Replicating Portfolio techniques in Life Insurance ALMMichele Gaffo, Head of Global ALM & Strategic Asset Allocation Team, ALLIANZ INVESTMENT MANAGEMENT Filippo F.G. Della Casa, Global ALM & Strategic Asset Allocation Team, ALLIANZ INVESTMENT MANAGEMENT
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Agenda
Framework description1
Case studies2
Replicating portfolios as a tool for portfolio optimization3
© Copyright Allianz Replicating Portfolio techniques in Life Insurance ALM
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Agenda
Framework description1
Case studies2
Replicating portfolios as a tool for portfolio optimization3
© Copyright Allianz Replicating Portfolio techniques in Life Insurance ALM
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Replicating Portfolio Techniques – Set Up
framework
Liability Cashflows
Book
Return
� Actual Assets
ProfitSharing
� Nature of Liabilities
� Investment Strategy
� Crediting Policy
� Economic Scenarios
Profit Sharing mechanism plays an important role
Life with-profit business: typical Policyholder payoff
� The chart shows the typical
payoff of a Life insurance with-
profit contract as a function of
the Book Return of Assets
Backing Liabilities. Target of
the replication is this payoff
� The diagram outlines variables
and mechanisms having an
impact on PH payoff. All of them
and their mutual interaction
must be taken into consideration
Book Return:deterministiccontribution
Book Return:stochasticcontribution
-3%
0%
3%
6%
0% 2% 4% 6%
Book Return
Pay
off
PolicyholderShareholder
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Assets – LiabilitiesEngine
Replicating Portfolio Techniques – Set Up
Actual Assets
Output ProcessingInput
Liabilities
Modeling Assumptions(e.g. Tgt Returns, ...)
Economic Scenarios
Liability Cashflows
MCEV, Sensitivities, …
Replicating PtfEngine
Replicating Assets (RA)
REPLICATING PTF:Vector of Optimal Holdings of RA that BEST replicates the behavior of Liabilities
framework
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Replicating Portfolio Techniques – ResultsActual Assets Portfolio Vs Replicating Portfolio – Macro Asset Classes
� Zero Coupon Bonds hedge the
minimum guarantee and the
deterministic contribution of the return
credited to PH
� Payer Swaptions allow for higher
returns with rising rates. They are the
consequence both of a negative A - L
duration gap and of PH Tgt Return
linked to the level of interest rates
� Equity and Property percentages in
RP reflect the starting asset allocation
and a participation to equity performance
lower than 100%
Assets RP
5.44.9Eff Duration
5.7%–Swaptions
1.0%1.0%Properties
6.3%6.7%Equities
87.0%92.3%Bonds
RP(R2 98.4%)
Assets
Bonds+Cash
Equities+Eq IF
Properties
ZCBs
Equities
Properties
Swaptions
Legend – Assets
Legend – RP
framework
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Statement
� The price of RP after a change in Market Risk Drivers is a valid proxy for ‘true’ MVL
Procedure
� Five ‘true’ MVLs have been computed using the A – L Engine over five different Scenarios.
RP has been repriced over the same Scenarios
Scenarios Outcomes
� Interest Rates
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� Xtreme Equity: a fall in Equity Market by
around -40% was assumed0.01%7.1537.152Xtreme Equity
0.19%6.5706.558Xtreme Up
0.10%8.1998.191Xtreme Down
-0.15%7.1937.204Up 50bps
0.11%7.6177.609Down 50Bps
–7.3977.397BE
%�MVRPMVLScenario
Replicating Portfolio Techniques – Robustness
framework
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Agenda
Framework description1
Case studies2
Replicating portfolios as a tool for portfolio optimization3
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Replicating Portfolios across products / countries &Replicating Portfolios over time
In the following, a comparison of RP
results is presented, both across
different product types and over
different time periods
� Explanations of differences across
products rely on different:
– asset allocations;
– nature of liabilities;
– modeling assumptions.
