ILS Investments and Portfolio Diversification

Imperial College - Workshop on Insurance-linked Securities London, October 31, 2008 ILS Investments and Portfolio Diversification 1 Characteristics of ILS as an independent asset class / ILS as a diversifier in a general investment portfolio 2 Intra-asset class diversification and ILS portfolio optimisation Dr. Karsten Bromann, Solidum Partners AG

1) Characteristics of ILS as an independent asset class / ILS as a diversifier in a general investment portfolio Slide 2 Karsten Bromann, Imperial College, London, October 31, 2008

Definition of event linked securities Event linked securities are contracts for which the return of notional value or payment of interest is contingent on the non-occurrence of a well-defined, insurance-related trigger event. Examples: Catastrophe bonds Industry loss warranties Side cars Derivatives on catastrophe indices Derivatives on (re-)insurance contracts Exchange traded catastrophe contracts Slide 3 Karsten Bromann, Imperial College, London, October 31, 2008

Catastrophe Bonds Counterparty credit risk minimised Yield curve risk minimised Insured Risk premium Insurance payment Special Purpose Vehicle LIBOR + Risk premium Investment (at maturity) Investor Investment (case of insurance event) LIBOR Collateral Trust Investment (at maturity) LIBOR & shortfall on investment Investment returns Swap Counterparty Slide 4 Karsten Bromann, Imperial College, London, October 31, 2008

Attractive compensation Strong historic performance in comparison with other asset classes 1.1.2000 to 24.10.2008 Cat bond vs. equity performance Cat bond vs. government bond performance 250.0 250.0 200.0 200.0 Index Performance 150.0 100.0 Index Performance 150.0 100.0 50.0 50.0 0.0 0.0 Sep 09 Mar 09 Sep 08 Mar 08 Sep 07 Mar 07 Sep 06 Mar 06 Sep 05 Mar 05 Sep 04 Mar 04 Sep 03 Mar 03 Sep 02 Mar 02 Sep 01 Mar 01 Sep 00 Mar 00 Sep 99 Mar 99 Sep 09 Mar 09 Sep 08 Mar 08 Sep 07 Mar 07 Sep 06 Mar 06 Sep 05 Mar 05 Sep 04 Mar 04 Sep 03 Mar 03 Sep 02 Mar 02 Sep 01 Mar 01 Sep 00 Mar 00 Sep 99 Mar 99 Cat Bond Universe S&P 500 NASDAQ DJ EuroStoxx 50 Cat Bond Universe JPM US Gov Bond Cat bond universe: 1.1.2000 to 31.12.2001 Solidum index based on price information from Aon Capital Markets, 2002 onward Swiss Re Cat Bond Performance Index Sources: Solidum Partners, AON Capital Markets, Bloomberg Slide 5 Karsten Bromann, Imperial College, London, October 31, 2008

Attractive compensation Strong historic performance in comparison with other asset classes Corporates: 1.10.02 to 24.10.08; Hedge funds: 1.1.00 to 31.9.08 Cat bond vs. corporate bond performance Cat bond vs. hedge fund performance 250.0 250.0 200.0 200.0 Index Performance 150.0 100.0 Index Performance 150.0 100.0 50.0 50.0 0.0 0.0 Mar 09 Sep 08 Mar 08 Sep 07 Mar 07 Sep 06 Mar 06 Sep 05 Mar 05 Sep 04 Mar 04 Sep 03 Mar 03 Sep 02 Mar 02 Sep 01 Mar 01 Sep 00 Mar 00 Sep 99 Mar 99 Mar 09 Sep 08 Mar 08 Sep 07 Mar 07 Sep 06 Mar 06 Sep 05 Mar 05 Sep 04 Mar 04 Sep 03 Mar 03 Sep 02 Mar 02 Cat Bond Universe FINRA US Corp High Yield FINRA US Corp Investment Grade Cat Bond Universe HFRI FOF Tremont HF Cat bond universe: 1.1.2000 to 31.12.2001 Solidum index based on price information from Aon Capital Markets, 2002 onward Swiss Re Cat Bond Performance Index Sources: Solidum Partners, AON Capital Markets, Bloomberg Slide 6 Karsten Bromann, Imperial College, London, October 31, 2008

