Goldfarb - Risk-Adjusted Performance Measures for P&C Insurers

Question 1

Why can standard return on capital measures such as ROE, ROA or total shareholders return (TSR) result in misleading indications of relative performance and value creation?

Answer 1

These measures often do not explicitly distinguish between activities with varying degree of risk or uncertainty.

Question 2

RAROC = Income/Risk-Adjusted Capital

What are the four relevant income choices for RAROC?

Answer 2

1. GAAP Net Income - It’s convenient to use when RAROC is intended to be used to guide managment decision makeing
2. Statutory Net Income - useful in countries where separate statutory accounting frameworks are used
3. IASB Fair Value Basis Net Income
4. Economic Profit - refers to total change in the “economic value” of assets (market value) and liabilities (discounted).

Question 3

Limitations of using economic value to measure income.

Answer 3

1. Need to ensure that changes in the value of its future profits be taken into account. (franchise value)
2. Complicates reconciliation to GAAP income
3. If economic profit measures are not disclosed to investors, regulators or rating agencies, management may have more difficulty communicating the basis for their decisions.

Question 4

What are the two capital measures that are not risk-adjusted?

Answer 4

1. Actual Committed Capital - actual cash capital provided shareholders generate income for the firm.
2. Market Value of Equity - the committed capital measure adjusted to reflect market values of the assets and liabilities.

Question 5

What are the four capital measures that explicitly reflect risk-adjustments?

Answer 5

1. Regulatory Required Capital - capital required to satisfy minimum regulatory requirements.
2. Rating Agency Required Capital - capital required to achieve a stated credit rating.
3. Economic Capital - capital required to ensure a specified probability that the firm can achieve a specified objective over a given time horizon.

The objective can vary depending upon whether the focus is on the policyholder, debtholder, or shareholder perspective.

• Solvency objective:
• focuses on holding sufficient capital today to ensure that firm can meet its existing obligations to policyholders.
• reflects a policyholder or debtholder perspective
• Capital Adequacy Objective:
• focuses on holding sufficient capital to ensure that the firm can continue to pay dividends, support premium growth in line with the LT business plan
  4. Risk Capital - the amount of capital that must be contributed by shareholders to absorb the risk that liabilities will exceed the funds already provided for in either the loss reserve or in the policyholder premiums.

Question 6

What are the four common risk measures?

Answer 6

1. Probability of Ruin:
   * probability that lossses exceed capital
2. VaR
   * the $ amount of capital required to achieve a specific probability of ruin target
3. Conditional Tail Expectation -
   * average loss of the scenarios worse than the x% percentile
4. Expected Policyholder Deficit
   * expected difference between the amount the company is obligated to pay and the amount it actually pays

Question 7

Methods to select risk measure threshold.

Answer 7

1. Bond Default Probabilities at Selected Credit Rating Level

• • Weakness: does not address the more fundamental question of which rating to target. -
• More important issue is the need to distinguish between
  
  • i) a probability of default assuming the firm is immediately place into run-off and
  • ii) a probability of being downgraded over a specific time horizon
• Several subtleties should be considered when using probability of bond default
  
  • 1) Historical vs. Current Estimates - former more stable, latter more accurately reflect current market conditions
  • 2) Source of Historical Default Statistics
  • 3) Time Horizon - default in risk capital models is often assessed over the lifetime of the liabilities, which have varying time horizons

2. Management’s Risk Preference -

• most relevant threshold is the one that matches the risk preferences of the firm’s management -
• Effective risk preference statements should reflect both the risk and the potential reward for taking risk.
• Shareholder value for an insurer is driven by events that may cause a rating downgrade or a weakened financial position. Risk preference intended to capture the shareholders’ perspective are unlikely to focus on the probability of default.

3. Arbitrary Default Probability, Percentile or EPD Ratio -
   * one could choose an arbitrary threshold such that the risk measure can be reliably estimated and reflect the appropriate relative views of risk ( not scientific)

Question 8

How do insurance companies overcome the weakness associated with conventional ROE measures?

Answer 8

Allocate, or more accurately attributing, their capital or surplus to different business units using either premium to surplus ratios or reserve to surplus ratios that vary by line of business. This can serve to “risk-adjust” the return on capital measure by attributing more capital or surplus to business segments with more perceived risk, though often the premium to surplus and reserve to surplus ratios used are selected judgmentally or without the use of quantitative models.

Question 9

What are the five main categories of risks?

Answer 9

1. Market Risk
2. Credit Risk
3. Insurance Underwriting Risk
4. Other Risk Sources

• Operational Risks: failure of people, system or processes
• Strategic Risks: related to competitors -
• These two are less quantifiable

Question 10

Describe Market Risk

Answer 10

1. Market Risk -

• measures the potential loss in value, over the selected risk exposure horizon, that results from the impact that changes in equity indices, interest rates, FX rates and other similar “market variables” have on the firm’s current investments in equities, fixed income securities or derivative securities.
• • Standard practice: 1). estimate the distribution of portfolio profits or losses over the selected horizon 2). use risk measures such as VaR or CTE - typically performed over a horizon on the order of 10 or fewer days - risk exposure horizon for insurance liabilities is much longer (ignored for now)

Question 11

Describe Credit Risk

Answer 11

2. Credit Risk - measures the potential loss in value due to credit events, such as counterparty default, changes in counterparty credit rating or changes in credit-rating specific yield spreads.

