Ch 23: Supervisory reserves and capital requirements 1

Question 1

Summary card

Answer 1

• Gross premium valuation method
• Net premium valuation method
• Valuing unit-linked policies

Question 2

Reserves: background

What are the 2 key fundamentally different purposes for calculating reserves? (2,3)

Answer 2

Reserves are mainly calculated to

1. demonstrate solvency
   
   1. ​to regulators, by meeting a min valuation standard, showing that the insurer is capable of meeting all guaranteed liabilities
   2. given uncertain future, valuation standards likely to require prudent assumptions; if FNB uses more best estimate assumption, additional solvency capital will be held to make the P(failing to meet L) acceptably small.
2. quantify the realistic position of a company which helps determine
   
   1. the long term sustainability of profit distribution rates which helps determine bonus declaration.
   2. realistic profitability of FNB for information for shareholders/management
   3. assist in general financial management of the FNB.

Question 3

Reserves: background

What 2 primary methods can be used for reserve calculations? (2,1)

Answer 3

The two primary reserving methods are

1. Gross premium valuation method
   
   • under unit-linked busines, special case of the gross premum arises where valuation of future non-unit cashflows may need a seperate method to identify and reserve for future negative CFs
2. Net premium valuation method

Question 4

Define the gross premium valution method ( 3 )

Answer 4

Calculates the value of a life insurance company’s liabilities that explicitly values

• the future office premiums payable,
• expenses & claims (with claims potentially including future discretionary benefits)

Reserves = PV(expected future benefit outgo) + PV(expected future expenses) - PV(expected future office premiums)

Question 5

Gross premium valuaiton method: Formula method

List the 5 key points surrounding the Formula method used for Gross Premium Valuations (5)

Answer 5

1. Method can often be expressed as a formula, eg for a without profits end:
   See picture below
2. CF approach (alternative method to formula approach)
   
   • Net CFs are calculated for each future point and discounted back.
   • Contract usually priced so office premiums > claims & expenses to make a profit
   • Therefore, reserves are theoretically negative at policy start , just before pmt of first premium/initial expenses
   • init expenses often higher than the first premium paid (for regular business), leading to reserves being even more negative
   • After contract start, no need to reserve for first premium/init expenses
   • however, any prudence in reserves (relative to pricing assumptions) may lead to reserves being positive even at policy commencement
   • 4. Cost of benefits and renewal expenses generally increase with policy term, but premiums remain level (for a reg premium, non-linked without-profits contract)
   • 5. Therefore over time V(future benefits + expenses) > premiums almost always except very early on in contract, giving a smooth progression of reserves, which start negative and finish with a value equal to the final benefit payment

Question 6

Gross premium vln mthd: unit-linked reserves

List the 2 key components of the liability that must be considered when valuing a unit-linked policy (2)

Answer 6

1. unit-reserve
   
   • part of reserve insurer sets up for its unitised contracts
   • represents liability in terms of the units held under these unitised contracts
   • calculated as number of units x ‘bid price’ of units i.e. price insurer is contractually obliged to buy units off policyholders
   • 2. non-unit reserves
   • part of reserve insurer sets up for its unitised contracts
   • represents liabitlies other than that attributed to the unit reserve e.g. future expenses, future guaranteed subsidy of allocation rate not covered by other margins within unit pricing, future cost of guarantees and mortality costs if not all paid for by unit deductions.
   • PV (non-unit outgo - non-unit income). A negative reserve may/may not be permitted depending on the regulatory regime.
   • Discounted CF method.

Question 7

Explain why a positive non-unit reserve may be required for a prudential valuation of a unit-linked contract (2)

Answer 7

• Life company will receive monetary payments in form of policy charges to cover non-unit liabilities…
  
  • …eg expenses of managing business..
  • …or benefit payments in excess of the unit fund
• If it expects the charges will not be sufficient to cover these liabilities at any point on a cashflow basis, it has to hold a non-unit reserve to provide for the deficiency

Question 8

Gross premium valuation method: non-unit reserves

What general features are associated with non-unit reserves?

(1,2,4,4,1)

Answer 8

General features of non-unit reserves

• Pattern of income not necessarily as smooth as without profits endowment.
  
