CM-17 Capital “Allocation”
Russ Bingham
Vice President and Director of Corporate Research
Hartford Financial Services
Don Mango
American Re / Munich Re
Risk and Capital Management Seminar
Washington, DC
July 29, 2003
1
Outline
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Background Basics
 Financial Model Building Blocks
 Risk / Return Decision Framework
 Financial Integrity
Questions to Consider
Price, Risk, Leverage and Return
 Risk Metrics
 Determination of Price and Benchmark Equity
 Risk-Adjusted Return vs Risk-Adjusted Leverage
Allocation?
2
“Building Blocks”: Valuation Fundamentals

Balance sheet, income and cash flow statements

Development “triangles” of marketing / policy / accident
period into calendar period

Accounting valuation: conventional (statutory or GAAP) and
economic (present value)
plus

Risk / return decision framework which deals with separate
underwriting, investment and financial leverage contributions

Don agrees completely!
3
Policy (or Accident) / Calendar Period
Development Triangles
Balance Sheet, Income, Cash Flow
Policy
Period
Prior
2000
2001
2002
2003
2004
Reported
Calendar
2000
X
X
====
Sum
Calendar Period
Historical
2001
2002
2003
X
X
X
X
X
X
X
X
X
X
X
X
====
Sum
====
Sum
====
Sum
Future
2004
X …...
X …...
X …...
X …...
X …...
X …...
====
Sum
Total
Ultimate
--> Sum
--> Sum
--> Sum
--> Sum
--> Sum
--> Sum
Internal analysis is usually across the policy period “row” but external
and regulatory review is often based on the calendar “column” sum
4
Risk / Return Decision Framework – Basic Principles

Insurance
leverage
=
underwriting,
investment
and
financial

Volatility is uncertainty of result

Risk is exposure to loss

Policyholder, company & shareholder risk transfer pricing
activities are a function of risk, and can be accomplished
independently of leverage

Underwriting and Investment returns are a function of
volatility (greater uncertainty, greater required return and
vice versa)
5
Risk / Return Decision Framework – Basic Principles

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Total return is underwriting and investment return
leveraged
Leverage simultaneously magnifies total return and
volatility in total return, but NOT necessarily risk
Leverage is the process by which surplus is introduced in
order to provide a financial buffer against adverse
outcomes (and also to allow for the expression of results in
the standard ROE language of management)
Cost of capital is as important as cost of underwriting
Ultimately, risk and return should be expressed in the
same metric
Principles apply to underwriting and investment activities
6
Financial Integrity
Financial Integrity is supported by the following

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Fully integrated balance sheet, income and cash flow
statements
Policy / accident period focus with calendar period provided
if needed
Nominal and economic accounting valuations
Clearly and consistently stated parameter estimates
 Premium, loss and expense amount
 Timing of premium collection, loss and expense payment
 Investment yield rates
 Underwriting and investment tax rates
 Specification of risks included
 Amount of capital and its cost
7
Financial Integrity(Continued)
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Virtually all models can be reconciled with this completeness
Analytical focus should be on parameter assumptions and inputs
and not be distracted by a particular model structure
 Differing and often incomplete forms of presentation make it
nearly impossible to understand and compare “opposing”
approaches
 Inconsistent parameter estimation, leading to biased
outcomes, is all too common and is not challenged effectively
The analyst / actuary’s role can be a key component of financial
management
 It is the actuary’s responsibility to see that ratemaking and
related activities are part of a disciplined financial process
 Actuaries risk being marginalized unless they adopt a bottom
line, ownership orientation - total return in comparison to the
cost of capital is relevant, for example, whereas return on
premium by itself is not
8
Questions to Consider

Does the model . . .
 Reflect all costs?
 Reflect all risks?
 Provide all metrics?
 Apply to underwriting and investment activities?
 Facilitate the application of fundamental risk / return
principles?

What is Risk, and how is it reflected in the Price?
What is the working Risk / Return Tradeoff?
What determines Leverage?
What is the Cost of Capital and how is it incorporated?
What is the Economic Value Added?
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9
Price, Risk, Leverage and Return
Price for Risk, Leverage for
Return
10
Total Return, Volatility and Risk
11
Comments by Don
Cannot praise this slide highly enough!
 Volatility is not risk
 A certain $500M loss is a risk issue!
 The risk in a return distribution with
certain CV depends on the location
parameter (how far “out-of-the-money”)