Question 12

The three most important impacts of credit-related risk exposures

Answer 12

• The three most important impacts of credit-related risk exposures 1). Marketable securities, Derivatives and Swap positions 2).Insured’s Contingent Premiums and Deductibles (that cannot be offset against claims payments) 3). Reinsurance Recoveries - most challenging source of credit risk to an insurance company.

Question 13

Reinsurance Recoveries is the most challenging source of credit risk to an insurance company. What are the three unique aspects to this source of credit risk?

Answer 13

i) . Definition of Default - a credit downgrade below the equivalent to an investment-grade rating could create a “death spiral” for the firm. Their ability to write future business will be substantially impacted and many existing policyholder will rush to settle o/s and potential recoveries. => create a liquidity crisis and result in settlement amounts far less than 100% of potential recoveries for the reinsureds. => require a broader definition of default disputes between insurers and their reinsurers are common and often result in settlements of < 100% of potential recoveries. => they maybe treated as the equivalent of a partial default
ii) Substantial Contingent Exposure - Potential exposure to reinsurers’ credit risk can far exceed the reinsurance recoverable balances. Balance sheet reflect only the receivables relating to paid claims and the expected recoveries against current estimates of gross loss reserve. They do not include the potential recoveries from reinsurers in the event of adverse loss development or in the event that losses on new written and earned premiums exceed their expected values.
iii) . Correlation with other insurance risk - reinsurance credit risk is highly correlated with the underlying insurance risks. => harder to rely on external credit-risk only models

Question 14

What are the three categories of insurance underwriting risk

Answer 14

1. Loss Reserve on Prior Policy years - potential adverse development from existing estimates (dominate risk to insurance firm)
2. Underwriting Risk for Current Period Policy Year - Potential losses in excess of premiums charged for the “current” policy period.
3. Property Catastrophe Risk - catastrophe risk associated with earthquake, hurricanes or other weather-related events

Question 15

What are the three components of loss reserve risk?

Answer 15

1. Process risk - actual results will deviate from the expected value due to random variation inherent in the underlying claim development process 2. Parameter Risk - actual expected value of the liability deviates from the estimate of the expected value due to inaccurate parameter estimation 3. Model Risk - deviation due to the use of wrong models

Question 16

What is reserve estimation error?

Answer 16

The range of uncertainty associated with a given reserve estimate, rather than the uncertainty with regard to the ultimate outcome. Usually depicted as a confidence interval for a given estimate.

Question 17

What are the four methods of allocating risk capital?

Answer 17

1. Proportional Allocation Based on a Risk Measure - calculate stand-alone risk measures for each risk source and then allocates the total risk capital in proportion to the separate risk measures.
2. Incremental Allocation - determines the impact that each risk source has on the aggregate risk measure and allocates the total risk capital in proportion to these incremental amounts.
3. Marginal Allocation (Myers-Read Method) - determines the impact of a small change in the risk exposure for each risk source (e.g. amount of assets, amount of reserves, premium volume) and allocate the total risk capital in proportion to these marginal amounts.
4. Co-Measure Approach (Kreps, Ruhm-Mango) - establish the capital requirement using a particular conditional risk measure, such as VaR or CTE, and then calculate the Co-Measure for each business unit by calculating the comparable risk measure for the unit subject to the condition applied to the entire firm.

Question 18

What is the mathematical challenges raised that suggest that the Myers-Read method is not appropriate for most insurance applications?

Answer 18

The method assumes that risk exposure in a business unit can be increased or decreased without impacting the shape of the loss distribution, referred as homogeneity. => insurance loss distributions will not exhibit homogeneity.

Question 19

What are the three simplifications of importance to using RAROC for pricing?

Answer 19

1. Investment Income on Allocated Capital - investment income expected to be earned on the allocated risk capital could be included in the calculation of economic profit.
2. Multi-period Capital Commitment - initial capital required to write the policy does not fully reflect the total capital costs. The risk will not be fully resolved in a single period and some risk capital will be needed in subsequent periods as well. One common approach to account for this is to assume an average pattern for the release of the risk capital.
3. Cost of Capital (Target RAROC Rate)

• • Significant issues:
    
    • 1. Use CAPM to establish the cost of risk capital. - risk adjustment in RAROC reflects a different definition of “risk” - CAPM measure the systematic risk. RAROC incorporates an entirely different measure of risk
    • 2. RAROC is artificially “leveraged”. Denominator reflects neither the total market value nor the firm’s actual capital.