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Croatian Quants DayZagreb, May 6th, 2011

A lookback on Solvency 2 negotiations

Dr. Mihael Perman

Insurance Supervision Agency, Slovenia

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Overview

• Introduction

• New approach to capital requirements

• Technical provisons and own funds

• Solvency capital and the standard formula

• Components of the standard formula

• Political side

• Issues under Slovenian presidency

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Genesis

Solvency 2 is a long overdue overhaul of insurance legislation in the EU. The new directive will introduce fundamental changes to the way the insurance industry manages risk and capital. The draft directive as published in July 2007 is the result of almost a decade of work. Full implementation is expected by 2013.

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Organization of the directive

• Solvency 2 is a principle based directive according to the Lamfalussy process.

• The articles contain only the fundamental principles, all the rest is dealt with in the implementation measures which are in the hands of the European commission.

• Some secondary legislation will be contributed by EIOPA.

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ExampleArticle 74

Valuation of assets and liabilities

1. Member States shall ensure that, unless otherwise stated, insurance and reinsurance undertakings value assets and liabilities as follows:

(a) assets shall be valued at the amount for which they could be exchanged between knowledgeable willing parties in an arm's length transaction;

(a) liabilities shall be valued at the amount for which they could be transferred, or settled, between knowledgeable willing parties in an arm's length transaction.

When valuing liabilities, no adjustment to take account of the own credit standing of the insurance or reinsurance undertaking shall be made.

2. The Commission shall adopt implementing measures to set out the methods and assumptions to be used in the valuation of assets and liabilities as laid down in paragraph 1.

Those measures designed to amend non-essential elements of this Directive, by supplementing it, shall be adopted in accordance with the regulatory procedure with scrutiny referred to in Article 304(3).

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Outlay of the Directive

Solvency 2

Pillar 1Financial requirements

Pillar 2Governance

Pillar 3Disclosure, reporting

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Capital requirements

Capital requirements will be risk based. There are many items on the asset side and liability side that effect the business result of an insurance company. All of them bear some risk. The idea is to take into account all the components and assemble them in a final and ultimate measure of risk=capital requirement.

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Comments

The risk based approach has been adopted by the US, Canada and Japan in the nineties. Japan added capital requirements for operational risk and catastrophe risk. However, those RBC approaches assume that risk groups are independent. Solvency 2 introduces correlations making the capital requirements stricter.

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Basic structure

Following the beaten path capital requirements will cover three areas:

Technical provisions. Own funds. Solvency capital.

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Technical provisions

Technical provisions are the backbone of the insurance business. According to IAIS guidelines they have to be:

Reliable. Appropriate. Unbiased.

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Determination of technical provisions

Solvency 2 proposes to base the computation of technical provisions on the current exit value increased by a risk margin. The exit value will be based on a best estimate increased by a risk margin based on the cost of capital method with respect to solvency capital. The univeral idea is to value a contract according to all cash flows arising, deiscounted and probability weighted.

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Own funds

Assets must cover technical provisions and the additional solvency margin requirement. Solvency 2 replaces administrative restrictions by the “prudent person” approach. However, there is “punishment” in form of higher solvency margins if there is insufficient diversification or quality of assets.

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Own funds-continuation

One rather substantial change is that Solvency 2 looks at all assets a company holds. There is no difference between assets covering technical provisions, solvency capital requirements and free assets. The effect is expected to be better management of all assets.

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Solvency capital requirement

Basic principles: Taking into account all risks. Provide a probability of 99.5% that all

insurance claims will be paid in full. No separation of assets and liabilities

when computing probability of insolvency.

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Determination of the SCR

There are two possibilities The standard formula provided by the

directive. While not simple it provides firm guidance to insurance companies. The disadvantage is “one size fits all”.

Internal models developed by the company itself. A major undertaking that will take time and entail considerable cost but will be tailor made.

