Incentives

1. Casualty Actuarial SocietyExperienced Practitioner Pathway SeminarLecture 3 – Critical Components of ERM: Incentives and Capital AllocationStephen P. D’Arcy, FCAS, MAAA, Ph.D.Robitaille Chair of Risk and InsuranceCalifornia State University – FullertonD’Arcy Risk Consulting, Inc.

2. Incentives EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

3. McFarland Memorial Bell Tower • 185 foot bell tower on South Quad of the University of Illinois • Primary funding was $1.5 million from H. Richard McFarland in honor of his wife • Tower contains 48 bells that can play over 500 songs based on player-piano like system EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

4. Problems • The University of Illinois already had a bell tower in Altgeld Hall • The chimes of Altgeld Hall can be played by a musician and are used as a teaching tool • The new bell tower took over space previously used by campus organizations • Why build a second bell tower on campus when there are other pressing financial needs? • Answer: Incentives EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

5. Critical Role for ERM:Tie Incentives to Organization’s Goals • People don’t do what you tell them to do, they do what you pay them to do • If employees are rewarded for production, the company will grow, but not necessarily be profitable • In order to achieve goals, reward employees for actions that lead toward the goals • One method to tie incentives to goals is appropriate capital allocation EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

6. Capital Allocation • Capital allocation is a theoretical exercise • Any business segment has access to the entire available capital of the firm, regardless of amount allocated • For some lines this is more likely than others • Property insurance subject to catastrophic loss • Workers compensation in areas with concentration of employees • Liability insurance • Policies without aggregate limits • Unintended exposure that affects many policies • Object is to reflect the likelihood of a business segment needing to utilize corporate capital No method yet developed is ideal for this purpose EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

7. Reasons for Allocating Capital • Pricing • Use the capital allocation to determine the investment income generated by a line of business for rate calculations • Risk management • Determine the risk adjusted rate of return as expected return divided by capital allocation • Use the risk adjusted return to decide if a business segment (line or investment) is worth continuing • Performance evaluation • Reward performance based on risk adjusted returns EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

8. Key Considerations in Allocating Capital • Must be accepted within organization • Understandable • Can be communicated • Sums to the total capital of the organization • Stable over time • Allocation not affected by other business segments • No negative allocations • Appropriate for particular application • Coherent No single method meets all these considerations EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

9. Properties of a Coherent Allocation Full allocation All of the risk capital is utilized Aggregation Invariance Equivalent risks should receive equivalent allocations No undercut No incentive to break away – i.e. capital allocation should be lower than capital needed if that section was a separate entity EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

10. Methodologies for Allocating Capital • Risk Based Capital (RBC) • Variance or Covariance Approach • Semi-variance • Value-at-Risk • Tail Value-at-Risk • Marginal Capital Allocation • Merton and Perold • Myers and Read • Game Theory • Shapley • Aumann-Shapley • Other methods EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

11. Approaches You Have Used or Seen in Capital Allocation Your Answers EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

12. Ruhm-Mango-Kreps Algorithm Based on conditional probability Incorporates a riskiness leverage factor (RLF) Application of Ruhm-Mango-Kreps Simulate a large number of potential outcomes for a firm Rank the iterations by aggregate results Determine a risk charge (riskiness leverage factor (RLF)) for each aggregate outcome Apply corresponding risk charge to each segment’s result whether it consumes or supplies capital Allocate capital based on total capital charges for each segment Advantage/disadvantage of Ruhm-Mango-Kreps Flexible enough by choice of risk leverage factors to duplicate any other capital allocation method EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

13. Ruhm-Mango-Kreps AlgorithmTVaR Example (based on 80% VaR) EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

14. Capital Allocation Methods • We’ll discuss: • Variance and semi-variance • Value-at-Risk (VaR) • Tail Value-at-Risk (TVaR) • Marginal capital - Myers-Read EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

15. Variance and Semi-variance • Variance • The whole distribution is relevant • Risk of good outcomes is treated same as the risk of bad outcomes • Impact of risk is proportional to the square of the difference from the mean • Problem – does a firm really need capital to protect against favorable outcomes? • For RMK approach, RLF = X-μ • Semi-variance • Only considers downside variance • Impact of risk is proportional to the square of the difference from the mean • For RMK approach, RLF = X-μ if X>μ otherwise 0 EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

16. Tail Value-at-Risk • Apply the TVaR risk measure to the total net asset profile (i.e. sum across all classes, then apply) • Apply the “TVaR weights” distribution for the risk measure to the individual risk profiles (e.g. by class) to calculate the capital allocation for that class • Note: This is NOT the same as applying the risk measure to each individual profile • If the capital to be allocated does not equal the capital requirement, use scaling such that the individual allocations add up to the total allocated • For RMK approach, RLF = 1 if cumulative probability above selected VaR, otherwise 0 EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

17. Marginal Models for Capital Allocation • Marginal models explicitly recognize diversification benefits within a multi-line organization when allocating capital to a specific line. • Two marginal methodologies have been popularized - both rely on option pricing theory to derive the marginal impact of a line on capital • Merton – Perold • Myers – Read • These marginal models view the equity holders of the insurance company as investors who have a contingent claim (call option) on the firm’s assets • As liabilities mature, equity holders have a claim on the residual (e.g., Assets – Liabilities) • If liabilities exceed assets, the equity holders lose their stake, but no more; this return profile is similar to a call option on the assets EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

18. Myers - Read • Given the firm’s assets and the present value of the losses by line, option pricing methods are used to calculate the firm’s default value • Default value is the premium the company would have to pay to guarantee payment of the losses if the company defaults • Surplus is then allocated to each line so that the marginal default value is the same in all lines. • M-R evaluates small incremental changes in a book of business • For RMK approach, RLF = 1 if cumulative probability is within ε of the ruin probability, otherwise 0 EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

19. Problems with Option Pricing Methods • Option pricing models assume either normal or lognormal distributions for assets and liabilities • Insurance liabilities are much more skewed than this • No closed form option pricing model exists for more realistic distributions EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

20. Choice of Method • Reason for capital allocation should drive the choice of method • Ease of application • Ease of interpretation EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

21. Applying Capital Allocation to Performance Evaluation • Dividing returns by allocated capital provides a risk adjusted rate of return • Base performance evaluation on risk adjusted returns • Compare this approach to having a different hurdle rate for each area EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

22. Capital Allocation References • R. Kreps, 2005. “Riskiness Leverage Models,” Proceeding of the Casualty Actuarial Society 91: 31-60. http://www.casact.org/pubs/proceed/proceed05/05041.pdf. • D. Ruhm and D. Mango, 2003, “A Method of Implementing Myers-Read Capital Allocation in Simulation,” Casualty Actuarial Society Forum, Fall, 451-458. http://www.casact.org/pubs/forum/03fforum/03ff451.pdf • S. D’Arcy, 2011, “Capital Allocation in the Property-Liability Insurance Industry,” Variance, 5(2):141-157. http://www.variancejournal.org/issues/05-02/141.pdf • D. Ruhm, D. Mango and R. Kreps, “A General Additive Method for Portfolio Risk Analysis.” Forthcoming, ASTIN Bulletin. EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation