Ch 25: Surrender values

Question 1

Summary card

Answer 1

1. Principles
2. Methods
3. Profit
4. Assumptions
5. Unit-linked contracts

Question 2

What do we mean by ‘surrender’? (1)

What kind of reserves is it important for us to consider to assist in setting surrender values? What do we compare these to? (2)

Answer 2

Surrender relates to policyholders terminating contracts early in return for an immediate cash payment

• Insurer no longer needs to hold a reserve for the contract, hence surrender value can be paid

It is normally useful to consider prospective and retrospective reserves when calculating surrender values.

• We compare these reserves to the asset share at time of surrender

Question 3

What type of contracts do we mainly consider surrender values for in this course?

Answer 3

We mainly consider surrender values for conventional without profits contracts

Question 4

For each of these, why may (or may we not) offer SVs?

Endowmwnt/whole of life (2)

Answer 4

Endowment/whole of life​

1. reserves increase with policy duration, hence SV can be paid
2. SV (and reserves) typically increases towards sum assured

Question 5

For each of these, why may (or may we not) offer SVs?

Term assurance (5)

Answer 5

Term assurance: usually no surrender value because

1. reserves always very small compared to sum assured
2. cost of selective withdrawals => reduced if no SV
3. recoup losses on early lapses (when ass share negative) by making some profit on later lapese (when ass share positive)
4. asset shares quite volatile, so difficult to devise SV which treats PHs fairly in relation to this
5. ass shares can be negative and/or decreasing at later durations/towards end of policy=> hard to sell this to PHs

Question 6

For each of these, why may (or may we not) offer SVs?

Immediate annuity (2)

Answer 6

Immediate annuity: usually no surrender values because

1. PHs would want to surrender only if think they’ll die soon
   
   • hence, giving SV would => improved longevity of remaining lives=> big cost
2. also, legislation may not allow this, if tax privileges were granted for certain contract types providing long term annuity income in retirement to releive burden on state
   
   • if SVs given, people would use these contracts as savings vehicle to benefit from tax concessions = defeating goverment aims

Question 7

List principles that should be considered when calculatings surrender values

(11)

Answer 7

1. PRE
2. Treat both surrending and continuing policyholders equitably
3. At early durations, not appear too low compared with premiums paid, accounting for any projected maturity values
4. At later durations, be consistent with projected maturity values
5. Not exceed asset shares, in aggregate, over reasonable time period
6. Competitors’ surrender values (and possibly also auction values, where applicable)
7. Not be subject to frequent change, unless dictated by financial conditions
8. Not be subject to significant discontuities by duration
9. Not excessively complicated to calculate, accounting for computing power available
10. Be capable of being documented clearly
11. Avoid selection against insurer

Question 8

Discuss the influence of PRE when setting SVs in terms of

Discontinuance at short durations (4)

Answer 8

Discontinuance at short duration

• SVs likely compared to premiums paid (sometimes with interest), but usually ass share less than this
• prospective policy value based on best estimates of future experience likely to be even smaller
• insurers may feel obliged to accept losses/reduced profit on SVs several years into contract
• could penalise later surrenders to cope/not offer SVs at all for some initial time

Question 9

Discuss the influence of PRE when setting SVs in terms of

Discontinutnace close to maturity (3)

Answer 9

Discontinuance close to maturity

• where maturity benefit payable, PHs will expect SV prior to maturity to be consistent with this
• SVs should progress smoothly at each year end into maturity value
• achievable for without profits contracts: base SV on prospective polcy values

Question 10

Discuss the influence of PRE when setting SVs in terms of

How they compare to auction values (4)

Answer 10

How SV compares with auction values

• auction value is what policy obtained if PH transferred ongoing policy to someone else, dealth with by specialist brokers)
• auction values assessed independently = hence PHs may accept as fair
• often unsuitable, though
  
  • difference in assumptions used eg optimism of future benefits of polcy
  • values flactuate unpredictably => hard to determine, without actually selling policy

Question 11

Discuss the influence of PRE when setting SVs in terms of

What was disclosed at new business (2)

Answer 11

New business disclosures

• new business sales sometimes accompanied by prospective SV illustrative values by duration (may be regulatory requirement)
• potentially embarrasing if SVs given/quoted in financial press surveys differ significantly from new busines literature

Question 12

Discuss the influence of Earned Asset Share when setting SVs according to following:

What does the asset share represent in general? (1)

What implication does this have for SVs? (2)

What does using asset share for SV calcs mean in terms of profit/loss distributions (1)

How might we achiev averaginge over time when using asset share for SVs? (3)

Answer 12

Asset represents

• money insurer has really accumulated in respect of policy, unlike supervisory reserve (represents how much money company must hold)

Earned asset share can be used interchageably with asset share

• SVs must not exceed earned asset share in aggregate over a reasonable time period

The implication is

• asset share theoretically guides the maximum the insurer can afford to pay out, measured over a reasonable time period
• but it is not unique value which can be afforded in all cases i.e could give some policies more, some less

Basing SVs closely on asset shares implies

• distributing accrued profits/losses to PHs, because asset share containg all of accumulated profits/losses from policies to date

Averaging over time for SVs can be achieved in 2 ways:

• by period of ass share calc eg. 1 per year (practical) => averaging over year
• smothed ass share as basis for SV
  
  • Decide time period(s) to smooth over, e.g. want to smooth individuals months’ ass share values so total impact of smoothing over 12 months is zero or smooth individual years’ asset share values so that the impact over perhaps five years is zero.

