Ch 24: Supervisory reserves and capital requirements 2

Question 1

Summary card (4)

Answer 1

1. Pricing and reserving assumptions
2. Market-consistent valuations
3. Solvency capital
4. Active and passive valuations

The key focus in this chapter is considering the reserving assumptions to use for demonstration of solvency (either prudent, or market consistent), and the need for additional solvency capital over and above these reserves.

Question 2

Discuss the relationship between pricing and reserving assumptions

(1,1)

(1,2)

Answer 2

1. 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
2. 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.

Question 3

Describe what we mean by ‘market consistent valuation’? (3)

Answer 3

A market consistent/fair valuation valuation

• can be used when setting reserves with assets also being valued at market value
• theoretically the price someone would charge for taking responsibility for the liability, in a market in which such liabilities are freely traded

Question 4

State how, in theory, the assets and liabilities should be ideally value when using a market-consistent approach (3)

Answer 4

1. Assets should be valued at market value
2. 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.
3. To determine the Ls, future unknown parameter values and CFs are set so as to be consistent with mkt values, where a corresponding mkt exists.

Question 5

Describe how the investment return assumption would be determined for a market-consistent valuation of the liabiltiies (4)

Answer 5

1. Future investment returns and discount rates would be based on the risk-free rate, irrespective of the type of asset actually held.
2. 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 where deep refers to a mkt of sufficient capacity that large trades would not materially affect the prices).
3. A deduction may be made for credit risk, if appropriate, because swaps are not entirely rf as one counterparty may default, even G bonds.
4. Credit might be taken for the illiquidity premium in corporate bond yields, provided the liabilities for which the rates are to be used
   
   • are long term,
   • predictable,
   • and for which matching assets can be held to maturity (eg immediate annuties)

Question 6

Explain what’s meant by ‘illiquidity premium’ in context of corporate bond yields (5)

Answer 6

Illiquidity premium

1. May be possible to derive market consistent disc rate from corporate bonds
2. 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

Question 7

Why might it be possible to take credit for the illiquidity premium when determining the risk-free rate of return from these yields? (5)

Answer 7

Why’s it possible to take credit for illliquidity premium?

1. Lack of liquidity is not a risk if the assets are held to maturity.
2. So, provided the liability cashflows have relatively fixed and predictable durations
   
   • illiquidity premium can be allowed for in the ‘risk-free’ rate
   • as there is no risk due to illiquidity and insurer is not exposed to risk of changing spreads on such assets (but still exposed to default risk)
   • in essence, choosing riskier corporate bonds to match liabilities can give higher returns ‘for free’ if liability CFs fixed/predictable durations
3. 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 or which types of contract this can be applied to.

Question 8

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.

(5)

Answer 8

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 quoted by RI companies - RI would not provide unless FNB intends to use their services.
   • expenses: may derive from expense agreements available in market eg 3rd party administrators - would not provide unless FNB intends to use their services.
   • with-profit endowment assurance contracts: traded as investment vehicles so there may be a current market price for these products as a whole - traded endowment mkt unlikely to be considered sufficiently deep and liquid.
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 BE 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.

Question 9

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.

(1,3)

(2,4)

(3,2)

(4,3)

Answer 9

1. Project required capital at each future time period to get the amt needed in excess of projected Ls.
   * project forward the future capital the company is required to hold iro these risks. Where this is determined at the end of each projection period ie. year during the run-off of the business.
   
   • The projected capital determined by the relevant regulatory basis.
2. Projected capital amts x a cost of capital rate for each future year.
   
   • this rate can be considered to represent cost of raising incremental capital in excess of the rf rate or representing the frictional cost (ie. tax) / loss in return caused by locking in this capital rather than being able to invest it freely for higher reward.
     * cost of capital rate, for example, may be determined as the excess of the weighted average cost of capital over the risk-free rate, in some cases it may be a fixed rate.
     *
3. Discount 2. using market consistent discount rates to give the overall risk margin.
   
   • Risk margin =
     Sum_OverT [k_(t) * C_(t) \/ (1 + r_(t)) ^t ]where k(_t) is the cost of capital charge/rate for time t, C_(t) is the required capital at time t and r_(t) is the risk free interest rate for maturity t.
   • 3. Discount at the appropriate risk-free rate of return for each term, and sum to obtain the risk margin.
   • 4. According to some regulatory frameworks the projection of future capital may be
        1. simple eg fixed percent of reserves, or
        2. complex, if the calculation requires:
     5. projections, stochastic modelling and correlation matrices
     6. approximations eg expressing capital required as simple formula based on drivers such as the size of the reserves and the sum at risk which has an approximately linear relationship with the required capital or its components.
        * The initial capital requirement can be expressed as a % of that driver, and the projected capital is then approximated as the same % of the projected values of the driver.
     7. A combination of correlations and drivers.

