Ch 25: Surrender values

Question 1

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 1

• Surrender relates to policyholders terminating contracts early
• 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
• SV>(AS) => loss on surrender

Question 2

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

Endowmwnt/whole of life (2)
Term assurance (5)
Immediate annuity (2)

Answer 2

Endowment/whole of life​
1. reserves increase with policy duration, hence SV can be paid
2. SV (and reserves) typically increases towards sum assured

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

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 3

List principles that should be considered when calculatings surrender values

(11)

Answer 3

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 4

Discuss the influence of PRE when setting SVs in terms of

Discontinuance at short durations (4)
Discontinutnace close to maturity (3)
Auction values (4)

Answer 4

• SV at insurer discretion / regulated
• Influenced by literature,past practice,competitors

Discontinuance at short duration
* SVs likely compared to premiums paid (sometimes with interest),
* but (AS)t less than this in the ST
* prospective policy value based on best estimates of future experience likely to be even smaller
* insurers may accept losses/reduced profit on SVs in the ST so SV does not seem too low to PH
* Penalise later surrenders to recoup these losses.

Discontinuance close to maturity
* PHs expect SV prior to maturity to be similar to maturity value
* SVs should progress smoothly at each year end into maturity value
* achievable for without profits contracts: base SV on prospective polcy values

Auction values
* auction value is the value obtained if PH transferred ongoing policy to someone else
* auction values assessed independently by specialist brokers = hence PHs may accept as fair
* Not suitable to use
* difference in assumptions used eg optimism of future benefits of policy
* Values are volatile => hard to determine, without actually selling policy

Question 5

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

What does the asset share represent in general? (2)

What implication does this have for SVs? (3)

What does basing SV on AS mean in terms of profit/loss distributions (1)

How might we achieve average AS over time? (3)

Answer 5

Asset share
* represents money insurer has actually accumulated in respect of policy,
* unlike supervisory reserve (represents how much money company must hold)

The implication is
* SVs must not exceed earned asset share in aggregate over a reasonable time period
* asset share = 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 share
* implies distributing accrued profits/losses to PHs,
* as asset share contains all of accumulated profits/losses from policies to date

Calc average (AS)t over period:
* Periodic cal of AS eg. 1 per year (practical) => averaging over year
* Smothed AS as basis for SV
* Decide time period(s) to smooth over, e.g. want to smooth individuals months’ AS 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 6

Discuss the factors that impact SV’s
NUB Disclosure and Competitiors 3
Changes in surrender scales over time 3
Ease of application 2
Selection against company 4
Surrender and re-entry 3

Answer 6

NUB Disclosure and competitiors
* Illus values for SV need to be provided @ NUB (regs)
* Competitors SV also published => influence SV offered
* Reputational risk if figures conflict with illus values

Changes in surrender scales over time
* Scales should not change unless financial cond dictate this
* Should not have discontinuity by duration
* eg SV > after PA when prem higher

Ease of application
* Not be overly complex to calc eg formula or table
* Smoothing req=>X-sub=> fairer dbn to all classes of PH

Selection against company
* Surr terms min risk of PH selection
* Cost of SV can be too high => don’t offer SV
* eg after mkt crash single premium UL risk of selection
* Revise terms quickly.

Surrender and re-entry
* Surr terms need to be compared to current premium rates
* Form of selection
* eg UL mkt crash lapse and re enter to buy units at lower value

Question 7

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 7

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
* 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 8

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 8

Advantages
1. Retro value represents AS @ surr = 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 9

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

Advantages (4)

Disadvantages (3)

Answer 9

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 hence maintain equity with continuing policyholders and any shareholders
3. The surrender values will run into the maturity value, for without-profits
4. It’s relatively easy to calc no past data req

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 10

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

(4)

Answer 10

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

Question 11

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 11

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 (need apply long duration)
  • …because small changes in interest rate => big effect on SV

Question 12

Calculate SV: Retained Profits
What do we mean by ‘profit retention’ in context of SVs? (2)
Retro retained profit
Prosp retained profit

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

Answer 12

Profit retention relates to
* excess of asset share - 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

SV is retrospective=> no profit retained
* wouldn’t want to use retrospective method for too long, since SV (retro reserve) is equal to asset share

SV is prospective => profit retained depends on Surr basis vs Pricing basis
* profit contained in the margins of assump
* see below

Question 13

Calculate SV: Retained Profits
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 13

Prospective method profit retention

• depends on relationship btwn SV assumptions vs pricing assumptions
• if profit allowance contained solely in assumption margins used to calc office premium then profit retained can be specified as
  
  • (AS - SV’) + (SV’ - SV”), where
    
    • AS = earned asset share
    • SV’ = prospective SV using office premium assumptions
    • SV’’ = prospective SV using surrender value basis assumptions.
• 1st part, (AS - 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 14

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

Answer 14

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

• if SV basis= exactly future experience (best estimate),
  
  • then total profit retained will be same as if contract had not surrendered
• if SV basis= 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

eg notes

Question 15

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

Answer 15

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 eg smoothing inv ret
• Deviate from past experience
  
  • eg lower inv ret=> lower val than AS => retain profit
  • eg lower expenses=> true val result in low SV

Question 16

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

Answer 16

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

Question 17

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

Interest (3)

Answer 17

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 18

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

Renewal expenses (3)

Answer 18

Renewal expenses

• most recent expense investigation will indicate level of renewal expenses, could be same as used in pricing basis
• unlikely include any margin, since would increase SV
• allow for renewal commission/expenses involved in surrendering policy

Question 19

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

Inflation (2)

Answer 19

Inflation

• probably chosen to be consistent 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 20

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

Mortality (including the effect of selection) (6)

Answer 20

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 21

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

(5)

Answer 21

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