Final Revision Flashcards
Describe the contribution method
Better interest
plus better mortality
plus better expenses and interest
Give the formula for contribution dividend
(V0+P)(i’-i)
+ (q-q’)(S-V1)
+ E(1+i) - E’(1+i’)
How is the contribution dividend paid, does it have a TB?
Dividend converted to paid up addition to benefit, not paid out in cash.
Yes.
Give the formula to reconcile data
Data(t-1)+NB-Run off Biz=Data(t)
What type of benefits can you have
Guaranteed (monetary/price index or similar)
Discretionary
Investment linked
What’s the formula for liability outgo?
Benefit payments + Expense outgo - Premium income
What is the words formula for appropriation price? Expropriation price?
NAV(offer basis)/#Units at valn date
NAV(bid basis)/#Units at valn date
In decided what goes into the NAV, what things are the same for both expropriation and appropriation?
What is different, how?
Same:
Current (Assets-Liabs)
+Accrued income
-Allowance for accrued tax
Different:
Market price of assets on offer basis+expenses incurred purchasing them (buying assets at high price)
MP of assets on bid basis-expenses incurred selling them (selling assets at low price)
Explain the bid offer spread? Which one is buying and selling, highest and lowest?
Offer = high price = price to buy Bid = low price = price to sell asset
Which is the lowest, bid or offer?
BID!
Is appropriation on offer or bid?
Offer
What basis are units prices if a net seller of units? What does that mean for the bid/offer price?
Bid basis
Find bid and offer using expropriation price
If company a net seller, what basis will it use, what’s the formula for offer price and bid price.
What about if it’s a net buyer?
Bid basis: Offer price: (buying) Expropriation price PLUS initial charge (bid-offer) Bid Price (selling) Expropriation price
Offer basis: Offer price: (buying) Appropriation price plus initial charge (bid-offer) Bid Price (selling) Appropriation price
Assets now = 10 Current assets = 2 Current Liabs = 4 #Units = 100 Selling cost of all assets = 3 Purchase cost of all assets = 1 Initial charge of 10% on bid and offer prices Net seller What is appropriation price? What is the bid price? (in words)
Net seller = exproprtiation basis for the bid price Appropriation price (buying) = (10+1+(2-4))/100 Bid price on expropriation basis = Expropriation price
Which price relates directly to whatever basis it’s on? Which price related to the basis including charges?
The bid price (appropriation or exp price)
The offer price (approp/exp price + init charge)
Explain what actuarial fund does?
Allows us to hold the present value of the unit fund
Explain the actuarial funding factor formula?
Unit fund at t * A(x+t:n-t)
ie. PV of current unit fund paid at death
T=0 normally
What formula shows the amount transferred to non-unit fund using actuarial funding
UF(0)*(1-A(x:n)) is transferred to the unit fund
ie. Difference between original unit fund and the PV of it
Give an alternative to actuarial funding factor that takes credit for future charges, what loan does it represent
Negative non-unit reserves
One from policyholders with positive non unit reserves repaid on future emerging profits
Give 3 constraints to negative non-unit reserves
Sum of all non-unit reserves >= 0
Sum of unit and non-unit reserve on policy >=guaranteed SV
Future profits must arise to repay loan
What risk is transferred BACK to company by guaranteed (maturity, surrender or annuity option), why?
Investment risk, attractive
What 2 guarantees are attractive on traditional policies?
GAO
Guaranteed minimum maturity value on EA
What’s the difference between risk of guarantees in a traditional policy or non-traditional policy
Company has no control over investment policy in non-traditional
How to value an option or guarantee (2 ways)
Option pricing technique
Stochastic simulated investment performance
Give 3 common mortality options
Additional benefit purchase without need for further health evidence Renewable policy (no further health evidence) Convertible policy - change part of SA from one contract to another
Why use T’s and C’s for mortality options, explain what it means for premium rates
Reduce anti-selection
ie. Those in poor health using option to get large amounts of life insurance at rates not reflecting their condition
Give some T’s and C’s examples for mortality options
Timing - fixed take up times
Birth child
Salary increase
SA(additional)<=SA(original)
Explain the cost of a mortality option
Difference between price should have charged given full underwriting information and price actually charged
What 2 assumptions over the normal pricing basis are needed to value a mortality option
P(option exercised)
qx of those who take-up option
How to get the EPV of cost of mortality option
EPV(ben) - EPV (prem)
Why is the conventional method the preferred choice in mortality option pricing?
NA requires double decrement tables
Difficult to obtain such data
NB won’t have it
What mortality assumptions are made in the North American method?
EPV(B) assumes lives not taking up option are Ult. Meaning average mortality is higher than Ult.
OR
Average mortality for all lives is Ult, change mortality of those who don’t take up to reflect
What assumptions underly the conventional method?
All lives eligible to take up option will do so
Mortality of those taking up option is Ult version of Select of those joiners
What data is needed in the conventional method?
