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From Economic capital to ERM CFA UK 17 April 2013 Servaas Houben Elliot Varnell 1

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From Economic capital to ERMCFA UK17 April 2013

Servaas HoubenElliot Varnell

1

Disclaimer

The views and opinions expressed in this presentation are those of the author and do not reflect the official policy or position of Prudential. Examples of analysis performed within this presentation are only examples. They should not be utilized in real-world situations as they are based only on very limited and dated open source information

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CFA UK 17 April 2013

Capital requirement under SII

3

CFA UK 17 April 2013

VaR limitations - subaddivity

4

CFA UK 17 April 2013

Risk 1Probability Loss

0.03 1 mln

0.97 0

95% VaR 0

Risk 2Probability Loss

0.03 1 mln

0.97 0

95% VaR 0

Risk 1 and 2

Probability Loss

One event 0.0582 1 mln

Two events 0.0009 2 mln

95% VaR 1 mln

QuizData:• Monthly capital return index S&P 500 returns from Dec

1927-Feb 2011• Dec 1927 index value 17.66, Feb 2011 1,327.22• Total number of 998 monthly returns

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CFA UK 17 April 2013

Question:When excluding 10 highest monthly returns (setting them to 0%) what would be the index value as at Feb 2011?

Answers

<250

250-500

500-750

750-1000

>1000

Results• Set highest 10 values to 0: 172.80 (-87%)• Set lowest 10 values to 0: 15,330.78 (+1.050%)

0

200

400

600

800

1,000

1,200

1,400

1,600

1927

1934

1941

1948

1955

1962

1969

1976

1983

1990

1997

2004

All inclusive

Top 10 excluded

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1927

1935

1943

1951

1959

1967

1975

1983

1991

1999

2007

All inclusive

Bottom 10 excluded

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CFA UK 17 April 2013

“Risk mitigation” through dividends

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-

1.000

2.000

3.000

4.000

5.000

6.000

Valu

e to

tal r

etur

n

Date

S&P500 Total return

total return index

without top 10

CFA UK 17 April 2013

Nominal yield curves

Risk Management Hedging uses assets quoted on OISPricing (Guarantees) Funding for hedging based on OISProvisioning Solvency II based on LIBOR & UFR

– One-off surplus (based on current market environment)– Hedging efficiency and provisioning risk due to LIBOR-OIS basis

EUR 24 August 2012

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

1 11 21 31Term (Years)

EUR / 24 August 2012 / Spot / Annual

Market LIBORMarket OISSolvency II Risk Free

Source: Bloomberg

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CFA UK 17 April 2013

?

The importance of discounting - 1• ILLUSTRATIVE EXAMPLE• 1 German and 1 Greek insurance company• Both selling an annuity product▫ 65 year old male▫ Life annuity of 1000 paid end of the year▫ Dutch mortality table 2010-2060▫ No other (life) risks▫ New business ensures liability mix is stable over time

• Balance sheet as per 30 June 2008▫ German insurance company invests in German government

bonds▫ Greek insurance company invests in Greek government bonds▫ Both companies have surplus of 120% as at 30-6-2008▫ Liability discounting on SII curves

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CFA UK 17 April 2013

The importance of discounting - 2

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CFA UK 17 April 2013

0%

20%

40%

60%

80%

100%

120%

140%

Solv

ency

ratio

Date

Solvency

German

Greek

The importance of discounting - 3

11

114%115%116%117%118%119%120%121%122%123%

Solv

ency

ratio

Date

Effect different yield curves

SII curve 30

SII curve 20

SONIA

CFA UK 17 April 2013

Liquidity premium adjustments

12

050

100150200250300350400450500

LQP

in b

asis

poi

nts

Date

LQP development over time

USD

GBP

EUR

CFA UK 17 April 2013

Source: Itraxx

(100)

(50)

-

50

100

150

200

250

300

350

400

MP

in b

p

Date

MP development

UK

US

EUR

Putting the picture together

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0%1%2%3%4%5%6%7%8%9%

Yiel

d

Date

Solvency II discount curves

SII discountcurve

credit spreads

LQP discountcurve

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

12.000

14.000

16.000

18.000

20.000

22.000

24.000

26.000

28.000

Valu

e as

sets

and

liab

ilitie

s

Date

Effects of LQP

Corp bonds

TB no LQP

TB LQP

SII discount

corp bond

70%

75%

80%

85%

90%

95%

100%

105%

110%

115%

120%

Solv

ency

ratio

Date

Effects of LQP

no LQP

LQP

CFA UK 17 April 2013

Insurance Balance Sheet RiskDivergent discount rates between markets and regulations.