Question 13

Consider the example of a without-profits whole life assurance for a sum assured of S, payable immediatley on death, with annual office premiums of G payable m times a year, where:

• x = policyholder age at date of issue
• I = initial expenses in excess of those occuring regulalry each year
• e = level annual expenses (incurred m times a year)
• f = normal claims expenses
• C = surrender expenses

State formulae for the retrospective reserve and the prospective reserve for the policy at policy duration t, and explain how these can be used to determine a surrender value.

Answer 13

Retrospective method

• Provided sufficient info + computing facilities, insurer may keep up-to-date asset share per contract to use to calc a SV
• however, rarely true for without profits contracts, so use retrospective reserve to deduce SV
• use formula/parameters chosen to produce acceptable results at duration required; starting point for basis is experience of policy.
• Retrospective reserve
  
  • D_(x) / D_(x+t) * { G*a^(m)_(x:t) - S*A_bar1(x:t) - f*A_bar1(x:t) - e*a^(m)_(x:t) - I } - C
  • *annuity factor should have double dots for ‘in advance’

Prospective method

• For without profits contracts, this is value of future benefits/expenses, net of future premiums due, using estimates of future expected assumptions
• Prospective reserve
  
  • S*A_bar1(x+t:) + f*A_bar1(x+t) + e*a^(m)_(x+t) - G*a^(m)_(x+t) - C
  • *annuity factor should have double dots for ‘in advance’

Table of surrender values by policy duration usually a blend of these 2 values, subject to minimum value of 0 (blending towards the prospective reserves at later durations).

Question 14

State the main advantages and disadvantages of using the retrospective method for calculating surrender values

Advantages (4)

Disadvantages (3)

Other points to consider (1)

Answer 14

Advantages

1. Represents maximum company could pay without making a loss
2. At early durations, may be reasonable compared with the premiums paid
3. It may be consistent with values quoted in product disclosure literature
4. Not overly complicated, provided necessary information available to build up earned asset share/determine suitable parameters if formula is used

Disadvantages

1. For without-profit contracts
   
   1. gives no indication of profit which would’ve been earned without surrender, hence, not easy to ensure equity either with continuing policyholders or with any shareholders
   2. will not necessarily run into the maturity value, except by chance
   3. future benefits/expected experience ignored. So values may be significanlty different from a realistic prospective value, which is likely to be the approach used to calculate auction value.
2. The most complex component of the method is obtaining the necessary historic information and computing resources availability

Other points

1. Consistency with competitors depends on the method and basis used

Question 15

State the main advantages and disadvantages of using the prospective method for calculating surrender values (7)

Advantages (4)

Disadvantages (3)

Answer 15

Advantages

1. If realistic basis used with the method it will produce a surrender value that represents what the contract is worth to the company
2. Therefore, it enables the company to quantify how much profit to retain and hecne maintain equity with continuing policyholders and any shareholders
3. Ther surrender values will run into the maturity value, for without-profits
4. It’s relatively easy to operate

Disadvantages

1. There is no guarantee that the surrender values produced will not consistently exceed the asset share
2. It could produce unreasonably low surrender values at early durations, from the policyholder’s point of view
3. Likely to produce comparable surrender values to those available at auction and for comparable competitors’ contracts - although the basis used will be more influential in the comparison than the method.

Question 16

List the steps that go into, and need to be broadly considered, to calculate SVs

(4)

Answer 16

1. Choose method
2. Consider profit retention implied by method used
3. Determining the basis for either
   
   1. retrospective value
   2. prospective value

Question 17

Calculate SV: Choice of method

How might we use retrospective and prospective methods for the eventual SV calculations? (1)

In early years/policy durations what do we have to pay particular attention to when calc’ing SVs? (3)

Discuss the use of retrospective method throughout policy duration for SVs (1)

In later years/policy durations what might we do for SV calcs? (4)

Answer 17

For eventual SVs

• produce a table of SVs by policy duration which is a blend of retrospective and prospective values, subject to min value of zero

In early years,

• pay close attention to actual expenses incurred (particularly initial expns)
• other factors are of lesser importance in short term
• retrospective values are likely to be more natural approach

Theoretically, could just use retrospective throughout policy duration for SVs

• but can become increasingly difficult to find right combo of factors to produce values which run into maturity if calc had to be done by devising some independent formula and setting parameter values for it

After earlier years

• prospective methods more convenient, since only necessary to value future benefits, premiums and expenses
• main difficulty is deciding appropriate interest rate
  
