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’? (6)

Answer 3

A market consistent valuation
* is often referred to as a fair valuation which can be used to set reserves
* with assets being valued at market value
* Aims to give value of liability if they were freely traded in the market
* Estimates of parameters and CF’s areset to be consistent with MV’s
* Use assets that exactly replicate CF’s of the liability eg ZCB
* MV replicating port = Mkt consistent value of liabilities
* OR Disc CF’s @ current Rf rate

A311 definitions

Question 4

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

Answer 4

1. 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).
3. A deduction may be made for credit risk, as appropriate.
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,
   • and have reasonably predictable duration,
   • and for which matching assets can be held to maturity (eg immediate annuties)

Question 5

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

Answer 5

Illiquidity premium

1. Derive and use 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 above the Rf rate
   • Disc liabilities at higher rates => Decrease val liabilities

Question 6

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 6

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 regs, there would normally be strict rules about how and when it can be applied,
4. eg there may be a requirement that matching bonds are held to maturity.

Question 7

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 7

1. Usually impossible to obtain market values of assumptions directly, because markets are insufficiently (a) deep or (b) liquid for these risks eg mort,expenses,persistency
2. Use some market-consistent indicators to det assump:
   
   • mortality: may derive from reinsurance risk premium rates
   • expenses: may derive from expense agreements available in market eg 3rd party administrators
   • with-profit EA contracts: traded as investment vehicle => possible current market price
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.

Question 8

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 8

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 on a regualtory 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;
   • OR represents the cost/loss in return caused 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
   • there may also be other frictional costs eg tax which affect CoC
   • Under SAM CoC = 6% fixed
3. Discount at the appropriate risk-free rate of return for each term, and sum to obtain 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.
4. Projection of future capital
   
   1. simple eg fixed percent of reserves, or
   2. complex, leading to:
      
      1. stochastic modelling and correlation matrices
      2. approximations eg expressing capital required req using a driver w/linear relationship to capital
         
         3. the size of the reserves
         4. the sum at risk

Question 9

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 9

Solvency capital requirements refers to:

1. Amt of capital that must be maintained above reserves.
2. Imposed by regulations to protect PH

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
2. based on a risk based measure, such as VaR (Value at Risk)

Question 10

Solvency capital requirements: relationship between reserves & solvency capital requirements

Discuss the relationship between the reserves and the solvency cpaital requirements

(1)

(1, 2)

Answer 10

1. Adequacy or reserves must be considered in relation to solvency capital requirements and not in isolation, and vice versa.
2. Relative balance between two varies between countries:
   
   • in some countrires, 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 relativesly prudent basis (relatively large margins), but with relatively small solvency capital requirement, which isn’t specifically related to the risks borned by the company.

Question 11

Solvency capital requirements: Value at Risk approach

What is the VaR approach to deriving solvency capital required by an insurer? (3)

Answer 11

VaR approach is

• risk-based solvency capital requirement approach,
• normally expressed at a min required confidence level over a defined period (eg 99.5% over 1 year)
• Under VaR approach, amount of capital needed:
  
  • is set so assets exceed liabilities in 1 years time, 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 12

Solvency capital requirements: Value at Risk approach

Outline the Projection method to deriving the risk-based solvency capital required by an insurance company.

(6)

Answer 12

Projection method:

• supervisory balance sheet=> market consistent approach
• conduct stress tests/shocks 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 liabitlities 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
• eg A=100 L=80 Surplus=20
  
  • Stress A=85 L=76 Surplus=9 => Cap req = 20-9 = 11
• Assets = Liabilities + Avail Capital
• Avail Capital = Required Capital + Free capital

Question 13

Solvency capital requirements: Value at Risk approach

Outline the Run-off method to dervicing the risk-based solvency capital required by an insurance company.

