Liability Driven Investment and Tail Risk Management in

Liability Driven Investment and Tail Risk Management in Insurance Products November 2018

Liability-Driven Investments (LDI) model Executive Summary • Liability-Driven Investments (LDI) as well as Asset and Liability Management refer to those situations in which investors must manage together their assets and their liabilities. Since it is unlikely that an investor has no liabilities at all, most real-world investment situations can be categorized as Liability-Driven Investment • Unlike Asset Allocation, which offers quite a well-established framework, LDI and ALM cannot refer to any well-identified theoretical body • As such, most financial institutions are forced to make their own way through the interactions between asset allocation and liability hedging within an ever-changing accounting and prudential environment • • Eurizon has been set up an intertemporal model for the asset allocation based on an LDI perspective • For the estimation of the traditional inputs that govern an allocation – expected returns and volatilities –Black&Litterman model (Expected Returns or the reverse engineering) and the Variance/Covariance Matrix have been respectively used • Based on these arguments, we design an objective function that returns the vector of weights maximizing the probability that, at a given maturity, the value of the assets is above the liability’s level • • The function depends also on past performances and on time to maturity • The model is further detailed in the following slides by focusing on three main aspects: Starting from the dynamics followed by assets and liabilities, and thinking in relative terms (asset over liability and not assets per se) we derived the dynamics of the funding ratio In order to regulate the optimization we add several constraints: no short selling, risk budgeting, an ex-ante variable (life Cycle) volatility constraint and ex-ante stop loss mechanism o 1 Objective Function o 2 Optimization Constrains o 3 Glide Path Constraints

1 Objective Function Protection break Success probability Where: Ft = Assett/Liability 1 t Risk adversion coefficient FT = Assett/Liability 1 t Pt = Assett/Liability 2 K 1 Ft , K 1 Pt , K 1 FT = Objectives A multi-objective function considering as optimal allocation the one that maximizes the probability of reaching several objectives within a predefined time horizon minus the probability of negative perfomances

2 Optimization Constraints Maximization is subject to a certain number of constraints • • For TEV we mean Tracking Error Volatility and is computed against the Liability: The third constraint impose a maximum percentage of risk contribution for each asset

3 Glide Path Constraints Risk Constraints Maximum Volatility Minimum Volatility Risk Budgeting • • • According to risk limit Decreasing according to the maturity and Glide Path Defined in order to preserve portfolio’s value proposition • These limits are set up for controlling risk budget allocation • They can be absolute or relative • They can be related to single stock, asset class or groups Allocation Constraints Upper and Lower bounds for each investment • • Weights’ cap by group type Leverage limits Duration Bounds introduce limit to long/short positions Objectives K 1 Ft Allowing to define investment limits for markets, sectors and geographical area • Both absolute and relative • Allowing to set up lower ed upper bounds according to each asset class duration (or even at group level) K 1 Pt K 2 Alpha • Funding Ratio objective (first target date) • Funding Ratio objective (second target date) • Second objective linked to first target date • Level of protection for the Funding Ratio • Coefficient of risk adversion

Eurizon uses LDI / Life Cycle Model to manage different products LDI Traditional application PENSION FUNDS Asset: contributions Liability: pensions INSURANCE Comp. Asset: premium Liability: refunds Extendable to MUTUAL FUNDS Asset: products Liability: benchmark/ financial variable

The dataset is quite wide Equity Assets Corp. Bond Gov. Bond Linkers Possible Liabilities Risk Free CSI 300 Index MSCI Europe • • • ML Global High Yield • CSI Aggregate Bond index • • • JPM United States • • • JPM EMU • • • JPM Linkers Europe • • • SHIBOR 1 M (CNH) • • • Annual Return 8, 5% • • • MSCI Emerging Markets MSCI North America MSCI Pacific ex Japan MSCI Japan ML Global Broad Market Corporate ML Emerging Markets Corporate Plus JPM United Kingdom JPM Japan JPM Emerging Markets CSI Aggregate Bond index JPM Linkers United States JPM Linkers UK Euribor 1 M USD Libor Consumer Price Index + Spread EURO STOXX 50% + W Aggregate Bond Index Yield 50%

Liability-Driven Investments (LDI) model Starting simulation Weight Equity Optiomal Allocation Area Government Bonds Money Market Corporate Bonds Function Value Optiomal Allocation Area International Bond Retirement TARGET Portfolio Value/Liability Risk Adversion Glide Path Volatility Limit 10 y 8, 5% 1 α 1 11, 50%

Liability-Driven Investments (LDI) model Take profit strategy Weight Equity Optiomal Allocation Area Government Bonds Money Market Function Value Optiomal Allocation Area International Bond Corporate Bonds Retirement TARGET Portfolio Value/Liability Risk Adversion Glide Path Volatility Limit 10 y 8, 5% 1. 2 α 1 11, 50%

Liability-Driven Investments (LDI) model Glade path constrain Weight Equity Government Bonds Function Value Money Market Optiomal Allocation Area International Bond Corporate Bonds Optiomal Allocation Area Retirement TARGET Portfolio Value/Liability Risk Adversion Glide Path Volatility Limit 7 y 8, 5% 0. 9 α 1 7, 50%

Focus on our risk mitigation techniques Risky Asset • • Tactical Asset Allocation models Factor investing: o Multifactor Equity Picking (Q -Value) o Smart Momentum o Reverse Strategies (Strategia Flessibile) o Risk Parity – Min Vol o Smart Max-Dividend Risk Control techniques • • • Dynamic Portfolio Insurance Option based portfolio insurance Risk On-Off Models (RISKOO) Switcher Risk parity techniques “Protected” based funds/Unit: • • Flexible target vol models Fund selection Multi Asset quantitative asset allocation models • • EL Base 24 – Base più bonus EL Prospettiva Protetta 2010 Exclusive Protetto Investment Solutions by Epsilon Soluzione Attiva Protetta Epsilon Difesa Attiva Eurizon Difesa 100 More than 10 bln of asset and more than 15 years of experience

EIS ASYMMETRIC STRATEGY: track record Euro Stoxx 50 min MAX Average 25 perc 50 perc 75 perc range MAX DD Vola daily 1 yr -2, 41% 3, 99% 0, 01% -0, 39% 0, 00% 0, 41% 6, 40% 2, 18% 11, 07% Eurozone Asymmetric Strategy -1, 44% 2, 14% 0, 00% -0, 21% 0, 00% 0, 20% 3, 58% 1, 24% 6, 31%

Solvency Capital Requirement (standard approach) Capital Requirements 21, 6% vs 37%

EIS TACTICAL GLOBAL RISK CONTROL Euro Stoxx 50 min MAX Average 25 perc 50 perc 75 perc range MAX DD Vola daily 1 yr -2, 41% 3, 99% 0, 01% -0, 39% 0, 00% 0, 41% 6, 40% 2, 18% 11, 07% Tactical Global Risk Control -1, 83% 1, 26% 0, 01% -0, 12% 0, 01% 0, 18% 3, 08% 0, 63% 4, 88%

Solvency Capital Requirement (standard approach) Capital Requirements 9, 6% vs 37%