB
Continued
-
8/4/2019 Earnings by Source K. Pledge
58/173
48 THE ANALYSIS OF INSURANCE EARNINGS
Gain Actual Earnings Valuation Earnings
Withdrawal Gain Wdrwl
WBR0
Start
v WBRw0
Survival End
RR10
Start
vv RRp10
Expense
StartUE Startv
UE
Commission
Cashflow
CM
Start
vCM
The advantage of this presentation of earnings by source is that insteadpresenting the resulting source formula is that the link with earnings is not
lost. This presentation also provides a test for reasonableness. The sum of
actual gains by source should sum to actual earnings, while the sum of
valuation gains by source should sum to zero. Any deviations may indicate a
problem with either the source data or the valuation projection. Presenting
the sum of the sources of earnings, which should sum to actual earnings,
would not identify whether the actual data or the valuation projection was a
problem.
-
8/4/2019 Earnings by Source K. Pledge
59/173
49TRADITIONAL LIFE VALUATION SOURCES
Sources by Gain
The results earnings by source formula are presented below.
Gain Valuation Sources
Premium Start
v
Cashflow
PPPP
Investment
Startv
Start iRiR 00
Mortality Claim CashflowDeath
QCQB
Mortality Gain Start
v
Death
QBRqQBR00
Withdrawal Claim CashflowWdrwl
WCWB
Withdrawal Gain Start
v
Wdrwl
WBRwWBR00
Survival Start
vv
End
RRpRR1010
Expense StartStart
v UEUE
Commission CashflowStart
v CMCM
The sources are discussed in detail on the following pages.
-
8/4/2019 Earnings by Source K. Pledge
60/173
50 THE ANALYSIS OF INSURANCE EARNINGS
Premium
The premium source is
Start
v
Cashflow
PPPP
Under a net premium valuation the valuation premium is the net premium.
The premium source is referred to as the premium load and represents the
allowance for expenses.
Under a gross premium valuation, the valuation premium is the policy
premium, and hence the premium source is not likely to be material. Large
discrepancies may indicate a problem with the source data or the valuation
process.
Investment
The investment source is Start
v
Start
iRiR00
Sometimes the analysis is to be carried out on an asset fund which contains
assets in excess of the reserves, i.e. it has its own surplus. For example aparticipating or with-profits fund. This can be done by allowing for the
additional investment income in both the actual and expected investment
income.
Mortality
The mortality source has been split into claim and gain source: the
former reconciles death claim transactions against policies terminating dueto death during the period, while the latter term is the traditional mortality
gain term base on policy death benefit.
The mortality claim source is CashflowDeath
QCQB
Claim payments are often adjusted from the raw policy amounts due to
advance or due premiums, interest and disputed claims. There may also be
delays between the claim payment and policy termination.
The mortality gain source is Start
v
Death
QBRqQBR00
-
8/4/2019 Earnings by Source K. Pledge
61/173
51TRADITIONAL LIFE VALUATION SOURCES
The actual term is calculated in a manner consistent with the valuation gain
using the policy amounts.
The full mortality source is
Start
v
CashflowDeath
QBRqQCR00
Withdrawal
The withdrawal source has been split into claim and gain source: the
former reconciles surrender claim transactions against policies terminating
due to withdrawal during the period, while the latter term is the traditionalwithdrawal gain term base on policy cash value.
The withdrawal claim source is CashflowWdrwl
WCWB
Claim payments are often adjusted from the raw policy amounts due to
advance or due premiums and interest. There may also be delays between
the claim payment and policy termination.
The withdrawal gain source is Start
v
Wdrwl
WBRwWBR00
The actual term is calculated in a manner consistent with the valuation gain
using the policy amounts.
The full withdrawal source is
Start
v
CashflowWdrwl
WBRwWCR00
Survival
The survival source is Start
vv
End
RRpRR1010
Where there is little difference between the actual and projected ending
reserves, particularly in a factor based net premium valuation, the survival
source will capture the difference between the actual and expected survivalrates, which will reflect the individual differences for the mortality and
withdrawal sources.
-
8/4/2019 Earnings by Source K. Pledge
62/173
52 THE ANALYSIS OF INSURANCE EARNINGS
The survival source will also capture impacts due to differences between
the actual and projected ending reserves such as when a non-forfeiture
option is exercised.
Expense and Commission
The expense source is StartStart
v UEUE
Under a net premium valuation, there is usually no explicit expense
assumption. Hence, the expense source only contains actual expenses, and
would need to be grouped with the premium source which contains the
premium load. Note that expense reserves may be held and deferrable
expense may be included in this term.
The commission source is CashflowStart
v CMCM
Again, for a net premium valuation commissions are not included in the
valuation projection, and hence the commission source only contains actual
commissions and needs to be grouped with the premium source.
For a gross premium valuation, there may be issues around the
completeness of the actual and valuation commissions, as well as the
correspondence between the terms. The valuation commission may only
contain base commissions, ignoring overrides and sales related expenses
such as incentives costs. The actual commission may not include incentive
expenses which will need to be unitized as commission related transactions.
Such discrepancies will undermine separating commission from expenses
as a separate source.
-
8/4/2019 Earnings by Source K. Pledge
63/173
53TRADITIONAL LIFE EXPECTED AND MARGIN SOURCES
Traditional Life Expected and Margin Sources
The earnings-by-source analysis presented above is useful forunderstanding and validating the reserve movement and valuation
assumptions. The main drawback is that valuation assumptions are
conservative, that is, they contain explicit or implicit margins for prudence.
Hence it does not represent a test of actual experience.
A more detailed approach is to introduce a best-estimate, or expected,
earnings projection into the above. Expected earnings provides a
meaningful test for actual earnings, as well as allowing the prudence in thevaluation assumptions to be quantified.
Expected income and gains statements are introduced below (which follow
the valuation statements), and then the earnings by source is adjusted to
accommodate the expected