Attractive compensation After a phase of moderate weakening, the reinsurance markets are expected to harden again Benfield, The 4 Seasons, Issue 1: Autumn 2008 Slide 7 Karsten Bromann, Imperial College, London, October 31, 2008

Independence Low correlation with other markets Though indication of only low tail dependence to other markets, cat bond segment of ILS is influenced by autumn 2008 events 01-2000 to 09-2008 Cat Bond Universe Cat Bond Universe S&P 500 NASDAQ Composite DJ EuroStoxx 50 Index JPM US Gov. Bond Index FINRA US Corp. Inv. Grade FINRA US Corp. High Yield HFRI FOF Index Tremont HF Index 1.000 0.162 0.139 0.109 0.138 0.398 0.341 0.277 0.267 S&P 500 1.000 0.807 0.841-0.367 0.270 0.702 0.499 0.426 NASDAQ Composite DJ EuroStoxx 50 Index JPM US Gov. Bond Index FINRA US Corp. Investment Grade FINRA US Corp. High Yield 1.000 0.695-0.308 0.186 0.623 0.604 0.577 1.000-0.452 0.091 0.531 0.499 0.414 1.000 0.574-0.120-0.113-0.061 1.000 0.631 0.397 0.472 1.000 0.539 0.574 HFRI FOF Index 1.000 0.950 Tremont HF Index 1.000 Slide 8 Karsten Bromann, Imperial College, London, October 31, 2008

Tail dependence - a closer look (1/2) λ = Lim x->0 P[ r a (t) <= VaR x (r a ) r c (t) <= VaR x (r c )] r a r c λ Asset class a returns CatBond returns Lambda, coefficient indicating tail dependence Tail dependence between equity indices 1 Indication of only low tail dependence between historic ILS and equity return data 1 Lamda - S&P 500 Lamda - CatBond Universe 0 0 PercentRank of monthly DJ EuroStoxx 50 returns 1 0 0 PercentRank of monthly DJ EuroStoxx 50 returns 1 Slide 9 Karsten Bromann, Imperial College, London, October 31, 2008

Tail dependence - a closer look (2/2) Tail dependence between cat bond universe and FINRA US Corp. Inv. Grade JPM US Gov. Bond Index Tremont HF Index Caution: statistics about tail characteristics or extreme value theory converge slowly! However: all indications point towards only low tail dependence between historic returns of cat bonds and other asset classes Slide 10 Karsten Bromann, Imperial College, London, October 31, 2008

Diversifier in general investment portfolio Back-Testing with historic return data (January 1994 to December 2007) 12% Return 10% 8% 6% 4% 2% 4) 1) 2) 3) 0% 0% 2% 4% 6% 8% 10% 12% 14% 16% Standard deviation Bonds + Equity Bonds + Equity + 20% Hedge Funds Bonds + Equity + 20% HF + 20% Cat Bonds 1) 100% Bonds (JPMorgan US Gov. Bond Index) 2) 100% Equity (S&P 500) 3) 20% HF (Tremont Hedge Fund Index); 32% bonds; 48% equities 4) 20% Cat Bonds; 20% HF; 24% equities; 36% bonds Slide 11 Karsten Bromann, Imperial College, London, October 31, 2008

2) Intra-asset class diversification and ILS portfolio optimisation Slide 12 Karsten Bromann, Imperial College, London, October 31, 2008

Cat Bond only or alternative instruments? Diversification benefit and return enhancement through incorporation of alternative ILS instruments 25% Nominal and expected annual return 20% 15% 10% 5% 0% 0% 5% 10% 15% 20% 25% 30% Stdev of Return Diversified ELS Fund, nominal Diversified ELS Fund, expected Cat bond market portfolio, nominal Cat bond market portfolio, expected AA-rated, nominal AA-rated, expected A-rated, nominal A-rated, expected BBB-rated, nominal BBB-rated, expected BB-rated, nominal BB-rated, expected B-rated, nominal B-rated, expected Efficient frontier (cat bonds, expected) Slide 13 Karsten Bromann, Imperial College, London, October 31, 2008

