Chapter 22 Reserves & solvency capital requirements

Question 1

Calculating reserves: reasons/purposes

Briefly list some of the reasons for calculating reserves (7)

Answer 1

• Determine liabilities for published accounts
• Determine liabilities for supervisory solvency
• Determine liabilities for internal management accounts
• Estimate cost of claims incurred in recent periods, hence provide base for future estimation
• Value insurer for merger or acquisition
• Influence investment strategy
• Assist with assessment of reinsurance arrangements

Question 2

Calculating reserves: various basis/important factors

Briefly describe the basis/key points to consider when setting/calculating reserves for the following exercises

• published accounts (5)
• solvency/statutory accounts (2)
• internal management accounts (5)
• for investment strategy/reinsurance assessment (1)

Answer 2

• Published Accounts:
  
  • should regard
    
    • legislation and
    • accounting principles of region.
  • consider
    
    • whether going concern,
    • whether true and fair view and
    • whether best estimate or other basis
• Solvency Accounts:
  
  • consider regulator rules.
  • may require break-up or run-off basis/going-concern basis
• Internal Management Accounts:
  
  • agreed with insurer.
  • may want to be realistic
  • will want to look at profitability, solvency, claims and exposure, expenses, reinsurance
• Investment Strategy and Reinsurance Assessment:
  
  • typically best estimate

Question 3

Health ins reserves: intro, long-term contracts

Briefly give an overview of the various things healthcare insurers may hold reserves for, and what methods maybe used to estimate them (5)

Consider

• CI policies (2)
• Policies providing annuity/income-type benefits (4)

Answer 3

• In most long-term insurance, benefit amount is known once claim is filed/submitted
  
  • ​most of these provisions held are for futre claims, acknowledging that a level premium pays cover of increasing probability of claim
  • actuaries may use deterministic or stochastic models to estimate potential claims outgo and set provisions.
• For CI
  
  • insurer can hold a reserve for claim that has been notified but not settled using amounts in policy doc,
  • and increase with inflation where appropriate
• For income benefit (annuity type contracts),
  
  • period for which payments may carry on is not known
  • can use statistical methods
  • case estimates can be used only for small volumes of important claims whereby claims manager estimates likely claim duration

Question 4

Health ins reserves: types, long-term contracts, intro

List the various types of reserves which may be found for healthcare insurance contracts which are long-term (12)

Answer 4

• reserves for in-force policies
  
  • typically discounted value of future expected claims, expenses and premium cashflows
• claims reserves
  
  • incurred but not reported reserves (IBNR) eg when policyholders didn’t know they had cover and logged claims late
  • reported but not fully settled reserves (RBNS) eg disability claims, LTCI insurance claims
• options reserves additional costs set aside in case a particular option is in the money at exercise date
• investment mismatching reserves (sometimes a regulatory requirement)
• for group contracts
  
  • unearned premium reserves (UPR) and
  • unexpired risk reserves (URR)

Question 5

Health ins reserves: intro, short-term

Briefly give an overview of the various things healthcare insurers may hold reserves for, and how what methods maybe used to estimate them (5)

Answer 5

Short-term healthcare contracts ie PMI, are indemnity:

• claim amount amount not known with certainty until course of treatment is complete.
• statistical approach is used to estimate amount of claim.
  
  • although certain large claims will warrant case-by-case reserving.
  • this involves calculating expected total claim amounts for outstanding claims based on relevant past experience
  • each claim is unique in that many different claim causes can arise, so cost of treatment can vary considerably.

Question 6

Health ins reserves: types, short-term

What are the main prospective and retrospective reserves for short-term healthcare contracts (2)

Answer 6

• Retrospective: Unearned prem resrv (UPR)
• Prospective: Unexpired risk reserve (URR)

Question 7

Health ins reserves: types, short-term

Briefly describe the main prospective and retrospective reserves for short-term healthcare contracts

UPR (4)

URR (3)

Answer 7

• Retrospective: Unearned prem resrv (UPR)
  
  • balance of premium received but period of insurance has not yet expired
  • (proportion outstanding risk)*(risk related premium)
  • premium covers claim payments, initial expenses, other expenses, profit.
  • apart from initial expenses, all other parts earned with incidence of risk i.e. risk premium
• Prospective: Unexpired risk reserve (URR)
  
