Supervisory reserves and capital requirements

Question 1

What are the thee methods for calculating reserves

Answer 1

1. gross premium valuation method
2. net premium valuation method
3. non-unit reserve method (variation of GP)

Question 2

Market-consistent approach (as apposed to prudent approach)
13 steps

Answer 2

1. Project cashflows - benefits and expenses, assuming these amounts are certain
2. cashflows are discounted at the RFR
3. How do we determine RFR - each cashflow at time t discount at the GRY of gov bond with duration t
4. or.. we could use the replicating portfolio approach
5. market value of portolio = value of liabilities
6. however, we need to make adjustments:
   - to reflect short term anomalies in market values
   - take credit for the fact the liabilities are long term and predictable and therefore take credit for the illiquidity premium by increasing discount rate
7. BUT - liabilities are not certain
8. Why are they not certain
9. Market value: price at which liabilities are sold
10. therefore, best estimate is to low, because purchaser need additional compensation for uncertainty
11. how can we allow for this uncertainty?
12. we can include margins in the assumptions
    market indicators can be used to get these:
    - difference between fixed interest and index linked bonds to get inflation assumption
    - TPA service fees could indicate the market value for expenses
13. or we can use best estimate and then determine an overall risk margin using the cost of capital approach

Question 3

Purposes of reserves

Answer 3

1. Demonstration of solvency
2. investigate realistic / “the true” position of the life company

Question 4

Purposes of reserves

Demonstration of solvency

Answer 4

• involve a minimum valuation standard
• to ensure that a life company is capable of meeting all of its guaranteed liabilities.
• Prudent assumptions since future experience in uncertain

Question 5

Purposes of reserves

Realistic / “True” position

Answer 5

• to quantify the “true” situation of the life company
• for internal management purposes to give a picture undistorted by the various margins / prudence inherent in the solvency valuation
• to help determine the long-term sustainability of profit distribution rates
• help determine the realistic profitability of the company for the information of shareholders (etc) and management
• to assist in the general financial management

Question 6

Gross premium valuation method

Answer 6

• simple valuation method
• valuing liabilities that explicitly value future office premiums payable, expenses and claims (including discretionary benefits)
• Reserves = PV(expected future claims) + PV(expected future expenses) -PV(expected future premiums)
• contracts are priced so that the present value of the premiums exceeds that of the claims and expenses
• reserves should theoretically be negative at the start of the policy life
• any prudence in the reserves (relative to the pricing assumptions) may lead to reserves being positive even at policy commencement
• the value of future benefits plus expenses will almost always exceed premiums at a stage
• giving a smooth progression of reserves
• start negative and finish with a value equal to the final benefit payment

Question 7

Non-unit reserves

Answer 7

non-unit reserve is defined as the amount required to ensure that the company is able to pay claims and meet its continuing expenses without recourse to further finance

• discounted cashflow method is used
• Why? greater variety of patterns of cashflow
• requirement for both a unit and non-unit reserve
• present value of the excess of non-unit outgo (eg expenses, benefits in excess of the unit fund) over non-unit income (eg charges, unallocated premiums).
• Could be negative - but depends on regulatory regime

Question 8

unit reserve

Answer 8

• part of the reserve that a life insurance company needs to set up
• in respect of its unitised contracts.
• The unit reserve represents its liability in terms of the units held under the contracts
• Caluclation: number of units multiplied by their “bid” value

Question 9

Non-unit reserves

Prudential valution

Answer 9

• consider the year-by-year incidence of the various components of the non-unit cashflows
• to determine if and when a non-unit reserve is required.
• project forwards its non-unit cashflows on the reserving basis.
• may need to be performed on a policy-by-policy basis
• Calculated as follows:

Step 1: start with the last projection period in which the net cashflow becomes negative
Step 2: amount is set up at the start of that period which is sufficient, allowing for earned investment return over the period, to “zeroise” the negative cashflow.
Step 3: amount is then deducted from the net cashflow at the end of the previous time period
Step 4: process continues to work backwards towards the valuation date, with each negative being “zeroised” in this way
Step 5: if the adjusted cashflow at the valuation date is negative then a non-unit reserve is set up equal to the absolute value of that negative amount.

