Calculating Market Value Margins with a Cost of Capital Approach CoC under the QIS 2 framework

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Calculating Market Value Margins with a Cost of
Capital Approach (CoC) under the QIS 2 framework

• Comité Européen des Assurances

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Calculating Market Value Margins with a Cost of
Capital Approach under the QIS 2 framework
Contents

• Introduction and methodology used
• Guide to the spreadsheet
• Other approaches

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MVM using CoC approach in QIS 2
Introduction methodology

• The industry clearly supports a CoC approach for
  the calculation of a Market Value Margin (MVM)
  for non hedgeable risks.
• The percentile approach requires significant data
  analysis and sophisticated calculation
  methodologies and is not clearly connected to the
  concept of a MVM. This was a major concern for
  SMEs in QIS1.
• The CoC is a workable solution for companies of
  all sizes and is the only suggested proxy so far
  for the MVM that is consistent with an economic
  approach.
• In order to facilitate the CoC approach in the
  QIS 2 exercise, the CEA project team has adapted
  the QIS 2 spreadsheets so companies can calculate
  the Market Value Margin in a simple way.
• The methodology followed is similar to the one
  applied for CEAs European Standard Approach
  (ESA). Full details about the methodology can
  be found in CEAs Working Document on Cost of
  Capital1.
• More sophisticated approaches towards the
  calculation of the MVM can be taken, we have
  described some of these options in the final
  section of this document.
• As a reminder, the Market Value Margin calculated
  with a cost of capital approach is based on three
  drivers.
• The amount of capital that needs to be held to
  cover non hedgeable risks.
• The annual cost of holding that capital
• The length of time that this capital needs to be
  held

1 This document is available at
www.cea.assur.org.
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MVM using CoC approach in QIS 2
Introduction methodology

• The amount of capital that needs to be held
  (SCRCoC) is calculated as defined in the QIS2
  specification with adjustments as explained in
  the next section.
• The cost of holding capital is set to 6 as in
  the SST, which is the default option for the
  calculation of the MVM under QIS 2.
• The method to determine for the length of time
  that the capital needs to be held is done in two
  possible ways. This is to maximise the
  participation on QIS2. The methods are
• Alternative 1 Relating the run-off of the SCRCoC
  to the development of the BEL.
• Alternative 2 Relating the run-off of the SCRCoC
  to a factor based on the duration of the
  liabilities.
• In order to avoid circularity the MVM is not used
  as an input for the calculation of the SCR
• This means that the SCR calculation is based on
  the BEL without including the MVM (neither the
  75th percentile nor the MVM calculated following
  the CoC approach)
• This approach is equivalent to making the
  assumption that the MVM will remain equal before
  and after the shock.
• As the MVM is a relatively small proportion of
  the market consistent liability, this simplifying
  assumption has only a second order impact on the
  results but means that circularity is completely
  avoided .

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Calculating Market Value Margins with a Cost of
Capital Approach under the QIS 2 framework -
Contents

• Introduction and methodology used
• Guide to the spreadsheet
• Other approaches

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Changes to the spreadsheet
Guide to the spreadsheet

• A spreadsheet is provided with this document to
  facilitate the calculation of the MVM.
• The spreadsheet is based in the one distributed
  by CEIOPS and no alterations to the formulas have
  been made. It is important to note that a new
  spreadsheet will be released by CEIOPS on the
  24th of May. As a result, this may require an
  update to this CoC spreadsheet.
• The calculation of the MVM has been introduced by
  creating additional worksheets where all the
  necessary calculations are made
• Worksheet CoC Calculation Contains the basic
  steps in the calculation of the MVM both using
  the run-off of Best Estimate Liabilities and a
  simplified factor based alternative.
• Some adjustments are made to the SCR calculation
  for credit risk and Non Life Underwriting
• Worksheet SCR Adjustment - Credit
• The credit risk does not include risk arising
  from financial assets. Only the exposure to
  reinsurance is included.
• Worksheet SCR Adjustment - NL Underw.
• Underwriting risk should only reflect run-off
  risks. The volume measure for premium and
  catastrophe risk is changed to undiscounted
  Unearned Premium Reserve.

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MVM using CoC approach in QIS 2 Alternative 1
Guide to the spreadsheet

• The calculation of the MVM is done on the
  worksheet CoC Calculation. Two alternatives are
  given for the calculation.
• Alternative 1 is based on the development of the
  BEL
• Step 1 Calculation of the SCRCoC at time
  0 (CELLS B5M35)
• SCRCoC is calculated by taking out market risk
  and using the adapted credit and underwriting
  risk SCR.
• SCR is considered before any risk absorption by
  future profit sharing.
• The ratio of the initial SCRCoC over the BEL is
  calculated (CELL D33).
• Step 2 Calculation of the projected
  SCRCoC (CELLS B40M96)
• The SCRtCoC is calculated for all the run off by
  applying the above ratio to the future
  development of the BEL.
• The run-off of the BEL is a required input for
  this calculation.
• Step 3 Calculation of the capital
  charges (CELLS B98M151)
• Capital charges are calculated by applying the
  cost of capital (6) to the SCRtCoC at each
  future point in time.
• Step 4 Calculation of the MVM (CELLS
  B154M208)
• The MVM is calculated as the present value of
  capital charges, calculated at the risk free rate
  using the term structure provided by CEIOPS.

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MVM using CoC approach in QIS 2 Alternative 2
Guide to the spreadsheet

• For those companies who may not be able to
  provide the future development of the BEL a
  simplified calculation is presented.
• Alternative 2 uses a factor applied to the
  initial SCRCoC in order to calculate the MVM.
• Step 1 Calculation of the SCRCoC at time
  0 (CELLS B5M35)
• SCR is determined in the same way as in
  Alternative 1.
• Steps 2-4 Calculation of the MVM (CELLS
  B211M221)
• The MVM is calculated by applying a factor to the
  initial SCRCoC.
• The factor is dependent on the duration of
  liabilities. It is calculated as an annuity
  factor times the cost of capital of 6.
• The annuity factor is based on the duration of
  the liabilities and the relevant yield rate for
  that duration following the term structure used
  for QIS2.

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Calculating Market Value Margins with a Cost of
Capital Approach under the QIS 2 framework -
Contents

• Introduction and methodology used
• Guide to the spreadsheet
• Other approaches

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More sophisticated methods
Other approaches

• The solutions suggested in this paper are simple
  and workable alternatives that will help maximise
  participation in QIS 2.
• More sophisticated approaches are possible that
  will tailor the methodology to a companys own
  individual circumstances. This include
• A full calculation of the SCRCoC for each year
  (most likely using an internal model)
• Relating the development of the SCRCoC to the
  risk drivers for the individual risks. For more
  details see A Primer for Calculating the Swiss
  Solvency Test Cost of Capital for a Market
  Value Margin by Philipp Keller.
• Implementation of an iterative process that would
  allow to include the MVM in the calculation of
  the SCR yet avoiding circularity.

2 This document is available at
www.cea.assur.org.
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Contact details

• CEA has opened a helpdesk to help participants
  with any questions they may have on QIS2.In case
  of you have any questions regarding this document
  or other QIS2 issues please contact
  QIS2-helpdesk_at_cea.assur.org

2 This document is available at
www.cea.assur.org.