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The standard formula

We will focus on the standard formula here and will try to explain how it works. This is a good starting point for internal models too. The starting formula is below. Here BSCR stands for basic SCR, Adj for possible adjustments and the last term for operational risk.

opSCRAdjBSCRSCR

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The standard formula-continuation

The focus here will be on the basic solvency capital requirement. The way to think about the BSCR is to view it as a measure of volatility of losses. If the volatiliy of losses is large, more capital is needed. Such a viewpoint will help to explain the aggregation methods in the standard formula.

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Idea behind standard formula

The BSCR can be viewed as an overall measure of volatility of the losses suffered by an insurance company. This measure is calibrated in such a way that it insures the 99.5% probability of meeting all insurance claims.

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Idea, continuation

A measure of volatility says how far the losses are likely to be from expected losses. All measures of volatility have this in common and all have similar properties to the standard deviation. We may therefore think of the BSCR as a multiple of the standard deviation of losses where the multiple is chosen right. Such an interpretation has a few advantages.

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Assembling contributions

If we have random variables X and Y the usual measure of volatility is the standard deviation. The standard deviation of the sum X+Y is computed as below with Corr(X,Y) beeing the correlation coefficient between X and Y.

)()(),(2)()()( 22 YSDXSDYXCorrYSDXSDYXSD

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Assembling contributions-cont.

The same formula is valid if instead of the standard deviation one chooses a multiple of the standard deviation. The formula produces the same multiple. This means that if all the random components entering the computation contribute a multiple of the standard deviation this multiple will be preserved at all levels. Simple-but clever!

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Top level

It seems cleaner to have a hierarchical structure of all risks. Here is the top level:

1. Capital charge for market risk - SCRmkt 2. Capital charge for counterparty default risk - SCRdef 3. Capital charge for life underwriting risk - SCRlife 4. Capital charge for non-life underwriting risk - SCRnl 5. Capital charge for health underwriting risk - SCRhealth.

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Top level-continuation

The formula that assembles there contributions into the BSCR is the usual formula for the standard deviation of sums of random quantities:

BSCR = rxc ccr SCRSCRCorrSCR r,

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Top level-continuation

The correlation coefficients at top level are part of the directive presented by the Commission.

CorrSCR = SCRmkt SCRdef SCRlife SCRhealth SCRnl

SCRmkt 1

SCRdef 0,25 1

SCRlife 0,25 0,25 1

SCRhealth 0,25 0,25 0,25 1

SCRnl 0,25 0,5 0 0,25 1

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Market risk

Market risk is again assembled from several components:

interest rate risk MKTint

equity risk MKTeq

property risk MKTprop

spread risk MKTspread

risk concentrations MKTspread

currency risk MKTfx

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Market risk-continuation

Risks are again assembled using the usual formula and correlations

CorrMkt MKTint MKTeq MKTprop MKTspread MKTspread MKTfx

MKTint 1

MKTeq 0 1

MKTprop 0,5 0,75 1

MKTspread 0,25 0,25 0,25 1

MKTconc 0 0 0 0 1

MKTfx 0,25 0,25 0,25 0,25 0 1

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Market risk-interest rate

The idea is to collect assets and liabilities sensitive to interest rate changes and subject them to upward or downward shocks depending on maturity. Example: for 4 years to maturity the shocks are 0.62 and -0.42 (QIS4). This produces changes in net asset values. It is possible to alter assumptions on bonuses and profit sharing. The bigger of the two changes is the interest rate risk.

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Market risk-interest rate, cont.

In formulae:

MktintUp = Δ NAV | upwardshock

Mktint

Down = Δ NAV | downwardshock

Δ NAV = Net value of assets minus liabilities

Altered term structure = current interes rate curve · (1+s ), s=shock

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Market risk-interest rate, cont.

If calibrated correctly the effect of shocks is a measure of volatility that conforms to the 99.5% requirement and can enter into the “assembly” formula.