Question 10

Non-unit reserves

Best estimate valuation

Answer 10

the calculation would value all future non-unit cashflows, ie
* would not disregard cashflows occurring after the last projection period in which there is a net outflow,
* no other restrictions
* generally the case that negative non-unit reserves can be held.

Question 11

Negative non-unit reserves

Answer 11

A negative non-unit reserve can be held for a policy under which future charges are expected to be more than sufficient to meet future non-unit liabilities (including expenses).

Negative non-unit reserves thus reduce the total reserves required by taking advance credit for the expected present value of these future positive cashflows.

negative reserve represents a “loan” from other contracts which have positive non-unit reserves

“loan” will be repaid by the emerging future profits from the policy for which the negative non-unit reserve is held

Contraints;
* sum of the unit and non-unit reserve for a policy should not be less than any guaranteed surrender value
* future profits arising on the policy with the negative non-unit reserve need to emerge in time to repay the “loan”
* there are no future negative cashflows for the policy After taking account of the future non-unit reserves
* the sum of all non-unit reserves should not be negative
* The negative non-unit reserves should be determined prudently
* Negative non-unit reserves need to be permissible under local legislation
* There should be adequate non-unit surrender penalties to ensure that the value of the future cashflows is not lost on a surrender.

Question 12

Calculating negative non-unit reserves

Answer 12

(1) Project the expected future non-unit cashflow from the policy, ie income from charges less outgo.
(2) Identify the last (most distant) cashflow (whether positive or negative).
(3) Set the reserve as an amount needed to meet that cashflow at that point in time (even if the cashflow is positive set the non-unit reserve as a negative amount).
(4) Check that the total reserve (ie unit plus non-unit) is greater than the surrender value (ie unit reserve less surrender penalty).
(5) Move back to the next previous cashflow, discount the reserve and then subtract from the reserve the new cashflow at the earlier time period. Repeat step (4).
(6) Carry on repeating the process working backwards over time to the valuation date.
(7) This will give the required non-unit reserve.

• Allow for prudence
• assuming psitive cashflows are lower than expected
• interest rate higher than expected (for discounting)
• survival rates are lower than best estimate

Question 13

Features of the gross premium method

Answer 13

• explicit allowance is made for expenses
• an explicit allowance can be made for vested and expected future bonuses
• the future premiums valued are the actual (“office”) premiums expected
• any differences between the pricing and valuation bases will immediately be taken as profit or loss
• reserves may initially be negative for non-linked business, partly due to initial expenses and partly due to capitalising the expected future profit
• the reserves tend to be quite sensitive to changes in basis.
• does not take withdrawals into account (formula approach)

Question 14

Net premium valuation method

Answer 14

Present value of expected future benefit outgo
less Present value of future net premiums

The net premium is the premium which the company would charge from policy inception to cover the initial guaranteed benefits only

Features:
* it is simple (the formula used, the data required)
* it makes no explicit allowance for future expenses
* it makes no explicit allowance for future bonuses
* for regular premium business, the reserves are relatively insensitive to changes in the valuation basis.

Can make implicit allowances:
Expenses: say that the future annual expense on a policy is less than the difference between the net premium that the company is valuing with this method and the office premium which it will actually receive.
Bonuses: implicit allowance for future bonuses can also come from this margin. usually also necessary to use a low valuation rate of interest in order to make a broadly suitable allowance for future bonus at all durations

Question 15

Explain why the net premium method is less sensitive to a basis change than the gross premium method.

Answer 15

When you do a GPV we essentially calculate:
EPV(Benefits + Expenses) - EPV (Premiums)
where the gross premiums are the future actual premiums payable under the policy.