� Explanations of differences over
time rely on different market
environments
Preliminary remarks Results at a glance
Bonds+Cash Equities+Eq IF Properties
ZCBs Equities Properties Swaptions
Legend – Assets
Legend – RPs
Assets RP
Assets RP
Assets RP Assets RP
Assets RP2007Q
42009Q
1
product 1 product 2 product 3
RP
sover tim
e �� ��
RPs across products ����
Assets RP
case studies
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Replicating Portfolios across products / countriesExecutive Summary
Swaptions↓↓↓↓↔↔↔↔↑↑↑↑dynamic surrenders
Swaptions↓↓↓↓↔↔↔↔↑↑↑↑PH target return– modeling assumptions
ZCBs↔↔↔↔↓↓↓↓↑↑↑↑average MG– nature of liabilities
Swaptions↓↓↓↓↔↔↔↔↑↑↑↑duration gap– asset allocation + nature of liabilities
Equities↓↓↓↓↑↑↑↑↔↔↔↔equity backing ratio– asset allocation
most affected RP asset classproduct 3product 2product 1variablecategory
↓↓↓↓lowest↔↔↔↔in between↑↑↑↑highest
� In addition to listed variables, the distance of book return deterministic contribution from the
minimum guarantees (cfr. slide 4) must be considered for a complete understanding of results
�The chart shows a comparison of main variables determining RP outcomes across the different
products / countries examined
case studies
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RPs across products / countries – Results
5.0–Eff Duration
7.9%–Swaptions
9.7%12.5%Properties
15.5%22.0%Equities
66.9%65.5%Bonds
RP
(R2 95.5%)Assets
Assets RP
7.5–Eff Duration
13.6%–Swaptions
2.6%2.8%Properties
14.4%18.5%Equities
69.4%78.8%Bonds
RP
(R2 89.4%)Assets
Assets RP
product 1
Assets RP
5.44.9Eff Duration
5.7%–Swaptions
1.0%1.0%Properties
6.3%6.7%Equities
87.0%92.3%Bonds
RP
(R2 98.4%)Assets
product 2 product 3
Bonds+Cash Equities+Eq IF Properties
ZCBs Equities Properties Swaptions
Legend – Assets
Legend – RPs
2007Q4
case studies
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Assets RPAssets RPAssets RP
RPs across products / countries – Results
5.84.0Eff Duration
4.5%–Swaptions
5.1%11.4%Properties
6.4%12.2%Equities
84.1%76.4%Bonds
RP
(R2 98.1%)Assets
8.66.3Eff Duration
9.1%–Swaptions
1.9%2.3%Properties
6.7%9.2%Equities
82.3%88.5%Bonds
RP
(R2 96.3%)Assets
product 1
7.15.5Eff Duration
2.7%–Swaptions
0.5%1.1%Properties
1.8%3.3%Equities
95.0%95.6%Bonds
RP
(R2 99.2%)Assets
product 2 product 3
Bonds+Cash Equities+Eq IF Properties
ZCBs Equities Properties Swaptions
Legend – Assets
Legend – RPs
2009Q1
case studies
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Replicating Portfolios over timeExecutive Summary
3
3.5
4
4.5
5
5.5
Dec-07 Feb-08 Apr-08 May-08 Jul-08 Sep-08 Oct-08 Dec-08 Feb-09 Mar-098
10
12
14
16
18
20
22
24
7yrs EUR Swap Rate 7x10yrs ATM Swpt iVol
�ZCBs and vanilla Payer Swaptions are the interest-rate-sensitive assets used for replication
�Strong decrease in IR caused an increase of ZCB prices
�Despite the increase in implied volatilities, falling rates brought the price of a vanilla 7x10 Payer Swaption, strike 3%, from around 12.6 down to around 11.6
Market-driven changes
Changes induced by a change in Asset Allocation
�For all three portfolios considered, a reduction of Equity Backing Ratio has been put in place, which caused a decline in implied Policyholder Equity exposure
For the three Replicating Portfolios, there is an increase in ZCBs and a decrease in both Swaptions and Equities
case studies
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Assets RPAssets RP
RPs over time – Results
2007Q4 2009Q1
7.5–Eff Duration
13.6%–Swaptions
2.6%2.8%Properties
14.4%18.5%Equities
69.4%78.8%Bonds
RP(R2 89.4%)
Assets
8.66.3Eff Duration
9.1%–Swaptions
1.9%2.3%Properties
6.7%9.2%Equities
82.3%88.5%Bonds
RP(R2 96.3%)
Assets
product 1
Bonds+Cash
Equities+Eq IF
Properties
ZCBs
Equities
Properties
Swaptions
Legend – Assets
Legend – RPs
case studies
