11. aos Flashcards
Shows financial effect of divergences between actual experience and what assumed in val basis, and financial effect of writing NB
Provide checks on val data and results, incl. checking reasonability and consistency of surplus items
Assist in distributing surplus by identifying items of surplus unlikely to recur
Trends in items of surplus may give useful info on trends in experience
New items identified in analysis may be used to inform risk id process
Assist in setting future assumptions
Analyse effect of policy alterations
Assist in decisions such as derisking BS to protect solvency levels
Regulatory return requirement
St-St-1=(At-At-1)-(Lt-Lt-1)
Due to divergence in val assumptions and actual experience + any profit margin
Surplus must be adjusted for dividends paid and capital raised/repaid
Changes in valuation assumptions
Release of CSM (published reporting only)
Release of RM / RA
Expected profit margin on group contracts (published reporting only when using PAA)
AvE investment return
AvE expenses
AvE mortality
AvE sickness/disability/morbidity
AvE other risk benefits (e.g. retirement)
AvE withdrawals
AvE charges under unit-linked and unitised w-p contracts
AvE tax
New business
Other policy alterations/changes
Changes in maturity guarantee reserves
Option and guarantee exercises
Formula or projection approach
Formula not often used but simplified versions be useful checks on projection approach
If doing aos on prudential supervision basis, must account for change in RM over period
Requires analysis of other factors, e.g.
Changes in size of non-hedgeable components of SCR
Run-off assumptions in non-hedgeable SCR
Changes in allowance for diversification in RM calc
Business decision changes that materially impact RM e.g. reinsurance strat
Amount of surplus for each source depends on order in which they’re calculated and direction of analysis, i.e. from A to E or vice versa
No unique method
Won’t usually change method from previous years
Once one source of surplus is determined, subsequent sources are determined that actual experience of first one is same as expected and vice versa.
May be unexpected residual to be investigated if significant
Change in val assumptions
At end or beginning of year
If end:
Value of L at end is recalced using beginning of year basis
Contribution to surplus is recalced value less original value of year end L
Investment return
Assuming net income arises halfway through the year,
Surplus≈I-iV0-12i(P-E-C)
I:actual investment income net tax;i:val interest rate net tax;
V0:L at beginning of year;
P:OP received;E:actual E;C:actual payments
If assumption above significantly diff, adj formula
Expenses
Surplus≈E’-RE1+12i
E’:expected E as val;RE:part of actual E relating to business in orce at start of year
For NP val:
E’=P-NP
For GP val, E’ depends on how expenses charged. If explicit allowing e_t of office premium plus e_c per contract then:
E’=etP+ec*n
n:average number of contracts in force
Can make adj for automatic increases to existing policies, can be treated as new policies
Mortality
Surplus ≈EDS-ADS
EDS:expedcted death strain;ADS:actual death strain
EDS:
EDS≈k1qxS-V1+k2qxP-E’
x:ave age at begining of year;S:benefit;V1:reserve at end of year ;
k1=1 if contracts in force for full yearexisted due to death
=12 if contracts entered during full year or withdrew during year
k2=12 if contracts in force for full yearexisted due to death
=14 if contracts entered during full year or withdrew during year
1st term: Expected death outgo minus expected L release on death
2nd term: Loss of expected premiums net expenses for remainer of val period
1st order impact > 2nd order impact
ADS:
ADS≈D+P’‘1+12i-V
D: actual payments made on death;
P’’: premiums not received in year from death net expenses
V:end of year reserve for contracts ended in death
Sickness
3 methods:
Manchester unity method
Inception annuity method
Multiple state model
Manchester unity
Surplus≈ expected sickness payments-actual(1+12i)
Surplus ≈{zx12Sx0+Sx1-actual payments}(1+12i)
zx=expected length of sickness in weeks for lives aged x
Sx(0)=sickness benfit per week at beginning of year for lives aged x
Sx(1)=sickness benfit per week at end of year for lives aged x
If exists explicit reserve for CIP, change in reserve included in surplus calc
Inception annuity
Surplus ≈expected ix-actual ixannuity factor benefit+expected tx-actual txannuity factor benefit(1+12i)
Multi-state model
Can derive formulae
Withdrawals
Surplus≈V0W*1+i+PW-W1+12i- EDSW
V0W=reserve at beginning for withdrawals
Pw=val premiums received net expected renewal expenses
W=withdrawal benefit paid
EDSW=contribution from withdrawals to EDS
May be easier to follow similar approach to mortality surplus where surplus is approx. expected – actual withdrawal strain
New business
Surplus≈PN-EN*1+12i-EDSN-V1N
PN=val premiums for NB received net expected renewal expenses
EN=actual NB expenses
V1N=reserve at end of year for new business
EDSN=contribution from NB to EDS
Formula contains CF items assumed to occur at inception of new contracts net L set up for them.
In practice, calc NB surplus before death strain and not subtract EDS from surplus
Applied to any type of business
Project A + L and analyse sources separately
Easier to understand
Need to recalc A and L under diff bases
Quantification effect of change in basis is same as formula approach.
Steps:
A allocated to contracts = value of L at start of year
Project A and L forward to end of year using beginning of year val assumptions as expected experience
Value of A and L at end of year are calced data from step above and beginning of year val assumptions
Repeat step 2 and 3, changing of experience items from E to A value.
E.g. switching from A to E mortality»_space; actual instead of expected death
Step ii must also allow for 2nd order impact on other CF, e.g. impact on premiums due to actual death movements
In step iii, A+L reclalced using changed CF and inforce policies determined in step ii
Steps ii and iii usually done together in one projection model iteration
Recalced surplus at end of year – surplus from previous step iii»_space; surplus from experience item
Steps iv and v repeated for each experience item
