Management Strategies and Dynamic Financial Analysis Dynamic Financial Analysis CAS Spring Meeting Martin Eling, University of Ulm Thomas Parnitzke, Baloise Holding San Diego, May 23-26, 2010 Hato Schmeiser, University of St. Gallen Hato Schmeiser, University of St. Gallen
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 2 Outline 1. Motivation 2. Model Framework 3. Management Strategies 4. Performance Measurement 5 5. Simulation Study Si l ti St d 6. Role of Non-linear Dependencies 7. Conclusion and Outlook
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 3 1. Motivation: Three pillars of Solvency II Solvency II Solvency II First pillar: Second pillar: Third pillar: Quantitative regulations for Qualitative elements of Market transparency and capital requirements supervision disclosure requirements → Technical provisions, → Technical provisions → Appropriate processes → Appropriate processes → A transparent process will → A transparent process will minimum capital, and decisions in the context require less regulation as target capital of a risk management market participants → Use of standard models system themselves force appropriate and internal models → Principles for internal risk insurer behavior (Dynamic Financial management and control → Harmonization with IFRS Analysis)
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 4 1. Motivation: Dynamic Financial Analysis (DFA) • Projects results under a variety of possible scenarios, showing how outcomes might be affected by changing internal and external conditions g y g g • Used in practice for Insurance Assets Liabilities Company cash flow projection and decision support Risk Management Environ- Capital Regulation Competition ment Market • Aim of this paper: Ai f thi 1. Implement management strategies in a DFA framework 2 Study the effects on the insurer’s risk and return position 2. Study the effects on the insurer s risk and return position 3. Give helpful insights for the development of DFA tools
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 5 2. Model Framework • Simplified model of a property-liability insurer Assets Assets Liabilities Liabilities • Balance sheet (t=0): Investments Equity (stocks, bonds, Reserves etc.) (Premiums) Investment Underwriting g Result Result • Statement of Income (t=1): Premiums - Claims Claims - Costs (Upfront, Claim Settlement) = Underwriting Result + Investment Result = Earnings Earnings
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 6 2. Model Framework: Earnings (1) EC EC E Insurance Assets Liabilities 1 Company t t t Risk Management (2) (2) max( max( ( ( ) 0) ),0) E E I I U U tr tr I I U U t t t t t Environ- Capital Regulation ment Competition Market EC : Equity Capital at the end of period t t E E : Earnings E i t I : Investment Result t U : Underwriting Result t tr : Tax rate
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 7 2. Model Framework: Investment result P (3) I r ( EC P Ex ) Insurance Assets Liabilities t pt t 1 t 1 t 1 Company Risk Management (4) (4) r r 1 1 r pt t 1 1 t t 1 2 t Environ- Capital Regulation ment Competition Market r : Return of investment portfolio pt P : Premiums t t 1 P Ex : Upfront costs (depending on premiums) t 1 : Portion invested in high-risk investments t 1 r 1 : Return of high-risk investment (e.g., stocks : Ret rn of high risk in estment (e g stocks ) ) t r : Return of low-risk investment (e.g., bonds) 2 t
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 8 2. Model Framework: Underwriting result P C (5) U P C Ex Ex Insurance Assets Liabilities t t 1 t t 1 t Company Risk Management EC EC (6) (6) P P cr MV MV t t 1 1 t 1 t 1 t 1 t 1 Environ- Capital Regulation ment Competition Market • Consumer response (cr) to changes in solvency cr 1, if EC MCR t cr 1, 1 if EC if EC MCR MCR t • Underwriting cycle ( π ): Markov chain with different states C Ex : Claim settlement costs t • Claims: C C C : Consumer response cr t cat ncat t t t : Underwriting cycle : Underwriting cycle MCR : Minimum capital required (Solvency I) : Portion in the underwriting market t 1
