TRIFURCATION. An Approach to Comparative Evaluation of Strategies 4/19/2012

Transcription

1 TRIFURCATION An Approach to Comparative Evaluation of Strategies 4/19/2012 Risk Mitigation Analysis An Aspect of Risk Management Requires certain prior steps: Identification of goals Identification and assessment of key risks Identifying measures for risks and goals Identifying scenarios and their effect on goals and risks ik Quantifying scenarios and assessing likelihoods 2 1

2 Quantitative approach: assumptions We can derive a distribution of future outcome scenarios (including probabilities/likelihoods) For each risk mitigation strategy, the effect on each scenario can be quantified wrt all significant outcome measures We can visualize the distribution of outcomes in several ways Common method PDF or CDF 3 Problem: Comparing Risk Mitigation Strategies Usually a strategy affects multiple scenarios and measures Often a trade-off: improvement/benefit in some scenarios in return for deterioration in others (sometimes identified as a cost). Often multiple output measures, each affected by strategy Question: how to compare Common approach: risk measures vs. return measures Efficient Frontier 4 2

3 Problem: Comparing Risk Mitigation Strategies Visual comparison CDFs: vs net 100% 90% 80% 70% 60% 50% gross net 40% 30% 20% 10% 0% Problem: Comparing Risk Mitigation Strategies Visual comparison XY plot: vs net

4 Beneficiaries of Risk Mitigation Key Observation: Often multiple stakeholders in an enterprise Different stakeholders have different interests Value of risk mitigation strategy differs by stakeholder Example: Insurer Stakeholders Policy holders Shareholders Debt holders Management Regulators 7 Trifurcation Approach Identify particular beneficiaries (say management) Identify significant scenarios for these beneficiaries Tranche scenarios in terms of effects on those beneficiaries Note that tranches are identified from a comparative analysis (usually comparing risk mitigation strategy to a base case) 8 4

5 Trifurcation: Simple Case Critical Threshold A value of a particular output which would cause a significant change (deterioration) in the position of the stakeholder In relation to the critical threshold, get 3 tranches: Earnings Impact Estate 9 Trifurcation Tranches with Critical Threshold Earnings Tranche: corresponds to scenarios where risk mitigation not needed (critical threshold not breached) Impact Tranche: scenarios where risk mitigation strategy improves stakeholder position (critical threshold not triggered after risk mitigation) Estate Tranche: scenarios where risk mitigation strategy t not helpful l to stakeholder (critical threshold h triggered even after risk mitigation) 10 5

6 Trifurcation Tranches and Stakeholder Interests Earnings Tranche: generally represents interests of shareholders. Most mitigation costs affect this tranche. Impact Tranche: generally represent interests of management, wrt Critical Threshold Estate Tranche: Generally represent interests of policyholders and regulators 11 Trifurcation Analysis Pick a return measure Compare over tranches Efficient strategies concentrate benefit on Impact Tranche Efficient strategies minimize benefits to other tranches (particularly Estate Tranche) 12 6

7 Case1 Private Equity Fund Threshold 10% loss of value Current Strategy 100% invested in S&P 500 index Current probability of breaching threshold 13.4% Alternate strategies- partial investment in money market instruments Cost of mitigation lower expected return 13 Case1 Private Equity Fund Mean Rate PP Stock MM Return Of Return CV P(<-10%) % % % % % % 4.9% % % % % 14 7

8 Trifurcation Tranches with Critical Threshold Case 1 How do we define the tranches? Earnings Tranche: before mitigation, loss < 10% (or a gain) Impact Tranche: before mitigation, loss > 10%. After mitigation, loss < 10%. Estate Tranche: before mitigation, loss > 10%. After mitigation, still loss > 10%. Compare expected returns to tranches 15 Case1 Private Equity Fund Change in Expected Value Stock MM Earnings Tranche (Pos Earnings) Impact Tranche Estate Tranche (12.62) (31.54) (42.52) (52.48)

9 Case 2 Stop Loss Reinsurance Threshold loss of 15% surplus Base Strategy Gross (no reinsurance) Base case probability of breaching threshold 10.93% Alternate Strategies stop loss reinsurance with various attachments (limit 10% of loss ratio) Cost of mitigation reinsurance premium 17 Case 2 Stop Loss Reinsurance Results of Trifurcation Analysis: Simplistic assumptions on reinsurance pricing Using expected earnings as return measure Looking for most efficient option 18 9

10 Case 2 Stop Loss Reinsurance Results of Trifurcation Analysis: Looking for efficient strategy Compare portion of benefit to Impact Tranche: 19 Case 2 Stop Loss Reinsurance Alternate Options 20% LR limit Maximal efficiency is now at a different retention 20 10

11 Case 2 Stop Loss Reinsurance Trifurcation and Structures Tranches do not necessarily correspond to a layer/structure Can still allocate cost/premium Comparative results can shift 21 Trifurcation Analysis - Visualization Visual comparison of Strategies XY plot: vs net

12 Trifurcation Analysis - Visualization Visual comparison of Strategies XY plot with Critical Threshold: vs net threshold threshold vertical Trifurcation Analysis - Visualization Visual comparison of Strategies XY plot with Critical Threshold and Earnings Tranche: vs net - Earnings Tranche threshold threshold vertical Earnings Tranche

13 Trifurcation Analysis - Visualization Visual comparison of Strategies XY plot with Critical Threshold and Impact Tranche: vs net - Impact Tranche threshold threshold vertical Impact Tranche Trifurcation Analysis - Visualization Visual comparison of Strategies XY plot with Critical Threshold and Estate Tranche: vs net - Estate Tranche threshold threshold vertical Estate Tranche

14 Trifurcation Analysis Summary A comparative method for analyzing risk mitigation strategies Tranches scenarios to represent particular stakeholder interests Simplest case identifies a Critical Threshold for a particular stakeholder Can sort strategies by relative efficiency of mitigation for Impact Tranche Can be combined with a Franchise Value return measure to yield further insight 27 14