  1. income = charges less outgo in terms of expenses and claims in excess of unit reserves
  • • Cashflow approach essential due to
      1. complexity of contracts
      2. greater CF patterns’ variety
  • • Liabilities for unit-linked contracts denominated in units and monetary terms, leading to a need for unit reserve as well as non-unit reserve. Non-unit liabilities include
      1. administration costs
      2. mortality costs if not paid by unit reduction
      3. future guarantee costs (eg min benefits related to premiums paid)
      4. future guaranteed subsidy of allocation rate if not covered by other margins in UP eg allocating 106% allocation of prems
  • • Non unit reserve=PV(excess non-unit outgo over non-unit income)
      1. outgo: expenses, benefits in excess of unit fund
      2. income: charges, unallocated premium
      3. discounted CF method is used
      4. if PV non unit income > PV non unit outgo => overall negative non unit reserve; may or may not be allowed by regs
  • • Calc depends on purpose and regulations

Question 9

Gross premium valuation method: non-unit reserve calculation

Describe how to calculate a non-unit reserve for a prudential valuation (8)

Answer 9

Prudential valuation

1. Prudental valuation requires reserves to be prudent
2. Defines non unit reserve as amount required to ensure insurer able to pay claims & meet continuing expenses without recourse to further finance
3. Required to consider year-by-year/month-to-month incidence of the components of the non-unit CFs to determine if and when a non-unit reserve needed
4. FNB should project its non-unit CFs on the reserving basis (may need to be done per policy)

Calculation of the reserve
1. Start with the last projection period in which the net cashflow becomes negative (allowing for discounting and survival)
2. Set up amount at start of that period which is sufficient, allowing for earned investment return over the period, to ‘zeroise’ the negative cashflow
3. Deduct the amount from the net cashflow at the end of the previous time period
4. Continue this process backwards towards valuation date, with each negative being ‘zeroised’ in this way
5. When the process is completed, 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

Gross premium valuation method: non-unit reserve calculation

Describe how to calculate a non-unit reserve for a

best estimate valuation (3)

Answer 10

Best estimate valuation

1. Value all future non-unit CFs, including CFs after last proj period with negative net outflow
2. There would be no other restrictions
3. Negative non-unit reserves can be held where future charges/income > future expenses and other costs/outgo . This is an asset representing a loan from contracts which have positive non-unit reserves. The repayments are made from emerging future profits from policies for which negative non-unit assets are held.

Question 11

Gross premium valuation method: negative non-unit reserves

Explain when a negative non-unit reserve may arise (1)

Describe some other features related to negative non-unit reserves (4)

Answer 11

Negative non-unit reserves may arise when

1. the life insurance company anticipates that future charges will be more than sufficient to meet future non-unit liabilities

A few other general points about negative non unit reserves

1. represent a loan from other contracts which have positive reserves, which will be repaid by emerging future profits from policy for which negative non unit reserve is held (simply taking credit for future profits from a policy)
2. improves capital efficiency, since it reduces total reserve under policy
3. used, in theory, whenever there are future positive CFs the company would like to take advance credit for to reduce NB strain (be careful not to take too much credit). For unit-linked its most likely to occur when a level allocation loading has been deducted from the regular premiums to recoup the heavy initial expenses producing a large negative CF in year 1 followed by excess positive CFs in future years.
4. needs adequate surrender penalty, to ensure value of future CFs not lost if PH withdraws

Question 12

Gross premium valuation method: negative non-unit reserves

Outline the conditions that the regulator may require to hold before a negative non-unit reserve can be held under a prudential valuation (5)

Answer 12

May be allowed by regulator if following conditions all hold

1. total reserves (unit + non unit) for a policy > guaranteed surrender value
   
   • ensures company holding enough money if policy surrenders
2. future profits arising on policy with negative non-unit reserve need to emerge in time to repay ‘loan’ effectively made from other contracts with positive non-unit reserves
3. no future valuation strain, after taking account of future non-unit reserves
4. in aggregate, the sum of all non-unit reserves should not be negative (including reserves even from non-unit contracts).
5. note even if negative non unit reserves allowed, for prudential valuation, safer to assume
   
   • future positive CFs are lower than best estimates
   • interest rate used to discount 1. is higher than best estimate
   • survival rates are lower than best estimates
     to not hold too much credit

Question 13

Gross premium valuation method: negative non unit reserves

How do we go about calculating negative non-unit reserves? (6)

Answer 13

(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.