Sel/Ult mortality tables
Give a problem with the conventional method?
How to get around it?
If multiple options/take up dates can’t be used
Choose worst option from a financial point of view is chosen with Probability 1.
Give the principle of surrender values
Simple PETS, DD CC ME
Take into account:
Simple
PRE
Equitable treatment of continuing and surrendering
TCF
SVmaturity, SV->Mat value
Discontinuities - don’t suffer by duration
Documented - clearly
Competitors - take account of them
Change - not too frequent
Minimal - Not exceed EAS in aggregate
Early - Not appear too low at early durations vs. premiums paid
Why don’t term assurance have SV?
Anti selection reduced
Cheaper premiums
Small reserve release anyway (reserves don’t tend to the sum assured)
What does A with a line on top of it mean?
An assurance of 1 payable at the exact moment of death
To calculate a proper retrospective reserve, not formula driven, what do you need?
Up to date EAS for reach policy
Give a formula for retrospective SV
(1+i)^t * 1/tPx * (Pax:t - SA(x:t)-I-Ra(x:t) - DA(x:t)) - C P = premiums annual S = SA I = Initial expenses R=Renewal expense D=Claims expense C = Charge for surrendering (admin type)
Give a formula for prospective SV
SA(x:t) + Ra(x:t) + DA(x:t) - Pa(x:t) - C
Value of Future sum assured plus expenses net of future premiums and charge
What does retrospective reserves represent, why is it not that good for companies?
The EAS at surrender, takes all the profits away so no loss, no gain. Profit = EAS-SV
Give 2 disadvantages of retrospective
SV does not run into Mat Value
Not say anything about what profit would have been made, so equity between policyholders hard
Give an advantage of retrospective
Not complex if EAS available
What does prospective SV represent if done on realistic basis?
Value of the contract to company
Why use prospective SV
Enables calculation of how much profit company wants to keep
So maintain equity
Give disadvantages of propsepective SV
total SV’s might be > total EAS
Possible unreasonable SV’s early on
Small changes in interest rate, for long durations, have big SV effect
Advantage of prospective SV
SV’s -> maturity value for without profits
Comparable to auction values
more likely comparable to competition
Easy to do, doesn’t require knowledge of past
How does a company profit from SV’s?
Pay out less that EAS
ie. profit is EAS-SV
What is the formula for Profit retained?
(EAS-SV(pricing assumps)) + (SV(pricing) - SV(actual assumps used))
What is EAS-SV(pricing)
SV(pricing)-SV(actual surrender assumps used)
Profit made to date
Value of profit that would arise in future due to prem rate and surrender value assumption differences
How do you choose assumptions for SV?
Somewhere between best estimate from now (profit that would be made is policy continues) and pricing assumptions (profit made to date)
What basis on assumptions would be used for the prospective assumptions? Why?
Blended, pricing near start, best estimate near end
Depends on how early want to claim profit as if not surrendered
How can you avoid lapse and re-entry to do with surrender values?
Make sure SV not above EAS
What actual experience is used in retrospective SV calcs?
Investment earnings
mortality
expenses
tax
Why won’t actual investment earnings be used in regular premium Retro SV’s?
Smooth the value
What assumptions will be used to find prospective SV’s. What is the most important?
Interest (most important) Expenses Inflation Mortality Tax
How to pick interest rate assumption in Prospective SV?
Premium basis if using those assumptions
Weighted average redemptions yield of FI liabs that it holds to back liabs
How to pick expense assumptions in Pros SV?
BE/Prudent?
What allowance needs to be made?
Recent expense investigation
Those used in recent pricing
BE
Renewal commission
How to pick inflation rate assumption in Pros SV?
Consistent with investment return
Use real return - investment return on FI to get inflation
How is mort assumption different from past experience in Pros SV?
Is it important?
Expected future mortality of those surrendering
Which is LIGHTER than those not
Will not have much effect on results
What happens when make a policy PUP, what stays the same?
Stop paying premiums, SA reduces
T’s and C’s stay same
What is making a policy paid up, equivalent of doing?
Using value of the original policy to purchase a single premium policy for new SA at PUP date
Give 2 reasons why PUP basis would be different than SV basis?
Alteration cost is different
Mortality selection reduces as policy still in force (mortality for those left won’t be as bad as in surrenders)
Why might a policy be altered?
Mismatch between policy and risks ph faces changes
How can P/H match current risks?
Purchase additional policy/alter current one
3 alteration examples
SA change
Premium change
Term change
How do you change term of a WOL
Convert to EA
Equivalent of reducing term to 0?
Equivalent of reduce SA so no premiums needed?
Equivalent of increasing SA?
SV
Paid up SA
Purchase new policy for increment at current rates
Principles on calculating PUP SA
What is the key one for all alterations?
Should be:
Supported by EAS at date of conversion and expected future experience (key)
Consistent with Mat Vals at later duration, reduced for just premiums not recieved
Surrender values before and after conversion approximately equal
Why should alterations be supported by EAS?
