22 Assumptions per purpose and embedded values

Question 1

Valuing life insurance contracts: liabilities

Ovierview

Answer 1

Liabilities = PV(claims + expenses+taxes-premiums)

Question 2

Valuing life insurance contracts: liabilities

Published accounts

Answer 2

Assumptions should be consistent with the legislation and accounting principles governing the preparation of those accounts in the country concerned

Considerations:
- whether the accounts are to be prepared on a going concern basis or a break-up basis
- whether the accounts are required to show a true and fair view
- whether reserves are required to be assessed as best estimates or on some other basis

Question 3

Valuing life insurance contracts: liabilities

Supervisory reserves

Answer 3

If separate accounts are required as part of the process of supervision of solvency:
- rules governing the preparation of those separate accounts may or may not be the same as those that apply to the published accounts
- Reference should be made to those rules and any guidance that may have been issued as to their interpretation.
- will almost certainly be some constraints on the assumption decisions
- most regulations require that the assumptions must be prudent

Question 4

Going concers vs break-up basis

Answer 4

going concern basis assumes that the company continues to issue new business into the future.

break-up basis will assume new business ceases, either immediately or at some point after the valuation date.
Two possible forms:
- existing business continues to be managed by the company as a closed fund
- the liabilities are transferred to another insurance company who will then administer them until run-off

Question 5

Valuing life insurance contracts: liabilities

Internal management accounts

Answer 5

• “Best-estimate reserves”:
• The aim is likely to produce expected values of the future experience, based on realistic assumptions.
• The principles to be followed are matters to be discussed and agreed (by the actuary) with the insurer

Question 6

Reserving basis compared to pricing basis

Uncertainty in assumptions: pricing vs reserving

Answer 6

• NB difference: for reserving, policies are already in force which can provide NB info on setting assumptions
• Reserving: know who p/h are, and historical experience will give good indication of future experience
• Hence lower parameter uncertainty for demographic assumptions
• Expenses, for reserving: no future initial expenses, less undertainty over volume and mix

Question 7

Reserving basis compared to pricing basis

Using pricing assumptions to calculate reserves for supervisory purposes

Answer 7

• only works for with-profit business
• Without profit: the pricing basis is unlikely to be sufficiently prudent to use for supervisory reserving, since margins are small for competitive reasons
• with-profits business can be priced with large margins, as any future surpluses can be returned to policyholders through bonuses
• where pricing assumes best estimate assumption plus allowance for risk through RDR, cannot use pricing basis for reserving.
• why? for reserving discount rate has to equal investment return assumption. RDR is irrelevant to reserves

Question 8

Best estimate reserves

Answer 8

• assumptions will be derived based on the actuary’s best estimate of future realistic experience NO MARGINS
• when management wishes to have a best estimate of the company’s financial performance
• where the insurer is to be sold or
• where directors wish to reward key staff for their specific contributions to the overall growth of the company.
• Basis: close to new business pricing without effect of underwriting (ie ultimate mortality)

Question 9

Best estimate reserves

In what way is a gross premium formula reserve likely to be unrealistic, and hence possibly inferior to a cashflow approach, for valuing non-linked products for this purpose?

Answer 9

• It does not take account of discontinuance.
• Losses or profits from discontinuance will affect the actual value of the business to the company,
• and will lead to error unless such profits and losses are expected exactly to cancel out.

Question 10

Valuing life insurance contracts:

embedded value

Answer 10

The present value of future shareholder profits in respect of the existing business of a company, including the release of shareholder-owned net assets.

• Embedded values are often used as a more realistic assessment of the value of an insurer
• recognises the value of any assets in excess of the reserves
• recognises the value to the shareholders of future releases of the margins in those reserves
• can be included as supplementary information in published accounts,
• or can be used for internal management purposes
• calculation is generally on a more realistic basis than the reserving basis
  *

Question 11

Valuing life insurance contracts: embedded value

Calculation of embedded value

Answer 11

sum of:
- The shareholder-owned share of net assets, where net assets are defined as the excess of assets held over those required to meet liabilities (reserves) (may be valued at market value or may be discounted to reflect “lock-in”)
- The present value of future shareholder profits arising on existing business. (Calculated like profit test without allowance for new business)

NB: reserves used in the determination of net assets should be consistent with those used in the determination of the present value of future profits.
NB2: Appropriate allowance for tax needed

Question 12

Calculation of embedded value

The calculation of future shareholder profits for different types of bus

Answer 12

need to know the reserves in the future in order to calculate the present value of future shareholder profits (as the change in reserves is part of the profit calculation)

Conventional without-profits business:
The present value of future premiums plus investment income less claims and expenses, plus the release of supervisory reserves.
Present value of shareholder transfers is effectively the release of any margins within the supervisory reserves relative to the assumptions used within the embedded value calculation

Unit-linked business: the present value of future charges (including surrender penalties) less expenses and benefits in excess of the unit fund, plus investment income earned on and the release of any non-unit reserves.

