Replicating Portfolio techniques in Life Insurance · PDF fileReplicating Portfolio techniques...

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

© Copyright Allianz Replicating Portfolio techniques in Life Insurance ALM

2

Agenda

Framework description1

Case studies2

Replicating portfolios as a tool for portfolio optimization3


3

Agenda


Case studies2



4

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


5

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


6

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


7

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

��

��

��

��

��

��

��

�

�

��

� ��

�

��

��

��

��

� 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


8

Agenda


Case studies2



9

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


10

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


11

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



Legend – Assets

Legend – RPs

2007Q4

case studies


12

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



Legend – Assets

Legend – RPs

2009Q1

case studies


13

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


14

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


15

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


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


16

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


Bonds+Cash

Equities+Eq IF

Properties

ZCBs

Equities

Properties

Swaptions

Legend – Assets

Legend – RPs

2007Q4 2009Q1

case studies


17

Agenda


Case studies2



18

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


19

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



20

��

��

��

��

��

��

��

��

��

!"��#$�%�&

��'��

��'��

��'�

��'��

��'��

Interest Rate Risk vs Equity Risk

Interest Rate Risk or Equity Risk?

Remarks

��

��

��

��

��

��

��

��

��

��

��

��

��#�� (�

��#��

��#�� (�

!"��#$�%�&

��#��'�(�

��#��'�

��#��'�(�

��#��'�

��#��'�(�

��#��'�

Actual Portfolio

��

��

��

��

��

��

��

��

�

�

��

��

� � ��

��

� 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)?



21

�(��

�(��

�(��

�(��

�(��

�(��

�(��

�(��

�(��

��

��

��

��

��

��

��

��

��

��

��

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 Equity +9%


Actual Ptf

��

��

��

��

��

��

��

��

��

� 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


Thank you for your attention

Replicating Portfolio techniques in Life Insurance · PDF fileReplicating Portfolio techniques...

Documents

Transcript of Replicating Portfolio techniques in Life Insurance · PDF fileReplicating Portfolio techniques...