  • reserve for UPR where premium is inadequate
  • UPR = m% of risk related premium where m% is the remaining percentage of the period
  • if UPR is inadequate, consider what else is needed, esimate expected loss ratio

Question 8

Health ins reserves: types, short-term

List the various types of reserves which may be found for healthcare insurance contracts which are short-term other than the UPR, and URR (9)

Answer 8

• Notified Outstanding Claims Reserve (NOCR) notified to insurer; not fully settled
• ​Incurred But Not Reported (IBNR) Reserves
• Incurred But Not Enough Reported (IBNER):
  
  • an adjustment to NOCR
  • eg not enough detail submitted during claim process
• Equalisation Reserve: held if current year is atypical; helps to smooth profits
• Catastrophe Reserve funds set aside just in case of future catastrophe
• Claims in transit reserve: reported but not assessed/recorded; i.e. in the pipeline
• Investment Mismatching Reserves, may be a regularoty requirement

Question 9

Reserve calcs: primary methods to calc health ins reserves

What two primary methods are used to calculate reserves? (2)

Which method is used in practice? (4)

Answer 9

Two primary methods to calculate reserves:

• Statistical Estimates
• Case Estimates

Method used depends on

• product characteristics, and
• purpose of exercise, and
• may be split into a
  
  • technical part (assessing actual value of pmts),
  • and a judgement part (deciding on level of margins)

Question 10

Reserve calcs: case estimates, overview

What do we mean by using ‘case estimates’? (1)

What is the key requirement/downside to using case estimates? (1)

What factors will the claims manager/assessor consider when making case estimates? (6)

Answer 10

Case estimates meaning

• Claims manager will inspect claim and estimate ultimate outgo.
• Claim must be reported before case estimate can be used

Will consider the following:

• procedure type and cost,
• hospital to be used,
• name of surgeon,
• policy coverage,
• age/gender/past claims history,
• current medical inflation

Question 11

Reserve calcs: case estimates, advantages disadvantages

Give the advantages (3) and disadvantages (6) of using case estimates to estimate reserves

Answer 11

Advantages:

• Only approach that makes use of all known data on oustanding claims
• Experienced claims assessor can allow for the various qualitative factors that can influence a claim
• Useful when statistical methods are unreliable

Disadvantages:

• May be time consuming and expensive, especially if there are plenty of outstanding claims
• Requires clinical expertise;
  
  • subjective
  • difficult to check
• Difficulty of accounting for inflation
• Only works for reported cases; IBNR reserves still need different method for estimation

Question 12

Reserve calcs: stat estimates, intro

Under what circumstances is the use of statistical methods most appropriate? (3)

What data source is most often used when using statistical methods to estimate claims? (1)

Answer 12

Appropriate for

• particular types of homogeneous claims where portfolio is
  
  • large enough and
  • is deemed to have stable experience.

Data used

• most statistical methods work from tabulations of claims that have recently been paid.

Question 13

Reserve calcs: stat estimates, description

Outline the overall procedeur involved in estimating outstanding claims using statistical methods (12)

Answer 13

Overall method

• claims are assessed en masse and statistical methods estimate outstanding claims for cohorts based on
  
  • historical trends and patterns,
  • and adjusting for known or anticipated future changes.
• assumptions are made about
  
  • the stability/smoothness of claim development and
  • that past patterns will continue into the future.
• statistical distribution is then fit to past experience
  
  • premium is generally better exposure unit than man-years.
  • current claim provisions derived by applying relevant premium, adjusting for trends
• portfolio might be split by
  
  • contract type, distribution channel, location, etc.
• can reserve for IBNR (incurred but not reported)

Question 14

Reserve calcs: stat estimates, main methods

Briefly list/descibe the main methods through which to derive of statistical estimates of outstanding claims (4)

What kind of variations may exist within the above methods of statistically estimating outstanding claims? (8)

Answer 14

Four methods of statistical estimate:

• chain ladder,
• average claim cost,
• loss ratio,
• blends

Main variations may exist with regards to the following:

• past inflation,
• claim cohort,
• different grossing up factors,
• choice of exposure,
• claim settlement expenses,
• hospital discounts,
• reinsurance recoveries,
• inflation assumptions

Question 15

Basic chain ladder assumptions

Give an overview of the basic chain ladder method of estimating

Answer 15

• Uses development ratios weighted by cumulative claim values. Applied to unadjusted paid claims during treatment year.
• Many variants of this method exist

Question 16

Reserve calcs: assumptions, basic chain ladder

What are the key assumptions which underlie the basic chain ladder method of estimating reserves? (4)

Answer 16

• Assumes amount of claims paid in each development year from each origin year is a constant proportion of the total claim amount from that origin year.
  