For the NPV we calculate:
EPV(Benefits) - EPV (Net Premiums)
where the net premiums are assumed future premiums, to pay for the initial benefits only, calculated using the reserving basis assumptions for mortality and interest.

• When we change the reserving basis for the GPV, the gross premiums used in the calculation don’t change.
• When we do the same for the NPV, then the net premiums used in the calculation do change.
• So, if we reduce the valuation rate of interest, say, then both sets of reserves will increase.
• But the NPV will increase by less,
• because the net premiums themselves will have increased in size,
• compensating for some of the overall increase in the value.

Question 16

How does supervisory authority ensure that insurance companies have sufficient assets to cover their liabilities with a high degree of certainty?

Answer 16

1. requiring insurance companies to hold reserves calculated on a prudent basis
2. requiring a minimum level of solvency capital to be held
3. requiring a combination of prudent reserves and solvency capital to be held.

Question 17

Market-consistent valuation

Answer 17

1. To determine a market-consistent value of liabilities, future unknown parameter values and cashflows are set so as to be consistent with market values, where a corresponding market exists. Market values are also used for assets, if market prices exist. the approach is to project their expected future amounts and then discount these as if they were known and certain
2. Future investment returns are based on a risk-free rate of return, irrespective of the type of asset actually held, and the discount rates are also based on risk-free rates.
3. Risk-free rates may be based on government bond yields or on swap rates. It may be appropriate to make a deduction to allow for credit risk.
4. Under certain conditions, it may be possible to take credit for the illiquidity premium available on corporate bonds and thereby discount liabilities at a higher yield than the risk-free rate.
5. It may be difficult to obtain a “market-consistent” assumption for some elements of the basis, such as mortality, persistency or expenses, for which there is not a sufficiently deep and liquid market in which to trade or hedge such risks.
6. It is then likely that a risk margin would be added to the best estimate of the liabilities. This risk margin would reflect the compensation required by the “market” in return for taking on those uncertain aspects of the liability cashflows.
7. This could be done by adding a margin to each such assumption or by using the “cost of capital” approach.

Question 18

Two ways for calculating the market values of liabilities

Answer 18

1. Replicating portfolio approach: devise a portfolio of assets whose cashflows exactly replicate those of the liabilities, and then the current market price of this “replicating portfolio” becomes the market-consistent value of the liabilities
2. Discount cashflows at risk free rate

Question 19

Why can we take account for illiquidity premium in MCV

Answer 19

• derive the market-consistent discount rate from corporate bonds
• higher probability of default than government bonds.
• more volatile than government bond prices
• higher yield than risk-free (eg government) bonds
• Due to default risk and “illiquidity premium” to the yield
• extra return that investors require to compensate them for the risk of greater price volatility of corporate bonds
• may be possible to take credit for the illiquidity premium and thereby discount liabilities at a higher yield
• restricted to long-term predictable liabilities for which matching assets can be held to maturity
• not exposed to the risk of changing spreads on such assets
• still exposed to default risk

Question 20

market-consistent indicators for setting the assumptions

Answer 20

• Mortality: determined from the risk premium rates quoted by reinsurance companies
• Expense: determined by reference to expense agreements available in the market, eg from third party administration companies
• with-profit endowment assurances may be traded as investment vehicles, so there may be a current market price for these products as a whole

Question 21

“cost of capital” approach

Answer 21

1. project the required capital at each future time period determined according to the relevant regulatory basis. the amount required to be held in excess of the projected liabilities at each period.
2. projected capital amounts are then multiplied by a cost of capital rate. represent the cost of raising incremental capital in excess of the risk-free rate. frictional cost to the company of locking in this capital to earn a risk-free rate rather than being able to invest it freely for higher reward.
3. product of the cost of capital rate and the capital requirement at each future projection point is then discounted, using market consistent discount rates, to give the overall risk margin.
4. For some chosen regulatory frameworks the projection of required capital can be relatively straightforward. Capital = % of reserves
5. for others it can be complicated if the calculation of required capital itself requires projections, stochastic modelling and/or application of correlation matrices
6. Simplified approach: selecting a driver which has an approximately linear relationship with the required capital or its components. initial capital requirement can be expressed as a percentage of that driver, and the projected capital is then approximated as the same percentage of the projected values of the driver.

