Ch 22: Assumptions 2

Question 1

Valuing liabilities: overview

Broadly speaking, how do we value the liabilities of a life insurer? (4)

Answer 1

• Liabilities determined as
• PV(claims + exp) + Tax - Premiums
• Bigger margins assumed => more prudent the liability is
• Decr Disc Rate=>
  
  • • Prudence on a + reserve => PV Liability is larger
  • • Prudence on a - reserve

Question 2

Valuing liabilities: Published accounts, key considerations

State the factors to consider when deciding assumptions for determining the value of liabilities to show in an insurance company’s published accounts (3)

Answer 2

• Assump to det liab consistent with regulations, accounting principles
• Matters to consider
  1. going concern or break-up basis
  2. required to show a true and fair value?
  3. best estimate basis or include margins

Question 3

Valuing liabilities: Supervisory reserves, key considerations

How might rules governing the solvency supervision process relate to rules for published accounts? (1)

Key considerations for supervisory reserves (3)

Answer 3

• If separate accounts required to show solvency , rules for preparation may not be same as rules for published accounts…
• Key considerations
  • going-concern basis: contnue to issue NUB
  • break-up basis: No NUB => closed fund, liab run-off/ transfer
  • Supervisory basis may impose restrictions on assumpt:
    
    • interest = rate used in pricing

Question 4

Valuing liabilities: Internal management accounts, key considerations

Answer 4

• Basis decided internally
• Aim is to have best estimates of the company’s financial performance, based on _realistic assumptions
• Best estimate basis

Question 5

Reserving basis vs pricing basis: uncertainty in assumptions

What kind of useful info can in force policies provide for setting assumptions?

(1,3)

(1,5)

(1)

Answer 5

In force policies can help with following

1. Demographic assumptions
   
   1. already know who PHs are => good info about class of lives
   2. historical experience investigation likely to indicate future experience well (if data volume credible)
   3. less parameter uncertainty in assumptions than for pricing
2. Expense assumptions
   
   1. should be easier to assess for reserving because
      
      1. no future initial expenses
      2. less uncertainty over volume/mix of future business
   2. contrib of fixed expenses covered by existing PHs affected by new policies expected…
   3. …so expense assumption still has some uncertainty
3. Uncertainty of reserving basis should not be greater than pricing, but need to consider size of margins used => prudent or realistic purpose

Question 6

Reserving basis vs pricing basis: using pricing assumptions for supervisory purposes

What is relationship between pricing and reserving assumptions in some countries? (1)

Answer 6

• If prems calc on prudent assump :
  
  • This basis can be used for reserves
  • W/profits=> surplus will emerge as act exp better than exp exp => + bonuses etc
  • Less justifiable on w/o profits => uncomp premiums => best est basis

Question 7

Reserving basis vs pricing basis: using pricing assumptions for supervisory purposes

How appropriate is pricing basis for supervisory purposes if expected experience is used? (2)

Answer 7

• Sometimes use expected experience for pricing, with risk allowed for through RDR.
• Inappropriate for supervisory reserving if reserves need prudent calc,
  
  • since RDR has to be investment return assumption (risk free rate, if market consistent) and
  • RDR is measure of return required by shareholders on their capital (hence irrelevant to reserve calculation, since unrelated to investment return assumption

Question 8

Reserving basis: best estimate reserves

What do we usually use best estimate reserves for? (3)
What are the key characteristics of best estimate reserves? (4)

Answer 8

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

Key factors to consider:

1. assumptions use company’s best estimate of future experience, with no margins
2. all experience items would be allowed for explicitly (expenses, persitency, investment return, mortality)
3. no zeroisation of negative reserves
4. cashflow method used for estimates of reserves needed

Question 9

Valuing liabilities: Embedded value, key considerations

Define embedded value (4)

Answer 9

• EV= PV future SH profits from existing business + release of net SH assets
• Embededed value is defined as sum of:
  
  • shareholder net assets
  • **present value of future shareholder profits from _existing business
• EV essentially recognises
  
  • value of assets in excess of reserves
  • and value to shareholders of future margin releases from reserves

Question 10

Embedded Value: Calculation

Shareholder net assets (6)

Answer 10

• 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
  • lock-in-value
    
    • required to be retained to cover SCR
    • invested more cautiously to ensure SCR met
    • expect lower ret=>worth less than MV
• eg MV =100 SCR, invest 10yrs @4%, RDR =5%
  
  • PV assets= 100* (1.04^10) / (1.05^10) = 90.874
  • Use this figure and not MV=100

Question 11

Embedded Value: Calculation
PV of future shareholder profits

Answer 11

PV of future shareholder profits:
* on existing business
* CF’s proj, est SH profit,Disc @ RDR
* Similar to profit test but excl NUB items

Calc:
* W/o profits = PV(prem) + Inv inc - Claims - Expenses + Release reserves
* UL= PV(charges) - Ben excess of UF - Expenses + Inv inc + Release of Non-unit reserves
* W/profits= PV future SH transfers eg bonuses

Question 12

Embedded Value: Calculation
Basis Used determines P\L

Answer 12

• If reserving basis is used to calc EV’s the profit emerging is ZERO.
  
