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Risk and Return - Part 1 Introduction to VaR and RAROC

Risk and Return - Part 1 Introduction to VaR and RAROC. Glenn Meyers - Insurance Services Office Tim Freestone/Wei-Keung Tang Seabury Insurance Capital LLC Peter Nakada - eRisk, Inc. Risk and Return - Part 1 Introduction to VaR and RAROC.

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Risk and Return - Part 1 Introduction to VaR and RAROC

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  1. Risk and Return - Part 1Introduction to VaR and RAROC • Glenn Meyers - Insurance Services Office • Tim Freestone/Wei-Keung Tang • Seabury Insurance Capital LLC • Peter Nakada - eRisk, Inc.

  2. Risk and Return - Part 1Introduction to VaR and RAROC • The purpose of Part 1 is to provide an overview of the issues involved in determining the cost of capital for an insurer. • We don’t all agree on how to deal with these issues. • Go to Part 2 to see some different points of view on this issue.

  3. Determine Capital Needs for an Insurance Company • The insurer's risk, as measured by its statistical distribution of outcomes, provides a meaningful yardstick that can be used to set capital needs. • A statistical measure of capital needs can be used to evaluate insurer operating strategies.

  4. Volatility Determines Capital NeedsLow Volatility

  5. Volatility Determines Capital NeedsHigh Volatility

  6. Define Risk • A better question - How much money do you need to support an insurance operation? • Look at total assets. • Some of the assets can come from unearned premium reserves and loss reserves, the rest must come from insurer capital.

  7. Coherent Measures of Risk • Axiomatic Approach • Use to determine insurer assets • X is random variable for insurer loss r(X) = Total Assets Capital = r(X) – Reserves(X)

  8. Coherent Measures of Risk • Subadditivity – For all random losses X and Y, r(X+Y)  r(X)+r(Y) • Monotonicity – If X Y for each scenario, then r(X)  r(Y) • Positive Homogeneity – For all l 0 and random losses X r(lX) = lr(X) • Translation Invariance – For all random losses X and constants a r(X+a) =r(X) + a

  9. Examples of Coherent Measures of Risk • Simplest – Maximum loss r(X) = Max(X) • Next simplest - Tail Value at Risk r(X) = Average of top (1-a)% of losses

  10. Examples of Risk that are Not Coherent • Standard Deviation • Violates monotonicity • Possible for E[X] + T×Std[X] > Max(X) • Value at Risk/Probability of Ruin • Not subadditive • Large X above threshold • Large Y above threshold • X+Y not above threshold

  11. Representation Theorems • Artzner, Delbaen, Eber and Heath Maximum of a bunch of generalized scenarios • Wang, Young and Panjer Expected value of X with probabilities distorted by g, where g(0)=0, g(1)=1and g is concave down.

  12. CorrelationMultiple Line Parameter Uncertainty • Select b from a distribution with E[b] = 1 and Var[b] = b. • For each line h, multiply each loss by b. • Generates correlation between lines.

  13. Multiple Line Parameter UncertaintyA simple, but nontrivial example E[b] = 1 and Var[b] = b

  14. Correlation and Capital b = 0.00 Chart 3.4 Correlated Losses 7,000 6,000 5,000 4,000 Sum of Random Losses 3,000 2,000 1,000 0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 Random Multiplier

  15. Correlation and Capital b = 0.03

  16. Positive Correlation Means More Capital • A good insurer strategy will try to reduce correlation between its insureds. • Unless the price is right • Example – Avoid geographic concentration in catastrophe-prone areas.

  17. Long-Tailed Lines of Insurance • Uncertainty in loss reserve must be supported by capital. • Release capital over time as uncertainty is reduced.

  18. Reinsurance • Reduces capital needs • Reduces the cost of capital • Adds reinsurance transaction costs • Insurer strategy - Minimize the combined capital and reinsurance transaction costs.

  19. Allocating Capital • Actually – Allocate the cost of capital • In total, the cost of capital must come from the profit provisions of individual insurance policies. • Allocate capital implicitly, or explicitly. • See session C-3.

  20. Measure Risk/Determine Capital • Build insurer’s aggregate loss distribution. • Claim count distribution • Claim severity distribution • Dependencies/Correlation • Catastrophes • Reinsurance • Hard part is to get the information. • Should be fast as to evaluate various line/reinsurance strategies.

  21. Measure Risk/Determine Capital • For various line/reinsurance strategies • Calculate your favorite measure of risk/needed assets/capital. • Allocate cost of capital to business segments. • Compare resulting costs with market driven premiums. • Select the most desirable strategy

  22. Measure Risk/Determine Capital • Links to a comprehensive example • “The Cost of Financing Insurance” • CAS Ratemaking Seminar http://www.casact.org/coneduc/ratesem/2002/handouts/meyers1.ppt • Papers http://www.casact.org/pubs/forum/01spforum/meyers/index.htm

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