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Market risk-equity risk

The idea again is to apply shocks to the value of equities. The shocks are 32% for the global index (EEA and OECD) and 45% for others. We get two measures of volatility and assemble them into one measure.

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Market risk-equity, cont.Mkt eq,i = max (Δ NAV | equity shocki ; 0) equity shocki = prescribed fall in the value of index i Mkteq,i = capital charge for equity risk with respect to index i

Mkteq = MktMktCorrIndex crrxc

rxc

Mktr, Mktc = capital charges for equity risk per individual index according to the rows and columns of correlation matrix CorrIndex

able 4: Correlation matrix CorrIndex

CorrIndex = Global Other

Global 1

Other 0,75 1 Source: European Commission, March 2008

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Political side

• EU legislation is usually drafted by the European commission.

• It has to be passed by the European Council which represents the Member states and the European Parliament.

• The European Commission plays a coordinating role.

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Political side-continuation

• Member states take 6 months turns as the presidency of the European council.

• Powers of the presidency are limited but nevertheless notable. The presiding country sets the negotiations agenda, drafts proposals and cooperates with the European parliament.

• Solvency 2 was negotiated under PT, SI, FR and CZ.

• It was passed on April 23th, 2009 by the European Parliament.

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Issues under the Slovenain Presidency

• The Ministry of Finance outsourced the Solvency 2 negotiations to insurance regulators.

• There were 10 two day negotiation rounds in Brussels and 3 meetings with the European parliament, and +∞ bilateral meetings.

• 140 articles out of 312 were negotiated

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Surplus funds

• Surplus funds are part of capital contributed by policy holders in AT, DE, DK and SE.

• They do not fit into the general idea of valuation by means of discounted, probability weighted cash flows.

• But … they are first class quality capital.

• What to do?

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Surplus funds 2

• UK and FR were strongly opposed to surplus fund (as a means to blackmail mamber states with surplus funds).

• SI took the position that surplus funds should be acknowledged as part of capital if the disclosure to consumers is correct.

• SI also argued that surplus funds have to be Tier 1 capital.

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Groups

• Big insurance groups in Europe are a fact.

• There should be some way of supervising the insurance group as a whole, which also includes assessing the capital positions of the groups as a whole.

• Some countries are almost exclusively host countries.

• What to do?

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Group support

• The big groups argued that taking a group as a whole reduces capital needs because of diversification.

• As a consequence you need to replace part of capital requirements on solo level of subsidiaries by a declaration of support from the parent company.

• Should that be allowed?

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Reservations about group support

• No standardized method to determine the diversification effects.

• Hurdles because of different corporate laws in member states.

• Competition issues: two companies with identical portfolios could operate in the same market with different capital requirements.

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Mathematical side excursion

• All insurance policies in a group can be thought of as random variables ...which are conditionally independent given exogenous factors (which usually cause positive correlation).

• The total liability is the sum X1+X2+…• One can group the r.v.s by subsidiaries which

means putting parentheses in the sum like (X1+X2+...+Xm)+(Xm+1+….

• The parentheses do not make the partial sums negatively correlated!

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Group supervision

• The European commission proposal transferred authority over groups to home supervisors exclusively.

• There were no provisions regarding burden sharing, crisis management, role of local language or local corporate law.

• In many countries there would be a fragmented supervision of the national market.

• What to do?

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Group supervision-cont.

• Many countries were opposed to the proposal (not only new members – CZ).

• There is still a priority to supervise national markets in a unified manner.

• There were proposals to transfer group supervision to a EU authority.

• In the end SI proposed to keep solo supervision with the local authorities.

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Conclusions

• Capital requirements are strict.• The risk based approach with correlations

encourages better risk management.• The computation is demanding even when

using the standard formula.• Transition to Solvency 2 will be a major

undertaking with substantial benefits.• Solvency 2 is also complex, complicated

and wrought with dangers.

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Disclaimer

• the currency or accuracy of statistical data used in the presentation is not guaranteed