Avoid company losses
How would profits look after alteration?
Same as expected amount if policy had originally been written on altered terms
Or
Same profit had it not been altered
Principles of General Alterations
SCILS BaCSS
Supportable by EAS
Costs are recovered
Increases in benefit subject to additional health evidence (depend on amount/time in policy)
Lapse/re-entry avoided by terms
Stable changes - small changes, if expenses incurred in alteration are ignored
Benefit increase consistent with buying new policy for increase
Conversion to PUP is limiting case of reduction in SA
Surrender is limiting case of reduction in term
Methods of alteration
Altering a PESPA motorbike:
Proportionate PUP value Equating policy value Surrender value respread PUP value plus premium for balance of SA Accumulation of premium arrears/surplus
Prop PUP value What products? Formula for calculation? Advantage? Disadvantage?
Without profits EA
PUP value = SA * (total prem paid so far/total prem payable)
A = Very simple to apply and explain
D = Unlikely to be consistent with SV’s
Equating policy values What types of alteration? What do we do? Formula equating values for a PUP SA? What is included if just change SA, not make PUP
Any type
Equate policy values (surrender) on a retro/prosp basis to prospective value after alteration
PUSAA(x+t) + R * a(x+t) + DA(x+t) = SV(t)
R = renewal expense
D = death claim expense
Have a -Pa(x+t) and +C (alteration cost)
Method of Surrender value respread?
Advantage?
Disadvatnage?
Calc premium on current premium basis for post-alteration
Calculate surrender value of existing contract making allowance for inital expenses
Reduce premium by spreading surrender value over outstanding term and deducting
A=Simple
D=not consistent with all terms offered
PUP Policy value plus premium for balance of SA
What can’t it be used for?
Disadvantage?
Conversion to PUP
Won’t reporoduce orginal premium if policy altered to itself
Accumulation of premium arrears/surplus
What can’t it be used for?
How does it work?
Conversion to PUP
Find premium if policy had been in new form from outset
Accumultate it to now
Adjust premium now by this
Product Design Factors
Profitability and its sensitivity Marketability Consistency with other products Competitiveness Financing Risk level Onerousness of guarantees X-subsidies Admin systems Regulations - TCF/Max charges Tax
What does non-unit reserve include?
Expenses, charges, benefits in excess of unit fund
How is a non-unit reserve set up
Discounted Cashflows of charges-expenses-extra benefits projected forward
Go to last date it’s negative
Set up amount at start of that time step to make net cashflow in period 0
Take that amount off the net cashflow of previous period (making more negative)
So non-unit reserves always >=0
So non-unit reserve covers all negative net cashflows if hadn’t been set up.
What can sensitivity analysis be used for?
To find MAD’s for supervisory reserves
Enable set up of any global reserves needed to cover potential FAD’s
What is solvency capital? Why use it? What combination needs to be looked at?
Solvency requirement required by supervisory authority
Add additional safety for policyholders
Reserves and Solvency requirements should be looked at together in their calculation.
(realistic reserves+ large solv req) or prudent reserves but solv req less based on risks)
What 3 ways are there to allow for risk in cashflow model?
risk discount rate
stochastic model
margins for adverse deviation
What is EV
Sum of shareholder share of net assets and present value of future shareholder profits on EB
Why monitor experience?
Find EAS
Update assumptions
Monitor experience trends and take action
MI
What do we need in data?
Volume Consistent Credible homogeneous groups No errors Complete
What’s the minimum desire for homogeneous groups
Separate by contract type
What effects withdrawal rates?
Economy
Competitiveness of product
Better products reach market
Perceived value of product to consumer
How can withdrawal rate be calculated
1-(#pols at end of year)/#pols at start (exclude deaths and maturities)
Why do an AOS for monitoring experience?
MI on experience
Regs
Show financial effect of NB
Show financial effect of divergence between actual and expected assumptions
Check valuation data and process
Identify one-off surplus items, enable decisions on WP bonuses
Why do an AOEV
MI Account information Validate calcs/data/assumps used Reconcile values for successive years Exec Remuneration
What will you do once a experience investigation, AOS, AOEV is complete?
Update views regarding future experience
Change assumps/models in pricing/valuation
Actuaries aren’t fortune tellers, so if we do it a million times we still won’t exactly be right
Split expenses into 2 groups
Direct (related directly to Volume of NB or level of in force)
Overheads (balance, relate to general management and service)
Split non-commission expenses into 4
Initital/renewal/terminal/invesment
What are the expense amounts proportional to?
contracts written/in force
SA written/in force
Prem written/in force
How do we proportion out marketing/underwriting/investment expenses
Related to init commission paid
related to size of benefit
percentage of funds under management
4 Main types of expense and examples
Salary/salary related
Property (rent/heat/light/cleaning)
Computer
Investment (commission/stamp duty/investments department)
