Chapter 24-Supervisory Reserves and Capital Requirements (2) Flashcards
Discuss the relationship between pricing and reserving assumptions
Premiums could be calculated using prudent assumptions, with same assumptions used for supervisory reserves
+suitable for with-profits, as surplus will emerge relative to the prudent assumption
+less justifiable for without-profits
Premiums could be calculated using broadly realistic assumptions, with risks to company being allowed for mainly through risk discount rate
+supervisory regime may require prudent reserving assumptions, in which case the premium and reserving bases will be different
+supervisory regime may use best estimate or market-consistent reserving assumptions, in which case the premium and reserving bases could be the same. However, additional allowances for risk would be needed for each.
State how, in theory, the assets and liabilities should be ideally value when using a market-consistent approach (3)
Often referred to as a fair valuation which can be used to set reserves
with assets being valued at market value
In theory, liabilities would be valued as price that someone would charge for taking responsibility for them, in a market in which such liabilities are freely traded. In the usual absence of such a market, an approximate approach has to be taken.
The value of the liabilities should be equivalent to the current market value of a notional portfolio of risk-free assets that match the liability cash flows exactly
Describe how the investment return assumption would be determined for a market-consistent valuation of the liabilities (4)
Would be based on the risk-free rate, irrespective of the type of asset actually held.
This risk-free rate may be based on government bond yields, or on swap rates (if there’s a sufficiently deep and liquid market for these).
A deduction may be made for credit risk, as appropriate.
Credit might be taken for the liquidity premium in corporate bond yields, provided the liabilities for which the rates are to be used
+are long term,
+and have reasonably predictable duration,
+and for which matching assets can be held to maturity (eg immediate annuities)
Explain what’s meant by ‘illiquidity premium’ in context of corporate bond yields (5)
May be possible to derive market consistent disc rate from corporate bonds
Compared to government bonds, corporate bonds
+higher default probability
+less marketable (hence, less liquid), => prices more volatile => problem if bonds need to be sold before redemption
+usually have higher bond yields due to higher default risk and lower liquidity
+illiquidity premium is portion of higher return due to illiquidity
Why might it be possible to take credit for the illiquidity premium when determining the risk-free rate of return from these yields?
Lack of liquidity is not a risk if the assets are held to maturity.
So, provided the liability cashflows have relatively fixed and predictable duration illiquidity premium can be allowed for in the ‘risk-free’ rate
Where this practice is permitted by regulation, there would normally be strict rules about how and when it can be applied, eg there may be a requirement that matching bonds are held to maturity.
Describe the risk margin based approach to market consistent valuations:
Explain the approach that normally has to be used to obtain market-consistent assumptions for mortality, persistency, and expenses.
(1) Usually impossible to obtain market values of assumptions directly, because markets are insufficiently (a) deep or (b) liquid.
(2) In some cases, may be possible to use some market-consistent estimates:
mortality: may derive from reinsurance risk premium rates
expenses: may derive from expense agreements available in market eg 3rd party administrators
(3) Instead, the approach is normally to take a best estimate of the future experience, plus a ‘risk margin’.
(4) The risk margin would reflect the extra price that the market would require, in order to compensate for the uncertainties inherent in the liability cashflows due to the assumption.
(5) Overall risk margin could be determined by
+adding a margin to each assumption
+alternatively, an overall reserving margin in respect of these risks could be determined using the ‘cost of capital’ approach.
Describe the risk margin based approach to market consistent valuations:
Outline the ‘cost of capital’ approach to calculating an overall risk margin for the mortality, persistency, and expense assumptions, for the purpose of a market-consistent valuation of the liabilities.
(1) Project required capital
project forward the future capital required to hold in excess of market-consistent estimate of the liabilities
determined at the end of each future year, for current in force book
projection guided by relevant regulatory solvency basis
(2) Multiply projected capital amounts by “Cost of Capital Rate”
+for each future year
this rate can be considered to represent cost of raising incremental capital, in excess of risk free rate; representing the frictional cost/loss in return cause by locking in this capital rather than being able to invest it freely for higher reward
+cost of capital rate, may, for example, be dertemined as excess of the weighted average cost of capital over the risk-free rate, in some cases it may be a fixed rate
there may also be other frictional costs eg tax which affect CoC
(3) Discount at the appropriate risk-free rate of return for each term, and sum to obtain the risk margin.