  • thus difficult to apply at short durations and, hence, long oustanding
  • …because small changes in interest rate => big effect on SV

Question 18

What do we mean by ‘profit retention’ in context of SVs? (2)

What other important feature must be checked when deciding on method for SV calcs? (2)

Answer 18

Profit retention relates to

• excess of earned asset share over SV paid,
• the higher SV paid compared to asset share, the less profit we retain

Also important to check for lapse and re-entry risk due to chosen basis

• can be done by ensuring earned asset share is greater than surrender value

Question 19

Comment on use of retrospective method for SVs in relation to retained profit (1)

Answer 19

Retrospective method profit retention => no profit

• wouldn’t want to use retrospective method for too long, since SV is equal as asset share

Question 20

For prospective method SV calc, show how insurer profit retained on surrender can be split into (a) past profit and (b) capitalised value of future profit by considering SV calculated on the premium basis (5)

Answer 20

Prospective method profit retention

• depends on relationship btwn SV assumptions vs office prem assumptions
• if profit allowance contained solely in assumption margins used to calc office premium then profit retained can be specified as
  
  • (EAS - SV’) + (SV’ - SV”), where
    
    • EAS = earned asset share
    • SV’ = prospective SV using office premium assumptions
    • SV’’ = prospective SV using surrender value basis assumptions.
• 1st part, (EAS - SV’), represents the profit that’s been made to date
• 2nd part, (SV’ - SV’’), represents capitalised value of profit that will arise in future.

Question 21

How can the SV assumptions used impact insurer’s retained profit? ( 6 )

Answer 21

Prospective meth SV assumptions used can impact insurer’s retained profit

• if SV assumptions represent exactly future experience (best estimate), then total profit retained will be same as if contract had not surrendered
• if SV assumptions same as premium basis assumptions, then profit retained will equal profit made to date
• suitable choice - btwn best estimate & premium basis can adjust profit retained in line with desired aim of insurer
• possible approach uses blended basis
  
  • start with premium basis near entry (retaining profit earned to date)
  • ….and running into best estimate basis closer to maturity
  • how quickly it runs into best estimate basis depends on how quickly it can start retaining same profit as form non-surrendered contract

Question 22

How might we determine the assumption basis for SV calcs using retrospective methods? (2)

Answer 22

If retrospective method is used in earlier years

• company will need to examine its actual experience for all relevant factors (including investment earnings, expenses, mortality and tax).
• may not follow past experience exactly for regular premium contracts (where policyholders are more likely to exercise financial selection against company) particularly regarding investment earnings, to smooth the value.

Question 23

List the assumptions that will usually be needed when determining a prospective surrender value basis (4)

Answer 23

1. Interest
2. Renewal expenses
3. Inflation
4. Mortality (including the effect of selection)
5. Tax (maybe)

Question 24

How might we determine the assumption basis for SV calcs using prospective methods?

Interest (3)

Answer 24

Interest (most important)

• insurer will likely cover without profit liabilities with fixed interest investments, chosen to give reasonable matching term assuming suitable securities exist
• hence insurer might consider
  
  • current weighted average redemption yield of suitable securities to be best estimate or
  • interest rate used in premium basis (for blended basis).

Question 25

How might we determine the assumption basis for SV calcs using prospective methods? Renewal expenses (3)

Answer 25

**_Renewal expenses_** * most recent expense investigation will indicate level of renewal expenses, could be same as used to set current prem rates * unlikely include any margin, since would increase SV * allow for renewal commission/expenses involved in surrendering policy

Question 26

How might we determine the assumption basis for SV calcs using prospective methods? Inflation (2)

Answer 26

**_Inflation_** * probably chosen to be consisten with investment return assumption * real return anticipated on index linked government stock will given indication of suitable margin below the full intrest rate assumption

Question 27

How might we determine the assumption basis for SV calcs using prospective methods? Mortality (including the effect of selection) (6)

Answer 27

**_Mortality (including the effect of selection)_** * most contracts with surrender values, mortality not have big impact on SVs...in fact, usually, contracts like term assurances, where mortality is important, often don't even have SVs * should reflect future expected mortality of those policyholders who are surrendering * reasonable to assume such people have lighter mortality, since unhealthy people would likely keep policies, not surrender them; little evidence of this selection in practice, since insurers can't really monitor mortality of surrendered folk! * either make explicit allowance for lighter mortality, or relay on other margins in basis * could use select mortality, but nature of selective process here is different to that underlying standard table (selection due to underwriting)

Question 28

Describe the typical terms for surrender of unit-linked contracts. (5)

Answer 28

1. Normally specified at outset 2. Surrender value normally equals unit-fund bid value, sometimes less surrender penalty 1. Penalty could be expressed as proportion of unit-fund value, or as monetary deduction 2. Any penalty tends to be relatively large at early policy durations, decreasing over time 3. Aims to recover any shortfall at time of surrender, where charges to date have been insufficient to recoup all initial expenses under policy