  • ie claims/payments (P_i;j) (in monetary terms) in each development month/year (i) are constant proportion of total for treatment in that origin month/year (j) (in monetary terms)
• BCL assumes past inflation continues into the future.
  
  • Inflation-adjusted BCL can be used.

Question 17

Reserve calcs: steps, basic chain ladder

Outline the key steps involved in using the basic chain ladder approach to estimating reserves (13)

Answer 17

• Determine
  
  • incremental run-off triangle
  • then cumulative run-off triangle
• Development factor
  
  • ​r_i = SUM_{over all j} (P_i;j) / SUM_{over j<span> to </span>n-1} (P_i-1;j)
  • (i.e. per column in cumulative run-off triangle)
• Ultimate development factor:
  
  • f_i = PRODUCT_{over k, from i to n} ( r_k)
• Proportion paid =1/f_i
• Proportion outstanding = 1-1/f_i
• Ultimate loss U_j = SUM_{over all i} ( P_{i;j x} f_n-j )
• IBNR_j= U_j - SUM_{over i} (P_i;_j)
• Sensitive to P_0;j (So may need adjustment for number of payment runs in a month)
• Retrospective IBNR
  
  • Can use to check actual IBNR and determine if previous IBNR estimate was close enough; IBNR now + claims payments since

Question 18

Reserve calcs: steps, triangles, basic chain ladder

In the context of a table of claims, what do we meant by an incremental triangle (2) and cumulative triangle (2)?

Answer 18

Incremental Triangle:

• treatment months as rows and development months as columns.
• can assume that all claims are fully settled at end of certain month after treatment (e.g. 3 months)

Cumulative Triangle:

• shows cumulative claims paid by each development month.
• simply sum subsequent amounts in incremental triangle

Question 19

Reserve calcs: steps, development factors, basic chain ladder

In the context of a table of claims, what do we meant by development factors? (3)

How do we calculate the ultimate development factors? (2)

How do we calculate the proportion of total claims paid from each development month? (1)

How do we calcualte the proportion of outstanding claims for each development month? (1)

Answer 19

Development Factor:

• can be thought of as the expected increase in claims from one development month to next
• to calculate:
  
  • see example in notes.
  • sum amounts in month 1 and divide by same sum in month 0 etc.

Ultimate Development Factor:

• total expected increase in claims paid thus far to end of development period for all claims outstanding.
• simply multiply development factor of this month by all factors of subsequent months
• Proportion paid: = 1/ultimate development factor
• Proportion outstanding: = 1 – proportion paid

Question 20

Reserve calcs: steps, IBNR calculation, basic chain ladder

How do we calculate the IBNR using the basic chain ladder method, having caclulated the development factors necessary? (4)

What adjustments might be needed to the IBNR? (4)

Answer 20

IBNR Calculation:

• First need to calculate ultimate loss for each month.
• Ultimate loss = cumulative claims paid to date/relevant proportion paid percentage
• IBNR = ultimate loss – cumulative claims paid to date
• (claims paid is what’s paid. IBNR is what’s not paid yet)

Adjustment for IBNR may be needed for

• Inconsistent Number of Payment Runs
• IBNR is sensitive to amount of claims paid in month 0.
• If more/less payment runs in a month, amount in month 0 will change.
• Can scale down 5 weeks to 4 by x4/5 or similar adjustment

Question 21

Reserve calcs: steps, retrospective IBNR calculation, basic chain ladder

How might we perform retrospective calculations of the IBNR? (2)

Answer 21

Retrospective IBNR Calculation:

