Risk Metrics in an Integrated Financial Discipline

David L. RuhmThe Hartford Insurance Group

2004 Bowles ERM Symposium

Session CS 3B: Risk Metrics

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Risk Metrics

• Risk measurement math is evolving.

• Quick pace of recent theoretical advances.

• Companies are advancing the state of the art in actual practice.

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Integrated Financial Discipline

• Risk control comes from financial discipline throughout the company.

• Integrate one consistent financial discipline standard into all company systems.

• Risk metrics provide objectivity, accuracy.

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Risk Metrics Evolution

Probability-of-ruin

Risk Control Criterion“How much capital is needed to have a 2%

probability of ruin by segment?”

Total Company Rollup: p(ruin) < 0.1%

Note: All numbers shown in this presentation are for illustration only and are not recommended for use.

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Risk Metrics Evolution

Probability-of-ruin

Strengths• Probably indicates enough capital to avoid bankruptcy.

Weaknesses• Capital-based, does not deal with risk directly in pricing.• “Tail wags the company” – extreme events dictate policy.• Misses most information in the return distribution.

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Risk Metrics Evolution

Probability of surplus drawdown (operating loss)

Risk Control Criterion

“What prices must be charged so that the probability of operating loss is less than 20% by segment?”

Total Company Rollup: p(operating loss) < 10%

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Risk Metrics Evolution

Probability of surplus drawdown (operating loss)

Strengths• Controls risk through pricing.• Includes full range of adverse results (not just extremes).

Weaknesses• Does not measure severities of adverse results.• Risk/return balance less consistent for non-normal lines.

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Risk Metrics Evolution

Risk Coverage RatioRCR = (Exp’d Op Return) / (Op Loss Freq x Op Loss Sev)

Risk Control Criterion

“What prices must be charged so that expected returns are proportionate to risks by segment?”

Total Company Rollup: RCR > 20

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Risk Metrics Evolution

Risk Coverage Ratio

Strengths• Balances risk / return profile to a fixed standard.• Includes both frequency and severity.• Like finance’s Sharpe ratio, but measures downside risk.

Weaknesses• Does not risk-weight highest levels of operating loss.• More complex to explain than other measures.

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Risk Metrics Evolution

Risk Coverage Ratio: ROE-basis formula

RCR = (R – r) / X

R = E[ROE]

r = risk-free rate

X = E[max(0, r - ROE)]

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RCR Calculation Example• E[ROE] = 16%, σ = 10%, r = 4%

• Risk Frequency– Area below 4% risk-free rate (“P”) = 11.51%

• Risk Severity– Average return in tail (“T”) = -0.87%– Severity = (r – T) = 4% - (-0.87%) = 4.87%

• Risk Freq x Risk Severity = (r-T)P = 0.56%

• RCR = (16% - 4%) / 0.56% = 21.4

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RCR vs. other metrics

• RCR resembles several popular metrics:

– Tail Value-at-risk (TVaR)

– Conditional Tail Expectation (CTE)

– Expected Policyholder Deficit (EPD)

• There are several important differences.

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RCR vs. other metrics

• Key differences:1) The base on which risk is measured.

2) How the tail is defined (“cutoff point”).

3) Frequency and severity inclusion.

4) Balance of risk and expected return.

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RCR & other metrics: differences

• The base on which risk is measured– Losses are the usual base for other metrics.– Risk is defined as loss above some percentile.– Underwriting also drives investment income.– RCR uses Total Return or Operating Return.– Risk is defined in terms of total return shortfall.

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RCR & other metrics: differences

• How the tail is defined (“cutoff point”)– Percentiles are used in other metrics.

– Operating return < 0 is used in RCR.

– Fundamental difference: risk is defined based on concrete return value instead of percentile.

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RCR & other metrics: differences

• Frequency and severity inclusion– Other metrics measure tail severity.– Other metrics include frequency implicitly, by

using a percentile as the cutoff point.– RCR incorporates both frequency and severity.– Explicit frequency factor makes it possible to

define the tail by value instead of percentile.

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RCR & other metrics: differences

• Balance of risk and expected return– Other risk metrics measure risk alone, not

relative to return.– RCR has risk in denominator and expected

return in numerator.– RCR is similar to Sharpe ratio in this regard.– Showing risk vs. return balance makes the RCR

risk metric more complete and descriptive.

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RCR compared to Default Rate on Surplus (DRS)

• DRS was introduced by Mango in 1999.• RCR and DRS are conceptually similar.

Differences:• RCR uses ROE distribution vs. loss distribution.• RCR can be used without allocating surplus.• DRS weights higher levels of loss (RCR could).

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Integrated Financial Discipline

Vital Component

One uniform standard for consistent measurement of financial performance across

all the company’s functions.

“Benchmark Return Model”

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Integrated Financial Discipline

• Important features for benchmark models:– Return and other financial measures come from

a complete set of financial statements.– Decision-level inputs link results to choices.– Underwriting function measured separately

from investment function.– Measurements account for both risk and return.– Comprehensive: all relevant contributions.

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Integrated Financial Discipline

• Benchmark Return Model used in each stage of decisions and performance:– Planning– Pricing– Monitoring

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Integrated Financial Discipline

• Necessary conditions:– Mandate from top levels of management.

– Financial discipline is an intrinsic part of the culture.

– Tools are integrated into the full range of processes.

• Sufficient conditions (maybe): – Everyone buys into the idea and knows what to do.

– No one wants to get caught going against it.

– Effective monitoring and actions.

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Summary

• Risk metrics vary in what they portray.

• Risk metrics are one tool of the financial discipline within a company.

• Ideally, a working financial discipline is integrated throughout the company, in both its functions and its culture.