12
Risk / Return Decision Framework – Risk Metrics
Policyholder oriented risk metrics
 Probability of ruin
 Expected policyholder deficit (EPD)
 Shareholder oriented risk metrics
 Variability in total return (sR)
 Sharpe Ratio
 Value at risk (VAR)
 Tail Value at Risk (TVAR)
 Expected Shareholder Deficit
 Probability of surplus drawdown (PSD)
 Risk Coverage Ratio (RCR)
 Others …
 RBC and other Rating Agency measures
In one way or another all risk measures address the
likelihood and/or the severity of an adverse outcome

13
Total Return Risk Schematic
14
Comments by Don
We use something similar at Am Re
 Total return framework (sans capital)
 Focus on P(D) [~ PSD] and D/U Ratio
[~RCR]
 Additional, more refined metrics
necessitated by different distributional
shapes and pricing needs of reinsurer

15
Comparison of Policyholder and Shareholder Risk Metrics

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Shortcomings of Policyholder oriented risk metrics
 Narrow focus on loss typically does not reflect variability in loss payment,
premium amount and collection, expense amount and payment and the
impact of taxes and investment income on float and surplus
 Reliability of results is questionable due to basis upon extreme outcomes
in tail of loss distribution
 Inconsistency between measures of risk and return make management of
the risk/return tradeoff difficult
Advantages of Shareholder oriented risk metrics
 Reflects all sources of variability
 Captures all relevant factors that impact bottom line
 Typically embodies more reliability
 Shareholder focus is more in tune with broader financial marketplace
 Should allow for diversification effects to be incorporated
 Addresses policyholder risks
 Provides an important link between price adequacy and solvency
 Consistency in measures of risk and return
16
Dealing With Uncertainty and Risk Two Key Questions
A critical modeling objective is to provide a framework for
addressing the risk / return tradeoff, specifically
addressing the following two questions:

What price should be charged (i.e. what is appropriate
risk-adjusted return)?

How much capital is needed (i.e. what is appropriate
risk-adjusted leverage)?
17
Determination of Price and Benchmark Equity

A. Step 1: Total return distribution is generated using overall
average leverage of 3 to 1.
 Risk is defined as the probability (and severity) that the
total return falls below the breakeven, or risk-free rate of
return. Same for all lines of business.

B. Step 2: The price is determined which satisfies the
specified risk condition. This establishes risk-adjusted return.
 Underwriting price expressed as target combined ratio

C. Step 3: Leverage is altered to restate all returns to 15% or
other risk-premium based level. This establishes riskadjusted leverage.
 Change in leverage does not affect Premium and Risk
determined in Step 2
18
Questions from Don


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Include investment income on allocated
surplus?
Done at what detail level: LOB, portfolio,
contract?
Step 1 seems to imply indifference,
preference, and fairness assumptions. How
has this been received and bought into
among leadership of HFS? Major
stockholders?
19
Total Return, Volatility and Risk
20
Determination of Benchmark Equity (contd.):
Risk-Adjusted Return
Step 2 establishes the risk / return tradeoff line
21
Determination of Benchmark Equity (contd.):
Risk-Adjusted Leverage
Step 3 Restates all businesses to a uniform 15% return with
uniform volatility via altered risk-adjusted leverage
22
Question from Don:

Reinsurance application question: Any
impact on Step 1 if you have
distributions with very different
shapes?

E.g., high excess vs quota share vs finite
23
Risk-Adjusted Return vs Risk-Adjusted Leverage
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Two equivalent alternatives which differ in the form of presentation
At same premium & combined ratio  Maintain a fixed leverage, but vary the total return based on
volatility
– This avoids allocation of surplus to lines of business

Maintain a fixed total return, but vary leverage to adjust for volatility
– This makes regulatory environment less contentious

Introduction of surplus into ratemaking (via the application of a varying
leverage ratio) is optional (but helps communication).
A leverage ratio (and thus surplus) serves a similar purpose in application
as do IBNR factors, yields, expense ratios and tax rates. While they do
not exist at the individual policy level, their necessary consideration in
ratemaking requires introduction by formula.
24
Pricing for Risk and Volatility of Return
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The Risk Pricing “Line” assumes higher returns from underwriting
and investment functions needed to compensate for greater
volatility (i.e., uncertainty) in order to satisfy desired risk criteria
Risk pricing is independent of Leverage
 Leverage magnifies underwriting and investment risk pricing
lines, creating a total return line, while maintaining risk profile
 Change in leverage causes total returns to move along this line
As long as prices are on risk-based line, leverage is irrelevant
YES this means that adequate risk pricing which generates a fair
total return connects the interests of the shareholder and the
policyholder and is in the best interest of both
 Adequate returns directly control solvency risk
25
Comment & Question