Question 10

Solvency 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)

Answer 10

Solvency capital requirements refers to:

1. insurance supervisors require insurers to maintain at least a specified level of solvency capital.
2. which can be viewed as an additional level of protection to policyholders.

Solvency capital requirements can protect polichyholders against:

1. reserve being underestimated, ie adverse future experience relative to reserving assumptions.
2. a drop in asset values (including individual asset defaults).

Level of solvency capital may be

1. specified as formula eg 3% of reserves to cover fall in asset value, and 0.3% of sum at risk to cover adverse mortality experience
2. based on a risk based measure, such as VaR (Value at Risk)

Question 11

Solvency capital requirements: relationship between reserves & solvency capital requirements

Discuss the relationship between the reserves and the solvency cpaital requirements

(1)

(1, 2)

Answer 11

1. Adequacy or reseves must be considered in relation to solvency capital requirements and not in isolation, and vice versa.
2. Relative balance between two varies between countries and regulatory jurisdictions:
   
   • in some, reserves are set up on a relatively realistic basis (relatively small margins from expected values), but with a requirement for a substantial level of solvency capital determined using risk-based capital techniques.
   • in others, reserves are set up on a relatively prudent basis (relatively large margins), but with relativesly small solvency capital requirement, which isn’t specifically related to the risks borned by the company.

Question 12

Solvency capital requirements: Value at Risk approach

What is the VaR approach to deriving solvency capital required by an insurer? (2)

Answer 12

VaR approach is

• An example of a risk-based solvency capital requirement approach, normally expressed at a minimum 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
  • eg VaR of R10 mil over next year with 99.5% confidence => only 0.5% expected probability of loss higher than R10 mil over next year

Question 13

Solvency capital requirements: Value at Risk approach

Outline the Value at Risk (VaR) approach to dervicing the risk-based solvency capital required by an insurance company.

(6)

Answer 13

Supervisory balance sheet subject to stress tests:

• supervisory balance sheet=>often on a market consistent basis for this approach
• conduct stress tests/shocks on supervisory balance sheet for each risk factor separately, at defined confidence level, over the defined period.
  
  • eg calculate R100mil capital required to cover mortality risk
• each stress test involves projecting the company’s future assets and liabilities, based on the actual liabilties 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.
• The market consistent surplus is then recalculated at the end of every period.
• Other possible methods: Run-off method: Looks at the amount of capital needed at the outset to ensure a firm’s ability to cover its Ls until the last policy has gone off the books, allowing for suitable stresses to the risk factors.
• Or 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

Aggregate capital requirement

• In order to arrive at an aggregated capital requirement the individual stress tests need to be combined in a way that reflects the diversification benefits that exist between the various risks eg via correlation matrix or copulas
• aggregate capital requirement =
• sqrt[ SumOver_i( SumOver_j (Corr_(i,j) * Cap_(i) * Cap_(j))) ]
  
  • where Cap_(i) is the capital requirement under risk i and Corr_(i,j) is the correlation between risks i and j
  • under extreme event condition being tested, correlations may differ from those observed under normal conditions.
• Additional capital may be needed across individual risks to cover any:
  
  • non-linearity - requires that the capital required in a linear function of the risk drivers eg. 1% increase in shock <> 1% change in cap required)
  • non-separability - the way in which risk drivers interact with each other eg. events happen together > if happen seperately. Separate allowance needs to be made for these effects.
  • Examples are on page 16 - first 2 paragraphs.
• Note: a combination of a certain subset of events happening at the same time with an overall P() level of 1 in 200 may product a higher capital requirement than when combining all of the individual capital requirements for separate 1 in 200 events using a correlation matrix.

Question 14

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)

Answer 14

For solvency capital requirements, stochastic models are typically used:

• to quantify capital requirements in relation to economic risks. The P() distribution used should properly reproduce the more extreme behaviour of the variable being modelled, both in the size of the tail of the distribution and in the path taken during the simulation period.
• a real-world asset model would be used, which should be arbitrage free ie. Ch 18
• in particuar, the model must not understate the frequency of the more extreme outcomes occurring. Therefore, it is generally appropriate to calibrate such models with reference to actual historic parameters and advanced techniques may be used to ensure appropriate fit to the tail of the distribution.