Question 14

Gross premium valuation method: key features

List key features of the gross premium valuation method (6)

Answer 14

1. Explicit allowance made for expenses
2. Explicit allowance can be made for vested/expected future bonuses (where appropriate…if done, also referred to as bonus reserve valuation)
3. Future premiums valued are actual (‘office’) premiums expected
4. Any differences between pricing and valuation bases immediately taken as profit or loss
   
   • Takes credit for PV[future profit], if future reality is assumed in the reserving basis
   • Therefore, if a realistic valuation basis (i.e. more lenient than pricing basis) is used then all future profits that FNB expects to make would be realised on account of the future premium being larger than it needed to be according to this basis. Dangerous for a supervisory reserve.
   • If a prudent valuation basis is used then a lower amount of profit would be initially capitalised by the company, which would be useful if experience turns out to be worse than expected on the realistic basis.
5. Reserves can initially be negative for non-linked business:
   
   • partly due to initial expenses and
   • partly due to capitalising expected future profit
6. Reserves tend to be quite sensitive to changes in basis

Question 15

Net prem vln meth: definition

How would we define the Net Premium Valuation method? (4)

Give a formula for the Net Premium Valuation reserve for a regular premium endowment assurance

Answer 15

Net Premium Valuation method is essentially

1. PV of expected future benefit outgo - PV future net premiums
2. calculated on interest & mortality basis only ie. no explicit expense allowance
3. benefit outgo includes bonuses declared to date but no explicit allowance for future bonuses
4. net premium is the premium FNB would charge from policy inception to cover initial guaranteed benefits only (so again, expenses are ignored), assuming the same basis as used for PVs (so this may not be same as original pricing basis

Net Premium Valuation reserve

• (S +B) * A_(x+t:n-t) - P * a_(x+t:n-t)

where S is sum assured, B is bonuses declared to date and P is net premium = S * A_(x:n) / a_(x:n)

Question 16

Net premium valuation method: key features

List key features of the net premium valuation method ( 10 )

Answer 16

1. Simple - the formula used and data required is simple
2. Makes no explicit allowance for future expenses
   
   • Could make implicit allowance.
   • Common approach for future expenses: future annual expense = the net premium that FNB is valuing with this method - the office premium FNB will actually receive. Only works for regular premium business.
3. Makes no explicit allowance for future bonuses
   
   • Could make implicit allowance.
   • On regular premium with-profits business, implicit allowance for future bonuses can also come from the margin as in expenses above. This is because the net premium is calculated to = the initial guaranteed sum assured while the office premium will likely be substantially higher than this.
   • Could also use low valuation rate to make broadly suitable allowance for future bonus at all durations.
4. Reserves relatively insensitive to changes in valuation basis
   
   • For regular premium business.
   • When you do a GPV we essentially calculate:

EPV(Benefits + Expenses) - EPV(Gross 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, so compensating for some of the overall increase in the value.

5. Used for conventional with profits
   
   • Since it does not capitalise the profit margins in the future gross premiums.

Question 17

For an internal valuation of a life insurer’s non-linked business, it has been suggested that a realistic gross premium valuation method is appropriate, because (realistically) we do wish to include the value of all the profits we expect to receive from the future gross premiums.
Comment on the validity of this suggestion.

Answer 17

It is certainly appropriate to value the future gross premiums that we expect to receive, if we wish to assess the realistic value of the liabilities. (Consistent with this, we would include any calculated negative reserve values, rather than assume all such negative reserves were zero.)

However, we do not expect to receive all of the gross premiums – we should allow for those policies that terminate early due to death or withdrawal. While the gross premium formula method allows properly for mortality, it ignores future withdrawals. In this way, the gross premium formula method may not fully satisfy the requirements of an internal realistic valuation, but explicit allowance could be made by using the gross premium cashflow approach instead.