  • Reserves + Inv inc = net outgo exactly
• Extent of the difference bet basis => profit /loss
• EV on realistic basis reserve + inv inc > net outgo => exp profit

Question 13

Define appraisal value (2)

Answer 13

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 14

Embedded Value: Assumptions

What is the key determinant of the basis used for EV? (3)
What are the 2 bases required for an EV calc?

Answer 14

Basis used for EV depends on:
* purpose for which EV is needed
* insurer offering itself for sale use best estimate/realistic (no margins)
* insurer purchasing may use cautious, wth margins
* published accounts=> best est + margins for prudence

2 Types off basis needed for EV calc
* Reserving:
* Calc reserves to get net assets
* Calc future reserves=> PV future SH profits
* Always done on a reserving basis

• Projection:
  
  • proj exp into future => PV SH profit
  • no impact on net assets

Question 15

Embedded Value: allowing for risk

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

Answer 15

Allowing for risk in EV cal

• Our reserving basis must use supervisory regulations (include risk margins)
• however the projection basis needs to also allow for risk
  
  • Incl risk margin for uncertainty of profit emergence
• purpose of EV is to give realistic val of insurer to SH so reduce EV to reflect risks of the business

Question 16

Embedded Value: allowing for risk

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

Answer 16

Approaches used to allow for risk

• RDR for future profit streams will traditionally reflect risk. All things equal, increasing RDR => increasing risk => use RDR > Rf rate
• Stochastic approach: would highlight range of possible values profits might take
• Market consistent approach: using RDR = Rf 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 17

Embedded Value vs Best Estimate Valuation

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

Best estimate basis (3)

Embedded value basis (3)

Answer 17

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 asset 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

• proj CFs across portfolio, 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)

eg notes

Question 18

Consistency of assumptions: in setting valuation basis

Discuss different aspects where consistency is important when setting a valuation basis

(7)

(2)

(3)

(1)

Answer 18

Consistency with previous basis

1. starting point used is previous basis
   
   1. any deviations need justification
   2. eg apprpriate to adjust to new evidence eg if gross redemption yield from gov bonds had changed
2. changing basis can have significant impact on published results
   
   1. weaker basis, justify not just to accelerate profits / + solvency position
   2. stronger basis, justify not just to defer profits (tax)
3. Balance of both needed
   
   1. SH need to believe interests best served by solvent company
4. indentify impact of basis changes seperately in accounts

Assets vs liabilities

1. basis for valuing liabilities, consistent with basis for valuing assets
2. eg if assets valued market value, then investment return assumption of liability basis must reflect current market yields (ie expected future market yields for risk free assets) if market consistent approach is taken

Pricing basis

1. allow for cost of setting supervisory reserves in pricing model used (these reserves will have been based on some reserving basis)
2. price determined will have allowed for CoC
3. essential that pricing basis reserves consistent with actual reserving
   
   4. Act reserves ar emore prudent+> CoC > than assumed in pricing => less profitable than expected => higher capital strain

Supervisory vs internal valuation

1. Doesn’t necessarily need to be close, but should be considered

Question 19

Consistency of assumptions: in setting embedded value basis

Discuss different aspects where consistency is important when setting an EV basis

Answer 19

Previous basis

1. starting point will be basis used for previous EV calc
2. difference to prev will immediately cause some movement in EV
3. any change must be justifiable, esp if EV being used to report externally on insurer’s real worth
4. basis change appropriate if best estimate assumptions have changed

Assets vs liabilities

1. Same comments as for setting valuation basis
2. basis for valuing liabilities, consistent with basis for valuing assets

eg if assets valued market value, then investment return assumption of liability basis must reflect current market yields (ie expected future market yields for risk free assets) if market consistent approach is taken

Pricing basis

1. EV basis likely to be more best estimate than pricing basis
2. However, 2 should be looked at side by side. Any differences will immediately lead to embedded value movements on writing new business different to those implied in pricing basis

Question 20

Valuation basis should reflect 4

Answer 20

Expected future experience
Margins to ensure adequacy of reserves
Regulations if published
Need for consistency