• Can calculate current IBNR, add back actual payments and compare to old IBNR
• Differences can be used to reconcile effectiveness of old IBNR estimate

Question 22

Reserve calcs: merits, Borhhuetter Ferguson, stat estimates,

Give an overview of the method behind the Bornhuetter Ferguson method of estimating oustanding claims (5)

Answer 22

Overview

• Combines estimate loss ratio with projection method (e.g. chain later)
• Determine initial method of ultimate claims from each treatment month using premium and loss ratios
• Multiply estimates by proportion outstanding (1-1/UDF). Then ad figures to claims paid to date to give estimate of ultimate loss for each treatment month
• Future Claims Development =
  
  • Premium x Estimate Loss Ratio x (1-1/UDF) = IBNR
• Ultimate Loss = IBNR + Claims Paid to Date

Question 23

Reserve calcs: steps, Borhhuetter Ferguson, stat estimates

Steps in calculating a reserve using BF method.

Answer 23

• Determine initial estimate of the total ultimate claims from each treatment month using premiums and initial expected loss ratios.
• Multipy these estimates by the proportion outstanding (1-1/f) determined from claims development table. These are estimates of the reserve for each treatment month.
• add these figures to the claims paid to date give an esitmate of the ultimate loss for treatment month.

Question 24

Reserve calcs: assumptions, Borhhuetter Ferguson, stat estimates

Assumptions underlying the Bornhuetter Ferguson method (3)

What key benefit lies in using this method to estimate oustanding claims? (3)

Answer 24

Assumptions

• underlying method is same as BCL.
• together with that the estimated loss ratio is appropriate
• this method could be viewed as using a Bayesian approach.

Key benefit

• It improves on the crude use of a loss ratio by taking into account information provided by latest development.

Question 25

Reserve calcs: stat methods, bootstrapping, overview

Explain boostrapping and what it is used for? (5)

Answer 25

• It can be used to estimate the variance of the IBNR reserve.
• Shows the extent to which a reserve can vary on either side of its mean.
• A reserve method is chosen and used to produce a fitted model for historical data.
• The residual values are re-sampled with replacement to generate a number of pseudo run-off triangles.
• These pseudo run-off triangles can then be used to estimate the distribution of IBNR values.

Question 26

Reseve calcs: stat methods, bootstrapping, assumptions, stat methods

Briefly list the assumptions underlying bootstrapping the basic chain ladder (4)

Answer 26

• the run-off pattern is the same for each origin period
• incremental claim amounts are statistically independent
• the variance of the incremental claim amounts is proportional to the mean
• incremental claims are positive for all development periods.

Question 27

Reserve calcs: stat methods, issues

What key issue(s) affects the accuracy of claim amounts estimated using statistical methods which have been covered? (3)

What causes the above-mentioned key issue(s) (4)

Answer 27

Biggest issues

• outstanding claims might be impaired by the errors, omissions or distortions in the data, which invalidate the underlying assumptions.
• these distortions however do not mean the statistical methods should not be used.

Cause of these data distortions

• external influences, such as inflation or changes in underlying nature of risk
• internal influences such as underwriting, claims settlement or recording procedures or reinsurance arrangements
• changes in the type of business attracted in each treatment class
• random fluctuation or large claims in a small portfolio.

Question 28

Pricing reserves: relationship between pricing and reserving

Discuss the relationship between pricing and reserving assumptions

(1,1)

(1,2)

Answer 28

• Premiums for pricing 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.

Question 29

Best estimate reserves: intro, uses

What do we usually use best estimate reserves for? (3)

Answer 29

We usually use best estimate reserves when

• management want best estimate of company’s financial performance e.g
  
  • if insurer is to be sold
  • directors to award key staff for specific contributions to overall company growth

Question 30

Best estimate reserves: key characteristics

What are the key characteristics of best estimate reserves? (5)

Answer 30

Key factors to consider:

1. assumptions use company best estimate of future experience, with no margin, and basis is closer to new business prices, without efect of undewriting (ie most select lives assumed to now be ultimate)
2. all experience items would be allowed for explicitly (expenses, persitency, investment return, mortality)
3. no eliminitation of negative reserves
4. cashflow method is used for estimates of reserves needed, case estimates may possibly be used
5. can use cashflow method, possibly case estimate, amounts needed to meet future claims, expense and tax outgo, netted against premiums and investment return
6. gross premium formula for non-linked business, with explicit best estimate assumptions for all variables and permitting negative values; likely to be unrealistic because doesn’t allow for discontinuance (and losses/profits therefrom)

