Chapter 22 Reserves & solvency capital requirements Flashcards

Question

Reserve calcs: stat methods, bootstrapping, overview Explain boostrapping and what it is used for? (5)

Answer 1

* 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.

Answer 2

* 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.

Answer 3

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.

Answer 4

* 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.

Answer 5

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

Answer 6

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)

Answer 7

**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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

**_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

Answer 12

**_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)

Answer 13

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

Answer 14

* non-linearity of individual risks * non-separability of individual risks

Answer 15

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.

Answer 16

* 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.

Answer 17

**_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

Answer 18

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

Answer 19

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)

Answer 20

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

Answer 21

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.

Answer 22

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.

Answer 23

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: 1. stochastic modelling and correlation matrices 2. approximations eg expressing capital required as simple formula based on drivers such as the size of the reserves and the sum at risk

Answer 24

* _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

Answer 25

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

Answer 26

* 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.

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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:

Answer 31

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

Answer 32

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

Answer 33

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)

Answer 34

**_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

Answer 35

**_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

Answer 36

**_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.

Answer 37

**_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

Answer 38

* 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.

Answer 39

* 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

Answer 40

* 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)

Chapter 22 Reserves & solvency capital requirements Flashcards

(64 cards)