Hedging the Solvency II risk-free rate

7/29/2019 Hedging the Solvency II risk-free rate

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Hedging the risk-free rate under Solvency II

David Johnson & Ross Evans

September 2012

www.dalactuarialservices.com


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2

Say hello to our working party

Remit Why hedge the risk-free rate?

How you hedge rates exposure in Solvency II world

Focus on best estimate liabilities

Practical considerations

Working party members

The views expressed in this presentation are the collective views of the working party

They do not reflect the view of any individual member, nor their employer, nor the Actuarial Profession

Alex Probyn

Angelina Lai

David Johnson

Oliver Firth

Paul Collins

Ross Evans

Derek McLean

Eamonn Phelan

Emily Penn


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Why hedge?


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Why hedge the risk-free rate in the first place?

Strategicobjectives

StabilitySolvency

monitoring

Riskappetite

ERM

ORSA


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Long-term guarantees package


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Time is fast running out

Source: ABI Bulletin May 20126

Impact

assessmen

t for LTGpackage

Next political

trilogue on 18th

September

?

LTG

report

Publication in

the Officialjournal?

Adoption of Level

2 delegated acts

Plenary vote

on 20th

November


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Compromises agreed at the ECON vote in March

Matching

Premium

Extrapolation

Duration

Approach

CountercyclicalPremium

Symmetrical

AdjustmentMechanisms


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What is the Matching Premium?

minus

Spread on matching assets

Fundamental spread

Expected default &

downgrade risk

Floored at 75% of long-term

average spread

Prior regulatory approval

Conditions!


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Conditions for application of Matching Premium

(Matching Adjustment)

ASSETS Bond like

Fixed cash flows (or inflation linked)

Currency matched to liabilities

Investment grade only

Limits on BBB

Buy-and-hold

(Prevents active trading of portfolio)

Tight cash flow matching

No issuer optionality(Assets with prepayment risk unlikely to

qualify for Matching Premium)

LIABILITIES No future premiums

Only underwriting risks are:

Expense, Longevity & Revision risk

No surrender option where surrender value

could exceed value of underlying assets

OTHER

Assets and liabilities must be ring-fenced

without possibility of transfer

2 month window to restore compliance

Restricted to insurance activities in country

of authorisation


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What is the risk-free rate?


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0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

0 10 20 30 40 50

11

The risk-free interest rate curve under Solvency II

(21 March 2012)

Extrapolated curve

Market swap rates 10bps

Cut-off point formarket data (LLP)


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Extrapolation of the risk-free rate under Solvency II

Extrapolation beyond Last Liquid Point (LLP)

Sterling: 50yrs (50yrs, QIS5)

Euro: 20yrs (30yrs, QIS5)

Smith-Wilson technique

Macroeconomic approach

Ultimate long-term forward rate = 4.2%

Convergence period: 10yrs (Parliament)40yrs (Council & Commission)

60yrs (QIS5)

0.1


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What this looks like in practice

(21 March 2012)

0.0%

0.5%

1.0%

1.5%

2.0%2.5%

3.0%

3.5%

4.0%

4.5%

0 10 20 30 40 50

0.0%

0.5%

1.0%

1.5%

2.0%2.5%

3.0%

3.5%

4.0%

4.5%

0 10 20 30 40 50

0.0%

0.5%

1.0%

1.5%

2.0%2.5%

3.0%

3.5%

4.0%

4.5%

0 10 20 30 40 50

0.0%

0.5%

1.0%

1.5%

2.0%2.5%

3.0%

3.5%

4.0%

4.5%

0 10 20 30 40 50

Forward rates

Market swap ratesMarket swap rates 10bps


10bps credit risk adjustment

Extrapolated curve


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Hedging some practical examples


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Consider two simple cases

1. Case 1: Bullet 10yr liability cashflow

2. Case 2: Bullet 50yr liability cashflow

EUR 10m in each case

Delta hedging technique used to construct swaps hedge

21stMarch 2012


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Market consistent / Economic hedges