Question 31

Solvency: statutory/solvency reserves, principles

Briefly list/discuss the principles that need to be met when setting solvency/statutory reserves (14)

Answer 31

General

1. Principles affected by professional guidance and supervisory regime
2. Appropriate approximations and generalisations allowed

Assets

1. Should account for nature, term and valuation method of corresponding assets by policy

Liabilities/valuation method

1. Amount of reserves should be sufficient to meet all liabilities
2. Amount of reserves should be suitably prudent and consider:
   
   1. Guarantees, options, expenses and commission, take credit for future contractual premiums
3. A prudent valuation is not Best Estimate, but should include a margin for adverse experience
4. Elements of statistical basis (demographic, persistency, expenses) chosen prudently, regarding territory and administrative costs and commission
5. Where valuation method defines in expenses amount in advance; this shold not be less than company’s own prudent estimate therof
6. EXTRA: allowance for expenses should allow for possibility of ceasing to write new business

​Discounting and calculation

1. Rate of interest chosen prudently, accounting for currency, yields on existing assets and yields on sums invested in future
2. Method of reserve calculation should recognise profit in appropriate way over policy duration
3. No arbitrary discontinuities due to changes in valuation base

​Disclosure

1. Should disclose methods and bases used in valuation

Question 32

Solvency: solvency capital, intro

What do we mean by solvency capital requirements? (2)

What purpose does solvency capital serve? (2)

Give 2 broad areas of risk where solvency capital can protect policyholders (2)

What equation must hold true for a healthcare insurer to demonstrate solvency? (1)

Answer 32

Solvency capital is

• an additional amount (capital) over and above reserves/technical provisions
• insurance supervisors require that an insurer maintain at least a specified level of solvency capital in addition to reserves or technical provisions held

Purpose of solvency capital: this solvency capital can be seen as

• providing an additional level of protection to policyholders
• protection against adverse future experience

​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).

To demonstrate solvency:

• admissible assets > best estimate reserve + margins + solvency req

Question 33

Solvency: solvency capital, framework, intro

How might the calculation of the solvency capital amount be specified? (2)

Answer 33

Calculation of solvency capital: level of SCR under regulation may be specified

• as a formula
• based on a risk based measure in a risk-based environment

Question 34

Solvency: solvency capital, framework, description

Briefly elaborate on how solvency capital may be specified using the following methods

• formulaically (1)
• using risk based measures (5)

Answer 34

Calculation of solvency capital: level of SCR under regulation may be specified

• as a 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 in a risk-based environment:
  
  • solvency capital depends will depend on the risks of the insurer
  • may be based on a risk measure such as VaR.
    
    • a risk capital charge is applied to each risk element, multiply by risk factor
    • capital risk charges can be reduced by reinsurance and managed care arrangements
    • Total solvency requirement allows also for diversification of risks

Question 35

Solvency: SCR calc, VaR approach, intro

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

Answer 35

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 confidene level, eg 99.5%, over a given defined eriod, 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% confidencec=> only 0.5% expected probability of loss higher than R10 mil over next year

Question 36

Solvency: SCR calc, outline, VaR and run-off approach

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

(6)

Answer 36

Supervisory balance sheet subject to stress tests:

• 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.
  
  • eg calculate R100mil capital required to cover mortality mortality risk
• 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, etc => currently too computationally difficult, so seperate stress test used instead

Aggregate capital requirement

• for individual stress tests done, combine capital required over all risk factors, allowing appropriately for interactions, eg via correlation matrix
• 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
• 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 37

Solvency: SCR calc, use of stochastic models

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 37

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 technuiqes 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 38

Solvency: SCR calc, non-linearity and non-separability

Combining separate risks will lead to higher SCR than if if risks were combined using diversification matrices.