With-profits business: the present value of future shareholder transfers, for example as generated by bonus declarations.

Question 13

Appraisal value

Answer 13

= embedded value + goodwill
* embedded value: starting point in valuing a life insurance company for sale or purchase
* important element of the price is goodwill, corresponding to the estimated profits expected from future business.

Question 14

Valuing life insurance contracts: embedded value

Assumptions

Answer 14

key determinant: purpose for which the EV is being calculated.
- always calculate the reserves using the supervisory reserving basis.
- published accounts or internal management accounts: likely best estimate - consistent with the legislation and accounting principles
- appraisal value (sale): based on realistic assumptions without margins
- appraisal value (purchase): cautious assumptions that include margins
- The final price agreed for the business will depend on the relative bargaining power of the buyer and seller.

Question 15

Valuing life insurance contracts: embedded value

Allowing for risk

Answer 15

Embedded value calculations need to include an appropriate risk margin to allow for the unpredictability of profit emergence for life insurance business.
- need to reduce the embedded value in some way to reflect the risks of the business.
- rate of interest used to discount the future streams of surplus will traditionally reflect the risk inherent in these amounts
- increasing the discount rate increases the degree of prudence.
- RDR>RFR
- A stochastic or market-consistent approach may be adopted

Question 16

What is the difference between a best estimate valuation and an embedded value?

Answer 16

two methods are trying to focus on something slightly different and work in different ways.
* best estimate valuation the present liability is calculated for each policy using realistic assumptions.
* sum over all policies is compared with the total asset value to give a measure of realistic solvency.
* gives a measure of policyholders’ benefit security,
* change each year in the retained profit (ie the change in the value of the assets less the value of the liabilities) can also be used to give a measure of profit as an extra piece of information.
* An embedded value calculation will consider the cashflows across the portfolio in each time period
* rather than the present value of cashflows for each policy
* focus of an embedded value calculation is shareholder profit
* takes full account of the cost of capital (S/h’s RRR) in the value of the shareholder transfers,
* because each year’s transfer has to be made from profits that arise in excess of the supervisory reserves held.

Question 17

Consistency

Consistency in setting a valuation basis

Answer 17

Previous basis
- starting point - always
- Any deviation from that must be justifiable
- change the basis if new evidence was available
- Changing the basis can have a significant impact on the published financial results
- weakening of basis requires jsutification to regulatory authorities to ensure profits aren’t being accellerated
- strenghtening of basis requires jsutification to fiscal authorities to ensure profits aren’t being delayed for tax

Question 18

Risks of:
1. Weakening basis too much
2. Strengthening basis too much

Answer 18

1
whilst it will accelerate profits and increase returns,
will weaken the company’s financial security and would increase its insolvency risk

2
The increase in capital strain per policy issued means that the company is more likely to become insolvent on the supervisory basis.
If this were a significant threat, then the company would either have to reduce sales or increase capital provision
Turning customers away would also send out very negative messages to the market
All of this reduces future returns on capital

Question 19

Consistency

Assets v liabilities

Answer 19

• The basis for valuing liabilities must be consistent with that for valuing assets.
• if assets are valued at market value then the investment return assumption of the liability valuation basis must reflect the current market yields

Question 20

Consistency

Pricing basis

Answer 20

• essential that the assumed reserves in the pricing basis are consistent with the company’s actual reserving basis for the contract.
• pricing basis will have allowed for the cost of setting up supervisory reserves
• If the actual reserves are, for example, based on more prudent assumptions than allowed for in the pricing model,
• then the cost of capital will be higher than that assumed and
• the policy will be less profitable than expected.
• premiums/charges will have to be higher to maintain the return on capital
• will make a price-sensitive product less competitive in the market
• leading to a (potentially devastating) marketing risk (inadequate sales)

Question 21

Supervisory valuation v internal valuation

Previous basis, Assets v liabilities, Pricing basis

Answer 21

• The start point in deciding on a suitable basis will be the basis used for the previous embedded value calculation
• any such change must be justifiable, especially if the embedded value is being used to report externally on a company’s real worth
• if best estimate assumptions have changed since the previous embedded value calculation, a basis change may well be appropriate and the effect of that change on the company’s value should be reported.
• The basis for valuing liabilities must be consistent with that for valuing assets.
• The embedded value basis is likely to be more “best estimate” than the pricing basis
• However the two should be looked at side by side
• differences will immediately lead to embedded value movements on writing new business different to those implied in the pricing basis.