Question 22

Solvency capital requirements

Answer 22

• Insurance supervisory authorities normally require that life insurance companies establish a certain amount of solvency capital.
• This is to protect policyholders from a company reserving too little for their liabilities, and from the harmful effects of asset volatility.
• Supervisory reserving needs to be considered in conjunction with the solvency capital requirements, and vice versa.
• The relationship between reserves and solvency capital requirements varies between different countries and regulatory jurisdictions. Normally it will be one of two cases: · 1 = strong reserving, with a small solvency capital requirement 2 = weak reserving, with a large solvency capital requirement where weak reserving means a basis close to best estimate.
• The level of solvency capital required under regulation may be specified as a formula(1), or it may be based on a risk measure such as Value-at-Risk (VaR)(2).

Question 23

Value at Risk approach

Answer 23

• expressed at a minimum required confidence level (eg 99.5%) over a defined period (eg one year).
• supervisory balance sheet subject to stress tests on each of the identified risk factors, at the defined confidence level and over the defined period.
• Applying stress tests to each different risk factor gives a capital requirement for each separate risk in isolation
• separate stress tests need to be combined in a way which reflects any diversification benefits that exist between the various risks (ie the degree to which individual risks are correlated)
• done through the use of correlation matrices or by copulas, for example
• Other issue: non-linearity and non-separability of individual risks
• Typically stochastic models are used to quantify the capital requirements in relation to economic risks

Question 24

non-separability of individual risks

Answer 24

= the ways in which risk drivers interact with each other. Separate allowance needs to be made in the capital requirement calculation for these effects.
* non-separability refers to situations where if two events happen together, the combined impact is worse than if they had happened separately

Question 25

Passive valuation approach

Answer 25

• valuation methodology which is relatively insensitive to changes in market conditions and
• a valuation basis which is updated relatively infrequently
• net premium valuation approach for liabilities
• valuation of assets: historic cost or “book value”, possibly with amortisation
• non-economic assumptions are updated if experience worsens, in order to recognise the related loss and the need for higher reserves at that time
• Solvency capital requirements may be determined using a simplified approach such as holding a prescribed percentage of base liabilities

Advantages:
tend to be more straightforward to implement
involve less subjectivity
(to the extent that they are used for accounting purposes) result in relatively stable profit emergence

Disadvantages:
A passive valuation is at risk, by its very definition, of becoming out of date
For example, if the stock market crashes then the book value of the assets will be overvalued relative to their value if sold in the market today
valuation basis is changed infrequently then it may not have taken account of important trends
provides a false sense of security
Management may fail to take appropriate actions in response to emerging problems until too late

Question 26

Active valuation approach

Answer 26

• based more closely on market conditions, with the assumptions being updated on a frequent basis
• market-consistent valuation approaches for both assets and liabilities,
• and a risk-based capital approach to solvency capital requirements.

Advantages:
* more informative
* aids in understanding the impact of market conditions on the ability of the company to meet its obligations
*

Disadvantages:
results are more volatile
to be more complex than a passive approach
the calculations could take longer to perform
and be more costly.

Question 27

Combinations of active and passive approaches

Answer 27

• can result in a greater mismatch between assets and liabilities
• hence greater profits / losses or changes in free surplus when market conditions change
• active market value of assets and passive net premium value of liabilities
• then solvency might appear to change dramatically when in reality it hasn’t changed
• change in interest rates would change the market price of assets but would have little impact on the net premium valuation of liabilities