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CFA UK 17 April 2013

LIBOR-OIS SpreadAnalysis of daily data points

Term 1-year 20-year 30-year0.5% percentile 44 bps 27 bps 17 bps

Median 66 bps 32 bps 26 bps

99.5% percentile 105 bps 39 bps 33 bps

EUR from 2 Jan 2012

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1 11 21 31Term (Years)

Source: Bloomberg / MillimanCFA UK 17 April 2013

Solvency II-OIS SpreadAnalysis of daily data points

Term 1-year 20-year 30-year

0.5% percentile 34 bps 17 bps 61 bps

Median 56 bps 22 bps 72 bps

99.5% percentile 95 bps 29 bps 93 bps

EUR from 2 Jan 2012

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

1 11 21 31Term (Years)

Source: Bloomberg / MillimanCFA UK 17 April 2013

SII-OIS Basis Value Difference of ZCBAnalysis of daily data points

20-year 30-year

0.5% percentile 3.48% 18.38%

Median 4.46% 21.58%

99.5% percentile 5.73% 27.80%

EUR from 2 Jan 2012

Difference in Value ≈ Spread x Term of Zero Coupon Bond

0%

10%

20%

30%

40%

50%

60%

1 11 21 31Term (Years) Source:

Bloomberg / Milliman

CFA UK 17 April 2013

Issues For Risk ManagementSolvency II • Significant difference between market and Solvency II for discounting long-term fixed

cash-flows• Currently Surplus.

– But… this depends on UFR relative to prevailing market conditions

• SCR Capital Charge for this basis and risk of reversal?

Risk Management• Added complexity and potential inefficiency in current hedge strategies.• Are there solutions?

– LIBOR-vs-OIS basis hedge-able via swap• Active markets currently for EUR (liquid to c20 years) plus GBP and USD

• Full Solvency II – OIS more challenging

CFA UK 17 April 2013

Insurance Balance Sheet RiskAnti-cyclical Regulation Proposals

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CFA UK 17 April 2013

Economic Capital (Insurance)

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We illustrate with a simplified balance sheet

of an insurer – so we are all on the same

page.

The asset side of the balance sheet contains mostly financial

assets.

Direct loans are possible and increasingly sought by some

firms.

Liabilities are mainly to policyholders – senior

liabilities being those at least equal in rank to

policyholders

“Economic Capital” is calculated using stresses to

assets and liabilities risk factors – and allowing for

diversification.

Own Funds in excess of the capital are what insurers need to control. But that

requires a large amount of computing power…

Historical Capital Analysis Daily Movements In Excess Capital – MA Added

Volatility in excess capital reduced by c70%

Including mitigation of SCR credit stresses reduces SCR by c15% providing a further boost to excess capital

Economic Capital to ERM

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CFA UK 17 April 2013

Poor Risk Appetite

Why Do Insurers Fail?What should we be focussed on?

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Source: FSA 2003

Operational Risk

This FSA paper from 2003

concluded that insurance failures were the cause of a

interconnected series of events.

CFA UK 17 April 2013

Governance

Valuations

Risk Events (Not Just Quantitative Risk)

Poor Decisions

(Wrong Product @

Wrong Price)

Fixing Economic Capital with ERMCapturing why insurers fail in our risk assessment

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Poor Risk Appetite

Operational Risk

Governance

Valuations

Risk Events (Not Just Quantitative Risk)

Poor Decisions (Wrong Product @ Wrong Price)

Include the full set of risk events – not just those where there is data.

Consider the governance structure, reporting lines, incentives as much as the

capital.

Develop operational models that capture operational uncertainty – i.e. that can show operational risk events not in the event set.

Project the economic balance sheet forward so it capture the business plan of the insurers

– as well as the business sold to date.

