C21 Surrender Values

Question 1

List ten principles that should be considered when calculating surrender values

PEEL CAF DCD P

Answer 1

Principles when calculating surrender values
1. Take into account PRE
2. Treat both surrendering and continuing policyholders equitably
3. At early durations, not appear too low compared with premiums paid, taking into account any projections given at new business stage
4. At later durations, be consistent with projected maturity values
5. Not exceed asset shares, in aggregate, over reasonable time period
6. Take account of surrender values offered by competitors (and possibly also auction values, where available)
7. Not be subject to frequent change, unless dictated by financial conditions
8. Not be subject to significant discontinuities by duration
9. Not be excessively complicated to calculate, taking into account computing power available
10. Be capable of being documented clearly

Question 2

Consider the example of a without-profits whole life assurance for a sum assured of S, payable immediately on death, with annual office premiums of G payable m times a year, where:
 x = age of policyholder at date of issue
 I = initial expenses in excess of those occurring regularly 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 2

Surrender value for without-profits whole life assurance

Retrospective reserve
Dx/Dx+t * (G ax:t -S Ax:t - fAx:t - eax:t -l) - C

Prospective reserve
S Ax+t + fAx+t + eax+t - Gx+t - C

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

Question 3

State the main advantages and disadvantages of using the retrospective method for calculating surrender values (eight points).

P	E	E	L	C	A	F	D	C	D R			Y							 P		Y		Y	Y				Y

Answer 3

Analysis of the retrospective method
 It represents the maximum that the company could pay without making a loss.
 At early durations it may be reasonable compared with the premiums paid.
 It may be consistent with values quoted in product disclosure literature.

 For without-profit contracts, it’s not easy to ensure equity either with continuing policyholders or with any shareholders.
 For without-profit contracts, it will not run into the maturity value, except by chance.
 Consistency with competitors depends on the method and basis used.
 Values may be significantly different from a realistic prospective value, which is likely to be the approach used to calculate auction values.
 The most complex component of the method is obtaining the necessary historic information.

Question 4

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

P	E	E	L	C	A	F	D	C	D R			Y							 P		Y	N	Y	Y	N			Y

Answer 4

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

 There is no guarantee that the surrender values produced will not consistently exceed the asset share.
 It could produce unreasonably low surrender values at early durations, from the policyholder’s point of view.

Question 5

Show how the profit retained by a company on surrender can be split into:

 past profit
 capitalised value of future profit,

by considering the surrender value calculated on the premium basis.

Answer 5

Profit on surrender

The profit retained by the company is the excess of the earned asset share
over the surrender value paid.

If the allowance for profit is contained solely in margins in the assumptions used to calculate the premium, then the profit retained can be specified as
(EAS - SV’) + (SV’ - SV’’)
where
EAS = earned asset share
SV’ = prospective surrender value using same assumptions as used to calculate the office premium
SV’’ = prospective surrender value using surrender value basis assumptions.

The first part, (EAS - SV’) , represents the profit that has been made to date.
The second part, (SV’ - SV’’) , represents the capitalised value of the profit that will arise in future.

Question 6

List the assumptions that will usually be needed when determining a prospective surrender value basis.

Answer 6

Assumptions for a prospective basis
 Interest
 Renewal expenses
 Inflation
 Mortality (including the effect of selection)

Question 7

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

Answer 7

Terms for surrender of unit-linked contracts

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