(4)

Answer 13

Run- off method:
* Amount of capital needed @ outset to ensure liabilty is covered until the last policy terminates
* NUB is ignored
* Stress testing to det cap req for each risk in isolation
* Scenario testing difficult to perform

Question 14

Solvency capital requirements: Value at Risk approach

Outline the method to Aggregate Capital requirements

(6)

Answer 14

Aggregate capital requirement

• for individual stress tests done, combine capital required over all risk factors eg via correlation matrix, copula
• Take into account diversification benefit that exists bet risks
  
  • Neg correlation => risks unlikely to occur at the same time
• 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=> copulas may also be use
• Set capital required to cover a 1 in 200 year event per year 99.5% CI
• Additional capital may be needed across individual risks to cover any
  • non-linearity (1% increase in shock <> 1% change in cap required)
  • non-seperability (events happen together > if happen seperately)

Question 15

Solvency capital requirements: Value at Risk approach

Non- linearlty and Non-separability of risks 4

Answer 15

• Combinations of certain subsets of risk may lead to increased cap req when combined than individually.
• Linearity req that req cap is linear function of the risk driver
  
  • eg -1% int => +1% req cap but this is not lnear
  • Guar=3.8%, int 4%=>3% =>+ liab high => large increase in req cap
  • but int 5%=4% => small incre in liab=> small incr in req cap
• Non-Separability
  
  • If events occur together combined impact is worse than if they occur separately
  • eg longevity and expense risk on annuities => pay higher expenses for longer
• Adj agg cap req upwards to account for these effects

Question 16

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 16

For solvency capital requirements, stochastic models are typically used:

• a real-world asset model would be used, which should be arbitrage free
• in particuar, 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
• sometimes advanced techniques needed to ensure good fit of data to estimate mean, though, important to remember thatn even with a good fit of data around the mean, this is not the part of the distribution we’re interested in for VaR

Question 17

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

Features of passive valuation approach (3,4)

Answer 17

Passive valuation approach uses a:
* valuation method that’s relatively insensitive to changes market conditions
* valuation basis which is updated infrequently
* eg net premium approach for liab valuation is not as sens to yield changes

Features of passive valuation approach:
* assumptions may be locked in from inception
* mortality/expense inflation assumptions rarely change
* assumptions remain unchanged from those used when policy first written and liability first determined
* non-eco assumption change when experience worsens
* in order to recognise related loss and need for higher reserves eg mort
* assets at book price
* possibly with amortisation/write down over time.
* thus ignoring market price change impacts, which would be suitable only if valuation of liabilities is also largely ignoring market conditions
* eg valuation interest rate locked in, or net premium valuation basis used
* simplified approach for solvency capital requirement
* eg holding presecribed % of base liabilities

Question 18

State 3 advantages of passive valuations (3)

Disadvantages of passive valuation approach (4)

Answer 18

Advantages of passive valuation approahces are that they:

• easier to implement
• involve less subjectivity
• results in relatively stable profit emergence, to extent that it’s used for accounting purposes

Disadvantages of passive valuation approahces 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

eg stock market crashes => book value of assets will be overvalued relative to value if sold in market today

Question 19

Define what is meant by an active valuation approach ( 3 )
Adv 1 and Disadv 5

Answer 19

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 market consistent valuation for both assets/liabilities, and risk based capital approach to solvency capital requirements

Advantages of active approach:
* 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.

Disadvantages of actuve valuation approach

• More volatile results
  
  • implications due to procyclicality
  • adverse equity market conditions => active approach using risk based capital would indicate higher capital requirements needed. To reduce this requirement, companies would have to sell equities, which itself could exacerbate the market conditions.
• Systematic risk
  
  • since this would be case for all insurers
  • regulators prohibit valuation approach under certain conditions to avoid systematic risk
• More complex
• More time consuming
• More costly

Question 20

In practice, what valuation approach would we expect between active and passive? (3)

Answer 20

• 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 approach using
    
    • net premium valuation for liabilities and
    • market value of assets
    • …could experience greater volatitlity of results than one using market consistation valuation for both.

Question 21

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 21

1. Reserve must be sufficient to meet all future liabilities
2. Prudent valuation of future liabitlities 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 approximations 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