What causes this? (2)

Answer 38

• non-linearity of individual risks
• non-separability of individual risks

Question 39

Solvency: SCR calc, linearity and non-separability of risks

What is linearity? (1)

What is non-separability? (1)

Answer 39

Linearity

• the capital required is a linear functions of the risk drivers

Non-separability

• refers to situations when if two events happen together, the combined impact is worse than if they happened separately.

Question 40

Solvency: relationship between reserves and SCR

Discuss the relationship between the reserves and the solvency cpaital requirements

Answer 40

• when considering the adequacy of reserves to be set up it is important to do this within the context of SCR and not in isolation.
• similarly, the adequacy of SCR cannot be looked at in isolation of the reserving requirements
• 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 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 41

Market consistent reserves: intro

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

Answer 41

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
• theoretically the price someone would charge for taking responsibility for liability, in a market in which such liabilities are freely traded

Question 42

Market consistent reserves: assets and liabilities

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

Answer 42

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. 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 cashflows exaclty

Question 43

Market consistent reserves: investment return

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

Answer 43

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 44

Market consistent reserves: illiquidity premium, intro

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

Answer 44

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 45

Market consistent reserves: illiquidity premium, taking credit

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 45

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 regulgation, 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.

Question 46

Market consistent reserves: risk margin

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 46

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
   • with-profit end contracts: traded as investment vehicle => possilbe 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. Overll 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 47

Market consistent reserves: risk margin, 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.

(1,3)

(2,4)

(3,2)

(4,3)

Answer 47

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 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; 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.
   • 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 may be
        1. simple eg fixed percent of reserves, or
        2. complex, leading to:
     5. 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

Question 48

Embedded value: definition

Define embedded value (4)

Answer 48

• Starting point for realistic assessment of value of insurer
• Embededed value is defined as sum of:
  
  • shareholder-owned share of net assets
  • present value of future shareholder profits from existing business, including release of shareholder assets
• EV essentially recognises
  
  • value of assets in excess of reserves
  • and value to shareholders of future margin releases from reserves

Question 49

Embedded value: uses

Why might we need to calculate embedded values? (5)

Answer 49

May need embedded values for

• to include in financial statements/published accounts as supplementary info
• to establish a value of the business, for internal purposes
• to assess the major part of an appraisal value for sale or purchase
• to analyse future surpluses for RI embedded value financing
• to assess growth in EV for the payment of bonuses to staff or salespeople

Question 50

Embedded value: calc, shareholder owned share of assets

Shareholder owned share of net assets (6)

Answer 50

• Net assets are defined as the excess of assets held over those required to meet liabilities.
• These assets may be valued at
  
  • market value or
  • may be discounted to reflect lock in, e.g. if they are required to be retained within the fund to cover solvency capital requirements.
• Net assets may have to be invested cautiously to ensure that solvency capital requirements are met and
  
  • may as a result achieve lower return than could be achieved with a less constrained investment strategy,
  • and so they will be worth less than their market value to the shareholders.

Question 51

Embedded value: calc, PV of future shareholder assets

Briefly outline the calculation for the PV of future shareholder assets (3)

Answer 51

By PV of future shareholder profits

• similar to conducting profit test, excluding certain elements (eg new business expenses)
• project future CFs on existing business to estimate future profits
• allowing for tax
• discount future profits at appropriate discount rate (shareholder required return) to determine PV

Question 52

Embedded Value: calc, PV of future shareholder assets, various products

List components that make up the present value of future shareholder profits from existing contracts, for the following types of business:

• conventional without-profits (3)
• unit-linked (2)
• with-profits (1)

Answer 52

Conventional without-profits business

• present value of future premiums plus investment income, less
• claims and expenses, plus
• release of supervisory reserves and required solvency capital

Unit-linked business

• present value of future charges less expenses and benefits in excess of unit fund, plus
• investment income earned on, and release of, any supervisory non-unit reserves and required solvency capital

With-profits business

• present value of future sharheolder transfers, for example, as generated by bonus declarations

Question 53

Embedded value: appraisal value, definition

Define appraisal value (2)

Answer 53

Embedded value is starting point for value of insurer, but doesn’t allow for future new business.

