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

2. 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
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
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
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
The model is further detailed in the following slides by focusing on three main aspects:
Objective Function
Optimization Constrains
Glide Path Constraints 1 2 3

3. Protection break probability Risk adversion coefficient
Objective Function 1
Protection break probability
Success probability
Where:
Ft = Assett/Liability1t
FT = Assett/Liability1t
Pt = Assett/Liability2
K1Ft , K1Pt , K1FT = Objectives
Risk adversion coefficient
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

4. Optimization Constraints2
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

5. Glide Path Constraints3
Risk Constraints
Allocation Constraints
Objectives
Maximum Volatility
According to risk limit
Decreasing according to the maturity and Glide Path
Upper and Lower bounds for each investment
Bounds introduce limit to long/short positions
K1Ft
Funding Ratio objective (first target date)
K1Ft
Funding Ratio objective (second target date)
Minimum Volatility
Defined in order to preserve portfolio’s value proposition
Weights’ cap by group type
Allowing to define investment limits for markets, sectors and geographical area
K1Pt
Second objective linked to first target date
Risk Budgeting
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 K2
Level of protection for the Funding Ratio
Leverage limits
Both absolute and relative
Alpha
Coefficient of risk adversion
Duration
Allowing to set up lower ed upper bounds according to each asset class duration (or even at group level)

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

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

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

9. Liability-Driven Investments (LDI) model Take profit strategy
Equity
Optiomal
Allocation
Area
Government
Bonds
International
Bond
Weight
Corporate
Bonds
Money Market
Retirement
10y
TARGET
8,5%
Portfolio Value/Liability
1.2
Risk Adversion
α 1
Glide Path Volatility Limit
11,50%
Optiomal Allocation Area
Function Value

10. Liability-Driven Investments (LDI) model Glade path constrain
Equity
Government
Bonds
Optiomal
Allocation
Area
International
Bond
Weight
Corporate
Bonds
Money Market
Retirement 7y
TARGET
8,5%
Portfolio Value/Liability
0.9
Risk Adversion
α 1
Glide Path Volatility Limit
7,50%
Optiomal Allocation Area
Function Value

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

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

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

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

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