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General form of return on capital (ROC)


ROC = income / capital


Issue with the general form of return on capital (ROC)


fails to recognize varying degrees of risk


Measures of income to use in ROC (4)


1. GAAP net income
2. statutory net income
3. IASB fair value basis net income
4. economic profit


Methods to reflect risk in ROC (2)


1. implicitly by using premium-to-surplus or reserve-to-surplus ratios
2. explicitly by adjusting income, capital, or both


Measures of capital to use in ROC that are not risk-adjusted (2)


1. actual committed capital
2. market value of equity


Measures of risk-adjusted capital to use in ROC (4)


1. regulatory required capital
2. rating agency required capital
3. economic capital
4. risk capital


Difference between IASB fair value income vs. GAAP/statutory income


IASB fair value removes biases in country-specific accounting standards (e.g. discounts loss reserves and includes a risk margin)


Economic profit


economic profit = (premium - expenses) * (1 + investment return %) - premium * LR discounted to t=1


Limitations of using economic profit as an income measure (3)


1. does not consider changes in firm value from future profits (franchise value)
2. difficult to reconcile to GAAP
3. decision rationale may not be clear to external parties if decision-making is based on economic profit but reporting is based on GAAP accounting


Actual committed capital


actual committed capital = contributed capital + retained earnings


Market value of equity


considers franchise value, so generally > committed capital


Economic capital


capital required to ensure probability of achieving a given objective


Possible objectives used for economic capital requirements (2)


1. solvency - hold enough capital that firm can meet future obligations to PH
2. capital adequacy - hold enough capital to reach other objectives such as paying dividends, gaining premium, or maximizing franchise value


Risk capital


capital contributed by shareholders to absorb the risk that liabilities will exceed premium & loss reserves


Risk-adjusted return on capital (RAROC)


RAROC = economic profit / risk-adjusted capital


Issue with RAROC


different capital allocation methods can lead to different conclusions


Common risk measures (4)


1. probability of ruin
2. percentile risk measure (VaR)
3. conditional tail expectation (CTE, aka TVaR)
4. expected policyholder deficit (EPD) ratio


Probability of ruin risk measure


estimated probability that a ruin scenario will occur

ex: insurer default or ratings downgrade


Percentile risk measure (VaR)


amount of capital required to achieve a specific probability of ruin target (= loss amount exceeded X% of the time)


Conditional tail expectation (CTE, aka TVaR) risk measure


average loss out of losses that exceed a given percentile


Approx. default probability using TVaR


approx. default probability = (1 - TVaR %) / 2


Expected policyholder deficit (EPD) ratio risk measure


avg value of shortfall b/w assets and liabilities relative to expected liabilities

(denominator is total # of scenarios/simulations, not just those generating a deficit)


Methods for selecting risk measure thresholds (3)


1. bond default probabilities for credit rating level
2. management's/shareholder's risk preferences
3. arbitrary default probability, percentile, or EPD ratio


Bond default probabilities for credit rating level risk measure threshold


set the threshold such that the probability of default = probability of default of bonds with the desired credit rating (e.g. AA-rated)


Weakness of the bond default probability method for selecting a risk measure threshold


does not address which rating firm's should target


Considerations for selecting bond default probabilities for selecting a risk measure threshold (3)


1. historical (more stable) vs. current (more responsive) default rates
2. can get different estimates from different rating agencies - should use the most reflective of current estimates
3. default probabilities should be adjusted to reflect the time horizon


Weakness of using management's risk preferences to determine risk measure threshold


management may have difficulty agreeing or preferences that clash with board/shareholders


Risk sources (aka risk distributions, 4)


1. market risk
2. credit risk
3. insurance UW risk
4. other risk sources: operational & strategic


Market risk


potential loss in value of current investments from
- changes in equity indices
- interest rates
- FX rates
- and other market variables


Credit risk


potential loss in value due to credit events such as
- counterparty default
- changes in counterparty credit rating
- changes in credit-rating specific yield spreads