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Assets RP
5.0–Eff Duration
7.9%–Swaptions
9.7%12.5%Properties
15.5%22.0%Equities
66.9%65.5%Bonds
RP(R2 95.5%)
Assets
product 2
Assets RP
RPs over time – Results
Bonds+Cash
Equities+Eq IF
Properties
ZCBs
Equities
Properties
Swaptions
Legend – Assets
Legend – RPs
5.84.0Eff Duration
4.5%–Swaptions
5.1%11.4%Properties
6.4%12.2%Equities
84.1%76.4%Bonds
RP(R2 98.1%)
Assets
2007Q4 2009Q1
case studies
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Assets RPAssets RP
5.44.9Eff Duration
5.7%–Swaptions
1.0%1.0%Properties
6.3%6.7%Equities
87.0%92.3%Bonds
RP(R2 98.4%)
Assets
7.15.5Eff Duration
2.7%–Swaptions
0.5%1.1%Properties
1.8%3.3%Equities
95.0%95.6%Bonds
RP(R2 99.2%)
Assets
product 3
RPs over time – Results
Bonds+Cash
Equities+Eq IF
Properties
ZCBs
Equities
Properties
Swaptions
Legend – Assets
Legend – RPs
2007Q4 2009Q1
case studies
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Agenda
Framework description1
Case studies2
Replicating portfolios as a tool for portfolio optimization3
© Copyright Allianz Replicating Portfolio techniques in Life Insurance ALM
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In the following we show how RP technique can be used to compare different
Investment Strategies, given expectations on future states of the world. Some
assumptions must be made:
� Market Risk Drivers: risk drivers to deal with
� Economic Scenarios: possible future scenarios = future outcomes of chosen Risk
Drivers must be assumed
� AAs: the different Investment Strategies to be compared. They should be
determined according to the Market Risk Drivers chosen. For each of them, a
corresponding RP must be derived
� For each given scenario, a repricing of A - RP portfolio is performed and used as a
proxy for Economic Surplus
Framework
portfolio optimization
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equity performance parallel shift
�(A
–R
P)/(
A-R
P)
Cross exposure to parallel shift & equity performanceActual Portfolio
� Typical non linear behaviour of A - RP as a function of the level of the yield curve
� The linear behaviour of A - RP as a function of the equity performance is due to the deterministic part of book return being far above minimum guarantees. It also causes put options on equity indexes to give no material contribution to RP R2
portfolio optimization
© Copyright Allianz Replicating Portfolio techniques in Life Insurance ALM
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Interest Rate Risk vs Equity Risk
Interest Rate Risk or Equity Risk?
Remarks
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Actual Portfolio
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� Top left chart shows changes in Interest Rate Sensitivity changing the duration of the Assets ptf� Top right chart shows Equity sensitivity for different Equity Backing Ratios� Let’s assume we believe in an upshift of Interest Rates and in a positive Equity Performance:
How can we select the ‘optimal’ pair (Duration, Equity Backing Ratio)?
portfolio optimization
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Scenario 2: IR up 30 bps & Eq perf +8%Scenario 1: IR up 30 bps & Eq perf +4%
Comments
Duration +2 Equity +6%
Duration +1.5 Equity +6%
Duration +2.5 Equity +9%
Duration +2 Equity +9%
Duration +1.5 Equity +9%
Actual Ptf
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� Top left chart shows that on Scenario 1 Actual Portfolio lies on the ‘efficient frontier’
� If the expectation is Scenario 2, Actual Portfolio is suboptimal: a more efficient choice is decreasing IR Risk by increasing Duration and taking higher Equity risk increasing Equity Backing Ratio
Investment Strategies in the Risk / Return space: towards an ‘efficient frontier’ approach
portfolio optimization
Thank you for your attention