Question 15

Define what is meant by a passive valuation approach (2)

Features of passive valuation approach (4)

Answer 15

Passive valuation approach uses a:

• valuation method that’s relatively insensitive to changes in market condition and a
• valuation basis which is updated relatively infrequently

Features of passive valuation approach:

• assumptions may be locked in
  
  • assumptions remain unchanged from those used when policy was first written and the liability for it first determined.
  • it may be a requirement that non-economic assumptions are updated if experience worsens in order to recognise the related loss and the need for higher reserves at that time such as mortality because if experience deteriorates the cost of benefits will rise without a corresponding change in A values.
  • i rate locked in because a change in As = a proportional change in Ls.
• Vassets at book value, historic cost or amortisation (write-down) over time.
  
  • Book value: Ignores market price change impacts, which would be suitable only if valuation of liabilities is also largely ignoring market conditions eg. valuation interest rate is locked in, or net premium valuation basis used
• Solvency capital may be determined using a simplified approach
  
  • eg holding a prescribed % of base liabilities

Question 16

State 3 advantages of passive valuations (3)

Disadvantages of passive valuation approach (4)

Answer 16

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 the extent that it’s used for accounting purposes

Disadvantages of passive valuation approaches are that they:

• can become outdated because:
  
  • it is relatively insensitive to changes in market conditions eg. a stock mkt crash leading to an A being overvalued relative to the value if it was sold in the mkt today,
  • and has a valuation basis which is updated infrequently. It may not take account of important trends eg rising expense inflation and worsening claims experience.
• Therefore it may provide a false sense of security. Management may fail to take appropriate actions in response to emerging problems until too late, because the solvency position hasn’t appeared to change

Question 17

Define what is meant by an active valuation approach ( 3 )

Answer 17

Active valuation approach would be

• based more closely on market conditions (than a passive valuation)
• with the assumptions being updated on a frequent basis eg
  
  • the use of market-consistent valuation approaches for both assets and liabilities, and a risk-based capital approach to solvency capital requirements

Question 18

What are the advantages and disadvantages of using an active valuation approach? ( 5 )

Answer 18

Advantages:
* More informative in terms of understanding impact of market conditions on a company’s ability to meet its obligations, particularly in relation to financial guarantees and options.

Disadvantages

• More volatile results
  
  • Which has implications such as due to procyclicality -> Under adverse equity market conditions an active approach using risk-based capital would indicate that higher capital requirements are needed. To reduce this requirement, companies would have to sell equities, which itself could exacerbate the market conditions.
• Systematic risk
  
  • Which this would be the case for all insurers at the same time
  • Therefore regulators may include amendments to the valuation approach under certain conditions to avoid this situation.
• More complex thus more time consuming and more costly

Question 19

In practice, what valuation approach would we expect between active and passive? (1)

What are the implications of point 1 above?

Answer 19

• Overall valuation approach may be somewhere between active valuation approach and passive valuation approach, including elements of each.
• Combinations of a active/passive valuation approach can results in greater mismatch between assets and liabilities
  • and hence greater losses/profits or changes in free surplus when market conditions change
  • eg an approach using a net premium valuation for liabilities and market value of assets could experience greater volatility of results than one which uses a market consistent valuation for both.
  • Explanation for the above example:
    If the assets and liabilities are well matched, then the true impact of market movements on the company’s solvency should also be quite small. Under an active valuation approach, any change in the value of the assets should be reflected in a corresponding change in the value of the liabilities (eg if interest rates fall then both valuations should rise), so the solvency position should be little changed. Under a passive valuation approach, the value of the assets and liabilities might be little changed by market conditions, so again the solvency position should be little changed.

However, if a combination of active and passive approaches is used (eg active market value of assets and passive net premium value of liabilities, as suggested by the Core Reading) then solvency might appear to change dramatically when in reality it hasn’t changed. A change in interest rates would change the market price of assets but would have little impact on the net premium valuation of liabilities.

Question 20

Principles of supervisory reserving & capital requirements.

What are some of the key principles to bear in mind when setting supervisory reserves and solvency capital requirements? (9)

Answer 20

1. Reserve must be sufficient to meet all future liabilities
2. Prudent valuation of future liabilities on existing business
3. Prudence can be allowed for by including margins for adverse experience
4. Take into account term, nature, valuation method of assets
5. Appropriate approimations are allowed/should be made
6. Assumptions should be chosen prudently, having regards past/expected exp
7. Lower interest rates where no explicit allowance for future bonuses
8. Recognise profit in appropriate way over term
9. Valuation method should be disclosed