Back to Basics, Gross Premium Valuation - Grant Mackay
FIA, FIAA
Experience in New Zealand
Australia
United Kingdom
Indonesia
Vietnam
Helped introduce actuarial standards for Australia:
Actuarial liabilities (Margin on Services, forrunner to IRFS)
Capital Adequacy
Solvency (mid 1990’s; forerunner for parts of Solvency II)
Tutoring and guest lecturer
2
1
Aims:
A refresher course on actuarial valuation.
To ensure everyone is up-to-speed for the more
technical training to follow
- Gross Premium Valuation:
What is it?
Why do it?
How does it work?
What needs to be done to implement it?
3
Before we start:
Remember:
Life insurance is
1) Intangible (not physical, it’s a “promise”)
2) Contingent (mortality, maturity, surrender,
lapse,..)
3) Long Term (could be a “life time”)
For each policy, we don’t know what the actual profit will be
until that individual policy finishes.
Reporting can be likened to posting an “interim” result.
4
2
Gross Premium Valuation:
Definition:Gross Premium Valuation
= liability equal to the discounted value of future net cashflows
Cashflows (CF):
- Premiums
- Expenses
- Commission
- Contingency
- Death
- Disablement
- Surrender
- Maturity
- Tax
GPV = - PV (CFt)
all t
CFt = total net cashflow
at time t
∞
= - Σ vt CFt
t=0
Does not include investment income.
- This is covered in the discount factors
5
Schematic:
Policy data
- premium
- cover
- age/sex
- term
Output:
Cashflow
1
Valuation Model
Assumptions
- economic
- actuarial
2
3
4
Premiums
Expenses
Commission
Death
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
6
3
Net Premium Valuation
Gross Premium Valuation
(using commutation factors)
- Artificial (eg Zilmer/Sprague)
+ Accurate
+can exactly model policy features
- Inflexible
- level premium stream
+multiple decrements
- fixed payment
+economic assumptions
- single decrement
+yield curves
- level interest rate
+Simple
- More Complex
+Doesn’t need computing power
- Computing Power
7
Why the need to change?
- Gives a truer picture of liabilities
In conjunction with fair valuation of assets gives a ‘realistic’
picture of balance sheet (and therefore earnings and value
creation)
International trends
• IFRS
• Fair value reporting
• Models can also be used for
•Embedded value
•Scenario analysis
•Solvency testing
8
4
As an aside:
IFRS Reporting
- Fair value assets
International Solvency
Regimes
- Fair value liabilities
- Margins / PADS
- Costing for guarantees
- Stochastic
The big difference is increased
disclosure
- Margins can be calculated as
“Liabilities” on conservative
assumptions
- Projection models also used for
Scenario testing
-Assumptions
-Sensitivities
- Analysis of earnings
9
Fun Facts!
- GPV Liabilities can be less than zero
- If assumptions hold true then reported profit will = exactly 0
- “Profit” at inception
-t = 0
-The moment just before the policy starts
- “Planned Profit”
- Release of margin in GPV liability
-Higher discount rate
-fixed %
- $ amount
- “re-run” GPV
-Set to make profit at inception = 0
10
5
Term Life
5 Years
50% ROP on Maturity
Annual premium: $10
Sum assured on Death: $5000
Surrender Value after 1 year
Projections:
Yearly
(best practice is monthly)
Cashflow assumed to occur at the end of each period
(best practice is some cashflow is at the beginning eg premiums)
11
Schematic:
Policy data
- premium
- cover
- age/sex
- term
Output:
Cashflow
1
Valuation Model
Assumptions
- economic
- actuarial
2
3
4
Premiums
Expenses
Commission
Death
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
12
6
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Net Cash Flow
Present Value
Cummulative
10
5
0%
0.0%
0%
nil
1.000
0
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Net Cash Flow
Present Value
Cummulative
Term Life
5,000
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
2
10.00
3
10.00
4
10.00
5
10.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(15.75)
(15.750)
(15.750)
(2.50)
(5.00)
(5.000)
16.250
10
5
0%
0.0%
10%
nil
1.000
0
9.25
9.250
21.250
9.25
9.250
12.000
9.25
9.250
2.750
9.25
9.250
(6.500)
(12.000)
(2.750)
6.500
15.750
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
Expenses
Product is profitable
therefore reserve at
time t =0 is negative
Term Life
5,000
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
2
10.00
3
10.00
4
10.00
5
10.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(15.75)
(9.780)
(9.780)
50% ROP
If no decrements then
that is needed is to
fund:
Expenses
Maturity
(2.50)
Gross Premium Valuation Reserve
(14.542)
If no decrements then
that is needed is to
fund:
13
(2.50)
(5.00)
(5.000)
14.542
50% ROP
Maturity
(2.50)
Gross Premium Valuation Reserve
(16.250)
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
9.25
8.409
19.542
9.25
7.645
11.133
9.25
6.950
3.488
9.25
6.318
(3.462)
(12.246)
(4.221)
4.607
14.318
Future cashflows are
discounted
14
7
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
10
5
10%
0.1%
10%
nil
lx
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
Net Cash Flow
Present Value
Cummulative
0.899
0
0.653
0.587
1
10.00
2
8.99
3
8.08
4
7.27
5
6.53
0.00
(5.00)
0.90
(4.50)
1.62
(4.04)
2.18
(3.63)
2.61
(3.27)
(14.68)
(0.50)
(0.45)
(0.40)
(0.36)
(0.33)
Premiums are needed is
to fund:
Expenses
Surrenders
(2.50)
!
