11

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

22

Outline

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?

33

“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!

44

Policy (or Accident) / Calendar PeriodDevelopment Triangles

Balance Sheet, Income, Cash Flow

Calendar Period Policy Historical Future Total Period 2000 2001 2002 2003 2004 Ultimate Prior X X X X X …... --> Sum 2000 X X X X X …... --> Sum 2001 X X X X …... --> Sum

2002 X X X …... --> Sum2003 X X …... --> Sum2004 X …... --> Sum

==== ==== ==== ==== ==== Reported Sum Sum Sum Sum Sum Calendar

Internal analysis is usually across the policy period “row” but external and regulatory review is often based on the calendar “column” sum

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Risk / Return Decision Framework – Basic Principles

Insurance = underwriting, investment and financial leverage

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)

66

Risk / Return Decision Framework – Basic Principles

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

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Financial Integrity

Financial Integrity is supported by the following

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

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Financial Integrity(Continued)

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

99

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?

1010

Price, Risk, Leverage and Return

Price for Risk, Leverage for Return

1111

Total Return, Volatility and Risk

1212

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”)

1313

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 (R) 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 measuresIn one way or another all risk measures address the

likelihood and/or the severity of an adverse outcome

1414

Total Return Risk Schematic

1515

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

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Comparison of Policyholder and Shareholder Risk Metrics

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

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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)?

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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 risk-adjusted leverage. Change in leverage does not affect Premium and Risk

determined in Step 2

1919

Questions from Don

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?

2020

Total Return, Volatility and Risk

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Determination of Benchmark Equity (contd.): Risk-Adjusted Return

Step 2 establishes the risk / return tradeoff line

2222

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

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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

2424

Risk-Adjusted Return vs Risk-Adjusted Leverage

Two equivalent alternatives which differ in the form of presentationAt 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.

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Pricing for Risk and Volatility of Return

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

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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.

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Allocation?

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)

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Allocation? (Continued)

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

2929

Best Possible Portfolio (BPP)

Array of [ Premium, LR ] by LOB/segment, constrained by:

Capacity Return Requirement Other

This is what Glenn Meyers and many others are after

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Confusion

Allocation = dividing up a total among constituents

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

Capacity more would be GOOD Hurdle more would be BAD

3131

Underwriting Capacity

BPP exercises treat capital like capacity Compare required capital [CReq] and actual

capital Required capital (assets) is a function of

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

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Glenn’s Best Possible Portfolio

ERM model output used to calculate Ci = CReq for each segment i

Off-balance so Ci = CReq

By Proposition 4 BPP occurs when ri / Ci = target return

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Capacity

Glenn’s scarce resource to be allocated is underwriting capacity Absolutely agree! But the terminology is misleading

We really need underwriting capacity measures (aka “units sold”) Getting to use up more is GOOD Using up more is BAD Maximize return per unit of budget used

3434

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

3535

Return Requirement

… on Actual Capital! Second piece of the puzzle Function of the aggregate risk exposure to

that capital. What is the terminal distribution of capital? How do we translate that to RReq?

Puts an extra wrinkle into the BPP exercise

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Additional Constraints on BPP

Allowable “delta” off current portfolio Collateral business, “all-lines player” Relationship and “bank”

Realistic assessment of attainable portfolio mix [ Premium, LR ] 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

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Why Capital Consumption?

Realistic rather than fictional 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”

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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 non-decreasing 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”

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Why Capital Consumption?

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

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Why Not Capital Consumption?

New and different It will require us to formulate our own

industry-appropriate theory