10yr bullet liability cashflow 50yr bullet liability cashflow

-4

-2

2

4

6

8

10

12

1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y

-4

-2

2

4

6

8

10

12

10Y 12Y 15Y 20Y 25Y 30Y 35Y 40Y 50Y

Hedge Notionalm Hedge Notionalm


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-4

-2

2

4

6

8

10

12

10Y 12Y 15Y 20Y 25Y 30Y 35Y 40Y 50Y

17

Remove the swaps needed to eliminate coupons


-4

-2

2

4

6

8

10

12

1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y



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-4

-2

2

4

6

8

10

12

1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y

Market Consistent Solvency II

-4

-2

2

4

6

8

10

12

10Y 12Y 15Y 20Y 25Y 30Y 35Y 40Y 50Y


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Economic hedge vs. Solvency II hedge

(after removing swaps needed to eliminate coupons)




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1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 5 10 15 20 25 30 35 40 45 50

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 5 10 15 20 25 30 35 40 45 50

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 5 10 15 20 25 30 35 40 45 50

19

Slope of the market swap curve prior to the LLP

50yr S-W discount rate UP

cut-off point

15yr Market rate DOWN

Solvency II

discount curve


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1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 5 10 15 20 25 30 35 40 45 50

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 5 10 15 20 25 30 35 40 45 50

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 5 10 15 20 25 30 35 40 45 50

20

(And the other way around)

50yr S-W discount rate DOWN

Solvency IIdiscount curve

cut-off point

20yr Market rate DOWN


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-4

-2

2

4

6

8

10

12

1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y


-4

-2

2

4

6

8

10

12

10Y 12Y 15Y 20Y 25Y 30Y 35Y 40Y 50Y


21

Economic hedge vs. Solvency II hedge




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Material drop-off in sensitivity to interest rates

PV01s Swap curve Solvency II

(20yr LLP, 10yr convergence)

Bullet liability 10yr 100% 101%





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Robustness of the hedge over time


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Hedge notionals Large degree of volatility over past 2 years

-8

-6

-4

-2

2

4

6

8

10

Dec-09

Feb-10

Apr-10

Jun

-10

Aug-10

Oct-10

Dec-10

Feb-11

Apr-11

Jun

-11

Aug-11

Oct-11

Dec-11

Feb-12

15Y swap notional 20Y swap notional

HedgeNotionalm

30 April 2010

29 Feb 2012


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0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

0 10 20 30 40 50

25

30 April 2010


Forward rates close to 4.2%

= 0.1

Market swap rates

Solvency II discount curve


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29 February 2012

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

0 10 20 30 40 50

Forward rates far away from 4.2%


= 0.4

Market swap rates

Solvency II discount curve


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Relationship between hedge notionals and Alpha

-8

-6

-4

-2

2

4

6

8

10

Dec-09

Feb-10

Apr-10

Jun

-10

Aug

-10

Oct-10

Dec-10

Feb-11

Apr-11

Jun

-11

Aug

-11

Oct-11

Dec-11

Feb-12

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

15Y swap notional 20Y swap notional Alpha

27

HedgeNotionalm

Alpha


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Relationship between hedge liability duration and Alpha

20

22

24

26

28

30

0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Alpha

Modifie

dDuration

28

M

odifiedDurationof

50yrliabilityunder

SII

Alpha


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Other (practical) considerations

30 ilt i ld 30 t


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30yr gilt yield vs. 30yr swap rate

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

5.5%

Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12

30yr GBP swap 30yr UK

G t b d N t d ti d t i b d ld


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Government bonds Not a duration product in a swaps-based world

-20%

-15%

-10%

-5%

0%

5%

10%

Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12

Net Assets

Oth ti l id ti


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Other practical considerations

How to construct an appropriate hedge portfolio

Conflicting metrics

Implementation

Active management of interest rate risk?

Central clearing (ESMA)

Individual circumstances

Interaction with interest rate risk sub-module

Potential for changes to the UFR

Next steps for the

working party


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Q&A

Hedging the Solvency II risk-free rate

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