(4) Projection of future capital may be
+simple eg fixed percent of reserves, or
+complex, leading to:
stochastic modelling and correlation matrices
+approximations eg expressing capital required as simple formula based on drivers such as the size of the reserves and the sum at risk
olvency capital requirements:
What do we mean by solvency capital requirements? (2)
Give 2 broad areas of risk where solvency capital can protect policyholders (2)
How might the level of solvency capital required by regulation be specified? (2)
(1) Solvency capital requirements refers to:
the usual that insurer supervisory bodies impose which requires insurers to maintain at least a specified level of solvency capital (i.e. capital to display solvency
can be viewed as an additional level of protection
(2) Solvency capital requirements can protect polichyholders against:
reserve being underestimated, ie adverse future experience relative to reserving assumptions.
a drop in asset values (including individual asset defaults).
(3) Level of solvency capital may be
specified as formula eg 3% of reserves to cover fall in asset value, and 0.3% of sum at risk to cover adverse mortality
based on a risk based measure, such as VaR (Value at Risk)
Solvency capital requirements: relationship between reserves & solvency capital requirements
Discuss the relationship between the reserves and the solvency cpaital requirements
Adequacy or reserves must be considered in relation to solvency capital requirements and not in isolation, and vice versa.
Relative balance between two varies between countries:
in some countries, reserves are set up on a relatively realistic basis (relatively small margins from expected values), but with requirement for substantial level of solvency capital determined using risk-based capital techniques.
in other countries, reserves are set up on a relatively prudent basis (relatively large margins), but with relatively small solvency capital requirement, which isn’t specifically related to the risks borne by the company.
Solvency capital requirements: Value at Risk approach
What is the VaR approach to deriving solvency capital required by an insurer? (2)
VaR approach is
risk-based solvency capital requirement approach, normally expressed as a min required confidence level over a defined period (eg 99.5% over 1 year)
Under VaR approach, amount of capital needed:
set min required confidence level, eg 99.5%, over a given defined period, eg 1 year => assets won’t exceed liabilities over 1 year, with 99.5% confidence
Solvency capital requirements: Value at Risk approach
Outline the Value at Risk (VaR) approach to deriving the risk-based solvency capital required by an insurance company.
supervisory balance sheet=>often market consistent for this approach type
conduct stress tests/shocks on supervisory balance sheet for each risk factor separately, at defined confidence level, over the defined period.
each stress test involves projecting the company’s future assets and liabilities, based on the actual liabiltiies and assets currently held.
for each risk factor, amount of capital needed at the present time, in excess of its liabilities due to stress test, is calculated to ensure that assets exceed liabilities at the end of the defined period with the required probability.
alternatively, determine single shock scenario with 99.5% confidence which involved simultaneously shocking mortality, expenses, investment return, withdrawals, etc => currently too computationally difficult, so separate stress test used instead
for individual stress tests done, combine capital required over all risk factors, allowing appropriately for interactions, eg via correlation matrix
Additional capital may be needed across individual risks to cover any
+non-linearity (1% increase in shock <> 1% change in cap required)
+non-separability (events happen together > if happen separately)
Solvency capital requirements: use of stochastic modelling
In what way may stochastic models be used for supervisory solvency capital requirements? (2)
Comment on the calibration of such stochastic models used for solvency capital requirements (3)
a real-world asset model would be used, which should be arbitrage free
in particular, the model must not understate the frequency of the more extreme outcomes occurring.
Calibration of stochastic models used for solvency capital assessment
calibration can be made by reference to historical experience
it’s important to reproduce the more extreme ‘tail’ behaviours accurately, both in terms of size of the tail of the distribution and (where appropriate) the path taken
Define what is meant by a passive valuation approach (2)
Features of passive valuation approach (4)
valuation method that’s relatively insensitive to market condition changes
valuation basis which is updated relatively infrequently
assumptions may be locked in
mortality/expense inflation assumptions rarely change
non-economic assumption change when experience worsens in order to recognise related loss and need for higher reserves
assets at book price
possibly with amortisation/write down over time.
simplified approach for solvency capital requirement
eg holding prescribed % of base liabilities
State 3 advantages of passive valuations (3)
Disadvantages of passive valuation approach (4)
Advantages of passive valuation approaches are that they:
+Tend to be more straightforward to implement
+Involve less subjectivity
+Results in relatively stable profit emergence, to extent that it’s used for accounting purposes
Disadvantages of passive valuation approaches are that they:
+can become outdated
+relatively insensitive to changes in market conditions
+valuation basis updated infrequently (may not take account of important trends eg rising expense inflation, worsening claims experience)
+false sense of security eg management failing to take appropriate actions in response to emerging problems until too late, because solvency position hasn’t appeared to change
Define what is meant by an active valuation approach ( 3 )
Active valuation approach would be
+based more closely on market conditions (than a passive valuation)
+with the assumptions being updated on a frequent basis
+market consistent valuation for both assets/liabilities, and risk based capital approach to solvency capital requirements
more informative in terms of understanding impact of market conditions on company’s ability to meet obligations, particularly in relation to financial guarantees and options.