Appraisal value is sum of:

• embedded value (shareholder share of net assets + PV future profits from existing business)
• goodwill, which represents an estimate of the present value of future shareholder profits from future new business

Question 54

Embedded value: assumptions

What is the key determinant of assumptions used for EV? (3)

What 2 different kinds of basis do we need for EV calculations? (2)

Answer 54

Key determinant of assumptions used for EV is

• purpose for which EV is needed
• insurer offering itself for sale likley use best estimate/realistic (no margins)
• insurer purchasing may use cautious, wth margins

We need 2 basis for EV calculations

• Reserving basis:
• Projection basis:

Question 55

Embedded value: allowing for risk, intro

What risk do we need to allow for on EV calculations for the 2 different basis used? (2)

Answer 55

Allowing for risk in EV cal

• Our reserving basis must use supervisory regulations (which will inherently include risk, however the projection basis needs to also allow for risk adequately.
• Risk allowed for in projection basis is for unpredictability of profit emergence for life insurance business

Question 56

Embedded value: allowing for risk, approaches

What approaches may be used to allow for risk we need to include for the 2 basis needed for the EV calc? (3)

Answer 56

Approaches used to allow for risk

• RDR for future profit streams will traditionally reflect risk. All things equal, increasing RDR => increasing risk
• Stochastic approach: would highlight range of possible values profits might take
• Market consistent approach: using RDR as discount rate, then risk margin deducted from EV to reflect non-investment risks e.g using cost of capital approach to be covered in next chapter

Question 57

Embedded value: compared to Best Estimate

What are the key differences between Embedded Values and Best Estimate Values?

Best estimate basis (3)

Embedded value basis (3)

Answer 57

Both basis may use realistic assumptions, but try to focus on different things.

Best estimate basis

• present liability calculated per policy using realistic assumptions
• sum over all PHs compared with total aset value to give measure of realistic solvency (measure of PH benefit security)
• but change in retained profit each year can also be used to give measure of profit as extra piece of information

Embedded value basis

• consider CFs across portfolio each time period, rather than PV for each PH. Focus of calculation is SH profit
• takes full account of cost of capital in value of SH transfers, because each year’s transfer has to be made from profits that arise in excess of supervisory reserves held (increase in supervisory reserves will postpone emergence of profit for SHs, at least for without profit business and thereby give reduced PV when discounted at the RDR)

Question 58

Valuation approach: passive valn approach, intro

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

Features of passive valuation approach (4)

Answer 58

Passive valuation approach uses a:

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

Features of passive valuation approach:

• assumptions may be locked in
  
  • 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
• 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 59

Valuation approach: passive valn approach, advantages disadvantages

State 3 advantages of passive valuations (3)

Disadvantages of passive valuation approach (4)

Answer 59

Advantages of passive valuation approahces 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 approahces are that they:

• can become outdated
• relatively insensitive to chnages 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 60

Valuation approach: active valn approach, intro

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

Answer 60

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
• 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.

Question 61

Valn approach: active valn approach, disadvantages

What are the disadvantages of using an actve valuation approach? ( 5 )

Answer 61

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 may amend valuation approach under certain conditions to avoid systematic risk
• More complex
• More time consuming
• More costly

Question 62

Valuation approach: approach used in practice

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

What are the implications of point 1 above?

Answer 62

• 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 63

Comparing different basis

Compare the following types of basis which may be used to calculate reserves

• Reserving basis (2)
• Pricing basis (determining profitability) (3)
• Statutory basis (2)
• Embedded value basis (2)

Answer 63

• Reserving Basis:
  
  • generally prudent.
  • depends on purpose.
• Pricing Basis (or determining profitability)
  
  • may be best estimate/fairly realistic, although it will depend on the specific purpose
  • can project profits on best estimate, but allow for risk in risk discount rate.
  • prudence is to understate value of future profits with a high discount rate
• Statutory Reserve:
  
  • prudent!
  • if pricing is prudent, may use same assumptions
• Embedded Value
  
  • EV accounts for cost of capital…
  • …best estimate usually will not

Question 64

Modelling considerations when setting reserves

Briefly describe modelling considertaions to be made when setting reserves (5)

Answer 64

• Can use
  
  • deterministic or
  • stochastic models
• Sensitivity Analysis:
  
  • can be used to determine margins.
  • can also assess need for global reserves.
  • basis may be prescribed (in which case method for determining margins required would already be known)