Selection of individual investments Actuarial analysis of individual transactions - Cat Bonds: Re-evaluation and verification of critical parameters - Derivates: ground-up analysis - Application of proprietary pricing tools and licensed 3rd party risk assessment systems - Rating: only of secondary importance to specialised investors (though important for future market growth through entry of general money managers) Portfolio view - Clearly defined exposure limits by type of risk and geographic region - Modelling of whole portfolio including dependency structures between portfolio components - Optimisation of prospective performance key figures by marginal benefit analysis Slide 14 Karsten Bromann, Imperial College, London, October 31, 2008

Analysis of individual securities Critical re-evaluation of key risk figures - Bond 1: attachment = 2.71% expected loss = 2.09% - Bond 2: attachment = 1.38% expected loss = 1.20% 120% % of attachment index value 100% 80% 60% 40% 20% Bond 1 Bond 2 0% Daria Capella Lothar 87J Jeanette Martin Slide 15 Karsten Bromann, Imperial College, London, October 31, 2008

Exposure management Aggregation of all outstanding exposures by type of risk and geographic region Representation as function of a single transparent basis variable 40% 35% Impact contribution on NAV 30% 25% 20% 15% 10% 5% 0% 0 10 20 30 40 50 60 70 80 90 100 Industry loss [USD Bn] Slide 16 Karsten Bromann, Imperial College, London, October 31, 2008

Probabilistic ground up modelling of portfolio Risk-return characteristic of portfolio based on actuarial models - presented as VaR Basis for portfolio optimisation Portfolio Risk/Return Plot (12 month) 100% Cumulative Probability expected portfolio return distribution 90% 80% 70% 60% 50% 40% 30% 20% 10% -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% Portfolio Return (1 Year) 0% Slide 17 Karsten Bromann, Imperial College, London, October 31, 2008

Marginal benefit approach Modification of each position s weight in the portfolio Analysis of effect on portfolio performance figures 12.1% Return (e.g. Expected 12m Return) 12.0% 11.9% 11.8% 11.7% 11.6% 11.5% 11.4% 11.3% 11.2% Existing Portfolio Bond 1 Bond 2 Bond 3 Programme 4 11.1% 5.1% 5.2% 5.3% 5.4% 5.5% 5.6% 5.7% 5.8% 5.9% Risk (e.g. Standard Deviation of Return) Slide 18 Karsten Bromann, Imperial College, London, October 31, 2008

Omega optimisation Portfolio optimisation by omega maximisation at target return Ω ( target return) = + [ 1- F(r) ] target return target return - F(r)dr dr Price of Price of call at strike' target return' put at strike' target return' Ln (Omega) Portfolio omega after increase of position weight (+10% of NAV) -20% -15% -10% -5% 0% 5% 10% 15% Target return (threshold) 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 - Existing Portfolio Bond 1 Bond 2 Bond 3 Programme 4 Δ (Ln (Ω)) / Δ (x_i) Change of portfolio omega with position increase (1% NAV) 0.6 0.4 0.2 - -20% -15% -10% -5% 0% 5% 10% 15% -0.2-0.4 Bond 1 Bond 2-0.6 Bond 3 Programme 4-0.8 Target return (threshold) Slide 19 Karsten Bromann, Imperial College, London, October 31, 2008

Summary Insurance-linked securities offer an attractive risk-adjusted return potential Insurance-linked securities behave diversifying in an investment portfolio A cat bond-only approach is good, using the full ILS universe is better A deep understanding of the asset class is helpful for avoiding pitfalls, creating relative value, and efficiently managing a portfolio Dr. Karsten Bromann +41 43 521 2182 karsten.bromann@solidumpartners.ch www.solidumpartners.ch Slide 20 Karsten Bromann, Imperial College, London, October 31, 2008