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 9 2. Model: Implementation in R (simplified one period example) E=0 # Liabilities EC=15 mu=log(0.85)-0.5*log(1+0.085^2/0.85^2) MV=200 MV 200 sigma= (log(1+0.085^2/0.85^2))^(1/2) i (l (1 0 085^2/0 85^2))^(1/2) β =0.2 C<-rlnorm(1,mu,sigma)*P P=MV* β ExC<-0.05*C ExP<-0.05*P U<-P-C-ExP-ExC tr=0.25 # Aggregation α =0 2 α =0.2 E[i]< I+U max(tr*(I+U) 0) E[i]<-I+U-max(tr (I+U),0) } #end for i for (i in 1:10000) { hist (E) # Assets mean(E) rp<- α *rnorm(1,0.1,0.2)+ sd(E) (1- α )*rnorm(1,0.05,0.05) (1 α ) rnorm(1,0.05,0.05) summary(E) I<-rp*(EC+P-ExP)
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 10 3. Management Strategies Insurance Assets Liabilities • At the beginning of each period Company Risk management can change: management can change: Management - Portion of the risky investment ( α ) Environ- Capital Regulation ment Competition Market - Share in the underwriting business ( β ) g ( β ) • Three Strategies under consideration: Strategy St t S l Solvency Hi h Ri k High Risk G Growth th Risk Reduction and Target Risk Reduction Risk Taking Risk Taking EC t < EC t > Trigger EC t < MCR t ·1.5 EC t < MCR t ·1.5 MCR t ·1.5 MCR t ·1.5 α and β d β α and β d β α and β d β β β Rule 0.05 ↓ 0.05 ↑ 0.05 ↓ 0.05 ↑
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 11 4. Performance Measurement Symbol Measure Interpretation Return E(G) Expected gain per annum Absolute return ROI Expected return on investment per annum p p Relative return Risk σ (G) Standard deviation of gain per annum Total risk RP Ruin probability p y Downside risk EPD Expected policyholder deficit Downside risk Perfor- SR σ Sharpe ratio Return/total risk mance mance SR RP Modified Sharpe ratio (RP) Return/downside risk SR SR EPD Modified Sharpe ratio (EPD) Modified Sharpe ratio (EPD) Return/downside risk Return/downside risk
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 12 5. Simulation Study: Model Specifications • Time horizon: T = 5 years, equity capital in t = 0: €15 million • Trigger for the management strategies: Solvency I MCR·1.5 gg g g y • Investments ( α ): High-risk N (0.1,0.2), low-risk N (0.05,0.05) • Underwriting business ( β ): Market volume €200 million - Log-normally distributed claims LN (0.85,0.085) - Underwriting cycle with three different states 0.3 0.5 0.2 (1.05, 1, 0.95) and the transition probabilities p 0.2 0.6 0.2 sj 0.1 0.5 0.4 - Consumer response: 0.95 if EC < MCR·1.5 • Tax rate: 25% Assets Liabilities Insurance Company Risk Management Management Environ- Capital Regulation ment Competition Market
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 13 5. Simulation Study: Results Strategy No Strategy Solvency High Risk Growth Return E(G) in million € 5.57 5.46 5.70 7.30 ROI in % 23.35 23.05 23.73 27.99 Risk σ (G) in million € 2.88 2.95 2.89 4.19 RP in % 0.22 0.06 0.63 0.20 EPD in million € 0.0045 0.0006 0.0225 0.0035 Perfor- SR σ 1.93 1.85 1.97 1.74 mance mance SR RP 12.42 48.75 4.50 18.52 SR EPD 6.18 43.48 1.26 10.49
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 14 5. Simulation Study: Robustness Checks / Sensitivity Analysis • Variation of the equity capital in t=0 (from €10 to €20 million) • Variation of the time horizon (from 1 to 10 years) ( y ) • Variation of starting values (application of different α and β in t=0) • Variation of the step length (for changes induced by the management, different step lengths for α and β are assumed) • Variation of consumer response function
Eling, Parnitzke, Schmeiser| Management Strategies and Dynamic Financial Analysis Page 15 5. Simulation Study: Variation of the equity capital in t=0 per annum No Strategy Solvency Limited Growth 8 7 xpected gain p 6 5 ex 4 10 11 12 13 14 15 16 17 18 19 20 equity capital in t = 0 4% No Strategy Solvency Limited Growth in probability 3% 2% rui 1% 0% 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 equity capital in t = 0
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