Capture the true economic valuation of (adverse) financial outcomes – fair value.

See next section…

Sample ERM System

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Risk Appetite

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CFA UK 17 April 2013

Risk Appetite DesignQuantitative Criteria Examples

Avoid regulatory intervention due to a capital requirements breach.

(typically any regulatory intervention is considered undesirable)

Maintain capital at least high enough to maintain a AA rating

with 9 years out of 10.

(though of course rating is not just a function on capital)

Deliver an (economic) profit 7 years out of 10.

Ensure that economic profit and loss volatility is within a range of

+/10%

(In practice P&L measures may well differ in how “economic” they are – IFRS

Earnings, EEV Earnings are often referred to.)

Some statements can be mapped to the probability of future capital-at-risk (own funds).

These statements may well impose some tough constraints on the

distribution of Capital at Risk. There may need to be push-back from

finance / risk on what is achievable.

CFA UK 17 April 2013

Risk Appetite DesignQualitative Criteria Suggested by FSA

Risk Appetite DesignTypical Statements

Always have enough cash to meet financial obligations.

Maintain sufficientcapital to achieve at least a AA rating (19

in 20 years).

Zero tolerance forany kind of

reputational risk.

Ensure earnings volatility is in line with shareholder

expectations.

Risk Appetite ResearchTowards a solution from the Actuarial Profession

CFA UK 17 April 2013

Risk Appetite ResearchThe Risk Appetite Problem

Need to find a link between the operational indicators (including the non-quantitative ones for things like process, people and reputation)

and…

… the probability of the desires expressed in risk appetite statement being true or within the stated probability.

They identified that the mapping was complex and therefore turned to some on the tools of complexity science for a solution. Tools used were concept mapping and Bayesian Networks.

CFA UK 17 April 2013

Risk Appetite ResearchStage 1 – Cognitive Mapping

Key Nodes

Gaps

Source: Milliman

• Experts are able to map the way the business works and how risks in their area of the business emerges and is propagated.

• Complex maps are created but can be distilled down to a manageable size extracting the important nodes.

• Gaps in the “story” can be identified and explored in more depth.

CFA UK 17 April 2013

Risk Appetite ResearchStage 2 – Convert Concept Map to Bayesian Network

Implemented in AgenaRisk

After simplifying the concept map (using some well established mathematical techniques) … linking the risk appetite statements to the measurable indicators … the simplified concept map is converted to a

Bayesian Network.

The Bayesian Network is parameterised through conditional probabilities which have proven cognitively straightforward for stakeholders (including boards!) to relate to – aiding estimation and validation of the

probability of risks propagating.

CFA UK 17 April 2013

Risk Appetite ResearchStage 3 – Mapping Appetite to Operational Indicators

Once the network is developed the high level risk appetite variables are set to have the probabilities set out in the risk appetite statement.

The propagation properties of the Bayesian Network are used to derive the resulting distributions of the indicators.

CFA UK 17 April 2013

Risk Appetite ResearchStage 4 – Propagate Evidence

The network can be reversed too.

Operational indicator values can be propagated back through the Bayesian Network to the risk appetite variables.

The risk appetite variable distributions can be inspected to check they are in-line with the statement.

CFA UK 17 April 2013

2012 Insurer Risk Appetites

2012 Insurer Risk Appetites

2012 Insurer Risk Appetites

2012 Insurer Risk Appetites

About us

Servaas Houben heads the risk scenario generation team at Prudential, London. He

studied econometrics in the Netherlands and worked in life insurance for the first four

years of his career. Following this, he worked in Dublin and London. Besides actuarial,

Servaas completed the CFA and FRM qualifications, and regularly writes on his blog,

for CFA digest and Dutch actuarial magazines.

Email: [email protected]

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Elliot Varnell is a consulting actuary at Millman in London. He is a UK Qualified

Actuary and hold the Chartered Enterprise Risk Analyst qualification. He is a member

of the governing board of the UK Actuarial Profession and Chairman of the ERM

Research and Development Committee of the UK Actuarial Profession. He consults on

Economic Capital, ALM and ERM.

Email: [email protected]

LinkedIn: http://www.linkedin.com/in/elliotvarnell