Casualty Actuarial Society Experienced Practitioner Pathway Seminar Lecture 3 – Critical Components of ERM: Incentives and Capital Allocation Stephen P. D’Arcy, FCAS, MAAA, Ph.D. Robitaille Chair of Risk and Insurance California State University – Fullerton D’Arcy Risk Consulting, Inc. 1

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

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

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 4EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 5EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 6EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 7EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 8EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 9EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 10EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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

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 12EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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

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

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 15EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 16EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 17EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 18EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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 19EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

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

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 21EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation

Capital Allocation References R. Kreps, “Riskiness Leverage Models,” Proceeding of the Casualty Actuarial Society 91: D. Ruhm and D. Mango, 2003, “A Method of Implementing Myers-Read Capital Allocation in Simulation,” Casualty Actuarial Society Forum, Fall, S. D’Arcy, 2011, “Capital Allocation in the Property-Liability Insurance Industry,” Variance, 5(2): D. Ruhm, D. Mango and R. Kreps, “A General Additive Method for Portfolio Risk Analysis.” Forthcoming, ASTIN Bulletin. 22EPP Lecture 3: Critical Components of ERM: Incentives and Capital Allocation