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 insurer capable meeting all guaranteed liabilities
   2. given uncertain future, valuation standards likely to require prudent assumptions; using more best estimate assumptions=> more solvency capital required
2. quantify the realistic position of a company which helps determine
   
   1. bonus decs; determinine long term sustainability of profit distribution rates
   2. realistic profitability for information of shareholders/management
   3. general financial management

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 value of a life insurance company’s liabilities that explicitly takes into account

• the future office premiums payable
• expenses & claims (potentially including future discretionary bens)

Reserves = PV(expected future benefit outgo) + PV(expected future expenses) - PV(expectd 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:
   
   • SA*A_(x+t:n-t) + RE*a_(x+t:n-t) - P’*a_(x+t:n-t)
   • where: SA = sum assured, RE = ren expenses, P’ is office prem
   • 2. Contract usually priced so office prems> claims & expenses
   • so on CF approach (alternative meth to formula approach), reserves theoretically negative at policy start , just before pmt of first premium/initial expenses
   • init expenses often higher than firs premium (for regular bus), leading to reserves being even more negative
   • 3. 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 ren expenses generally increase with pol term, but premiums remain level
   • (for a reg prem, non-linked without-profits contract)
   • 5. There over time future benefits + expenses > premiums
   • except very early on in contract, giving a smooth progression of reserves, which start negative and finish with value equal to 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 and mortality costs etc

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 denomicated in units and monetary terms, leading to need forunit 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 benfts related to prems 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 non-unit CFs to determine if non-unit reserve needed
4. Model projected non-unit CFs on reserving basis (may need per policy)
5. Start with last projection period in which net cashflow becomes negative (allowing for discounting and survival)
6. Set up amount at start of that period which is sufficient, allowing for earned investment return over the period, to ‘zeroise’ the negative cashflow
7. Deduct the amount from the net cashflow at the end of the previous time period
8. Continue process backwards towards valuation date, wich each negative being ‘zeroised’ in this way
9. If the adjusted cashflow at the valuation date is negative then a positive 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 (occuring if future non unit charges expected to exceed future non unit outgo. Essentially we have an asset, used to loan finances to other contracts with positive non unit reserves

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 effeciency, 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 (be careful not to take too much credit)
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) > 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, 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 CFs are lower than best estimates
   • interest rate used is higher than best estimate
   • survival rates are lower than best estimates

Question 13

Gross premium valuation method: negative non unit reserves

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

Answer 13

1. Model projected non-unit CFs on reserving basis (may need per policy)
2. Identify last net cashflow whether positive or negative (allowing for discounting and survival)
3. Reserve = amount at start of that period which is sufficient, allowing for earned investment return over the period, to ‘zeroise’ that cashflow
4. Check that total reserve (unit + non-unit) > guaranteed surrender value i.e unit reserves less surrender penalty
5. Move back to next previous CF, discount the reserve and then subtract from the reserve the new cashflow at the earlier time period. Repeat step above.
6. Carry on repeating process working backwards over time to valuation date.

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
   • If realistic valuation basis (i.e. more lenient than pricing basis) is used then all future profits that it expected 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, less PV expected future net premiums
2. calcultd on interest & mortality basis only ie no explicit expense allowance
3. benefit ougto includes bonuses declared to date, no explicit allowance for future bonuses
4. net premium is premium insurer would charge from pol 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: formula used and data required is simple
2. Makes no explicit allowance for future expenses
   
   • Could make implicit allowance.
   • Common approach for future expenses: assume future annual policy expense is less than difference btwn net premium company is valuing with this method, and office premium will actually receive, but will only work 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 come from the margin btwn net premium and the office premium (since office premium will likely be substantially higher).
   • 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 the reserving basis changes for gross premium valuation, the gross premium used in the calculation doesn’t change, but for the net premium valuation, the net premiums used in the calculation changes.
   • If valuation interest rate reduces, both sets of reserves will increase, but net premium valuation will increase by less, because the net premium themselves have increased in size, compensating for some of the overall increase in value.
5. Used for conventional with profits
   
   • Since it does not capitalise the profit margins in the future gross premiums.