Your last point seems to imply that
(paradoxically) policyholders should
prefer a higher priced insurance
product because the carrier is less
likely to default. Conversely they
should be suspicious of a lower priced
insurance product.
26
Allocation?
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The COST of capital / surplus must be considered in ratemaking
Allocation versus attribution
 Objective is not simply allocation of given total capital
 Objective is better viewed as the determination of capital
required to satisfy desired total company risk/return criteria
which reflects the risk/return characteristics of individual
underwriting and investment product risks along with the
diversification benefits provided by them
Attribution of surplus is NOT necessary for risk-based pricing
Attribution of surplus IS necessary to determine total return and
speak the language of management
Connected risk and return metrics (e.g. by defining them in terms
of the same variable), further assists the dialogue (separating risk
from return is like toast cooked on one side)
27
Allocation? (Continued)
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Delineate Underwriting, Investment and Finance risk / return
contributions to assure consistency in risk pricing
Underwriting and investment risk addressed through pricing, not
capital
Solvency risk is controlled by price adequacy, not capital levels
Accounting and economic value based financials differ
Choice of risk metric from among several available is critical
Investment income, IBNR, taxes, AND CAPITAL do not exist at
the underwriting product level, yet all are important elements
which affect risk/return and MUST be reflected (by formula if
necessary) in the product pricing process
28
Best Possible Portfolio (BPP)
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Array of [ Premium, LR ] by
LOB/segment, constrained by:
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Capacity
Return Requirement
Other
This is what Glenn Meyers and many
others are after
29
Confusion
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Allocation = dividing up a total among
constituents
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Additive, current and deliberate
Also clear whether a larger allocation is good
(e.g., bonus pool) or bad (e.g., tax burden)
Sometimes insurance “capital allocation”
means underwriting capacity, and
sometimes return hurdle
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Capacity  more would be GOOD
Hurdle  more would be BAD
30
Underwriting Capacity
BPP exercises treat capital like capacity
 Compare required capital [CReq] and actual
capital
 Required capital (assets) is a function of
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Reserves, investments and other risk sources
Prospective portfolio [Premium, LR]
Dependence structure and variability parameters
Aggregate risk measure (e.g., TVaR)
Desired counterparty rating  targeted level of
risk measure
31
Glenn’s Best Possible Portfolio
 ERM
model output used to calculate Ci
= DCReq for each segment i
so S Ci = CReq
 By Proposition 4  BPP occurs when
ri / Ci = target return
 Off-balance
32
Capacity
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Glenn’s scarce resource to be allocated is
underwriting capacity
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Absolutely agree!
But the terminology is misleading
We really need underwriting capacity
measures (aka “units sold”)
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Getting to use up more is GOOD
Using up more is BAD
Maximize return per unit of budget used
33
Capacity
 Capacity
gets consumed by:
 Prospective
underwriting activity
 Reserve variability
 Investment risk
 Capacity
needs to be allocated each
planning period, and its usage tracked
 Instills
discipline
 Point-of-sale risk management
34
Return Requirement
… on Actual Capital!
 Second piece of the puzzle
 Function of the aggregate risk exposure to
that capital.
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What is the terminal distribution of capital?
How do we translate that to RReq?
Puts an extra wrinkle into the BPP exercise
35
Additional Constraints on BPP
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Allowable “delta” off current portfolio
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Realistic assessment of attainable portfolio
mix [ Premium, LR ]
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Collateral business, “all-lines player”
Relationship and “bank”
Not a fancier version of the elaborate fiction
which is insurance planning
Since RReq is a function of the aggregate
portfolio risk, we only want portfolios where
RExp > RReq
36
Why Capital Consumption?
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Realistic rather than fictional
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Capital is
– Not actually allocated to policy, segment,
business unit, etc.
– Available (via contingent claims) for any
segment, business unit, etc.
– Consumed when a policy, segment, business
unit’s results deteriorate – we call it “reserve
strengthening”
37
Why Capital Consumption?

More informative portrayal of the time
dimension of risk
Unreality of allocation is a serious issue for
long-tailed business, especially with nondecreasing capital starting at inception
 The real risk is reserve deterioration, which
emerges over many years, but often starts
after many years of maturity
 Could call it “B-F Risk”

38
Why Capital Consumption?
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Clearer presentation of the situation to
production unit leadership
ROE could lead to a “sunk capital costs 
maximize revenue” mentality
 Peer pressure of simultaneous contingent
claims on shared asset pool creates a
natural check/balance

39
Why Not Capital Consumption?
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New and different
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It will require us to formulate our own
industry-appropriate theory
40