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The Analysis of Insurance Earnings

An Enterprise Approach


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John McGarryInsight Decision Solutions Inc.

8920 Woodbine Avenue, Suite 205Markham, ON, L3R 9W9, Canada

[email protected]

Kevin PledgeInsight Decision Solutions Inc.

8920 Woodbine Avenue, Suite 205Markham, ON, L3R 9W9, Canada

[email protected]

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


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John McGarry

Kevin Pledge

The Analysis ofInsurance Earnings

An Enterprise Approach

www.insightdecision.com


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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


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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


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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].


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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.


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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.


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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


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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.


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5ENTERPRISE EARNINGS-BY-SOURCE METHODOLOGY

Section

1Enterprise Earnings-by-Source Methodology


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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


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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


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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


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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


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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.


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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.


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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.


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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


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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


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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,


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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


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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,


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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.


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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


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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


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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


33/173


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


34/173


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


35/173


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.


36/173


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


37/173


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.


38/173


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.


39/173

29DERIVATION OF EARNINGS-BY-SOURCE FORMULA

Section

2Derivation of Earnings-by-Source Formula


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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.


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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


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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.


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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.


45/173


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


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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,


47/173


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


48/173


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


49/173


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.


50/173


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


52/173


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


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,


54/173


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.


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


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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.


57/173


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


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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.


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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.


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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


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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.


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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.


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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

earnings by source k. pledge

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