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
0.727
Maturity
(0.25)
(0.22)
(0.20)
(0.18)
(0.16)
4.25
3.864
9.388
4.72
3.901
5.524
5.05
3.795
1.624
5.27
3.598
(2.171)
(9.29)
(5.769)
(5.769)
(6.077)
(1.965)
2.890
8.447
"
10
5
0%
0.0%
0%
nil
1.000
0
#
Future cashflows are
discounted
$ %&
Term Life
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
5,000
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
0.00
0.00
0.00
2
10.00
0.00
0.00
0.00
3
10.00
0.00
0.00
0.00
4
10.00
0.00
0.00
0.00
5
10.00
0.00
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(4.25)
0.00
(9.25)
0.00
(9.25)
0.00
(9.25)
0.00
15.75
0.00
(12.000)
(2.750)
6.500
(2.50)
50% ROP
If no decrements then
that is needed is to
fund:
Expenses
Maturity
(2.50)
Gross Premium Valuation Reserve
(16.250)
Death Claims
15
Gross Premium Valuation Reserve
(4.388)
lx
0.808
(2.50)
(5.00)
(5.000)
4.388
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
5 years
50% ROP
1.000
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Term Life
5,000
Change in reserves
matches cashflow
16
15.750
8
!
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
"
10
5
0%
0.0%
10%
nil
lx
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
1.000
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
0
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
(1.95)
0.00
0.00
2
10.00
(1.22)
0.00
0.00
3
10.00
(0.42)
0.00
0.00
4
10.00
0.46
0.00
0.00
5
10.00
1.43
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(2.30)
0.00
(8.03)
0.00
(8.83)
0.00
(9.71)
0.00
14.32
0.00
(12.246)
(4.221)
4.607
50% ROP
If no decrements then
that is needed is to
fund:
Expenses
Maturity
(2.50)
Change in reserve +
interest matches net
cashflow
17
!
lx
5,000
(2.50)
Gross Premium Valuation Reserve
(14.542)
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
Term Life
14.318
"
10
5
10%
0.1%
10%
nil
1.000
0
Term Life
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
5 years
5,000
50% ROP
0.899
0.808
0.727
0.653
0.587
1
10.00
(0.94)
0.00
(5.00)
2
8.99
(0.61)
0.90
(4.50)
3
8.08
(0.20)
1.62
(4.04)
4
7.27
0.29
2.18
(3.63)
5
6.53
0.84
2.61
(3.27)
(14.68)
(0.50)
(0.45)
(0.40)
(0.36)
(0.33)
Premiums are needed is
to fund:
Expenses
Maturity
(2.50)
Surrenders
(2.50)
Gross Premium Valuation Reserve
(4.388)
(0.25)
(0.22)
(0.20)
(0.18)
(0.16)
1.69
0.00
(4.11)
0.00
(4.85)
0.00
(5.56)
0.00
8.45
0.00
(6.077)
(1.965)
2.890
8.447
Death Claims
Future cashflows are
discounted
18
9
!
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
"
10
5
10%
0.2%
10%
nil
1.000
0
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
Actual
Term Life
5000
5 years
0.898
0.806
0.724
0.650
0.584
1
10.00
(0.94)
0.00
(10.00)
2
8.98
(0.61)
0.90
(8.98)
3
8.06
(0.20)
1.61
(8.06)
4
7.24
0.29
2.17
(7.24)
5
6.50
0.84
2.60
(6.50)
(14.60)
(0.50)
(0.45)
(0.40)
(0.36)
(0.33)
(2.50)
(2.50)
Gross Premium Valuation Reserve
Per policy
(4.388)
(0.25)
(0.22)
(0.20)
(0.18)
(0.16)
1.68
(5.01)
(4.11)
(4.49)
(4.84)
(4.03)
(5.53)
(3.61)
8.41
(3.24)
(6.759)
(2.431)
3.978
50% ROP
If actual experience
valuation assumptions
experience profits or
losses occur
Therefore valuations
often include explicit
margins of PAD’s
19
12.932
'
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
10
5
0%
0.0%
10%
nil
1.000
0
Term Life
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
5 years
5,000
50% ROP
1.000
1.000
1.000
1.000
1.000
1
10.00
(0.95)
0.00
0.00
2
10.00
(0.42)
0.00
0.00
3
10.00
0.18
0.00
0.00
4
10.00
0.86
0.00
0.00
5
10.00
1.63
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(0.30)
3.00
(6.03)
2.80
(6.83)
2.60
(7.71)
2.40
16.32
2.20
(4.246)
1.779
8.607
Expenses
Maturity
(2.50)
(2.50)
Gross Premium Valuation Reserve
(4.542)
If no decrements then
that is needed is to fund:
Extra Margin 10 , 8 , 6 ,
4, 2
Profit = Release of
Margin (+ interest)
20
16.318
10
Schematic: Next Steps
Policy data
- premium
- cover
- age/sex
- term
1) Will need policy
inforce data
Output:
Cashflow
2) Build a model to
project cashflowsPremiums
Valuation Model
Assumptions
- economic
- actuarial
3) Need best estimate
actuarial assumptions
4) Set economic
assumptions
1
2
3
4
Expenses
Commission
Death
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
5) Analyse results
21
Schematic: Next Steps
Policy data
- premium
- cover
- age/sex
- term
Output:
Start
practicing
Cashflow
1) Build
a model toby
1
building
your
own
Premiums
project
cashflows
1) Will need policy Valuation Model
Expenses
Commission
examples
inforce data
Death
Assumptions
- economic
- actuarial
3) Need best estimate
actuarial assumptions
4) Set economic
assumptions
2
3
4
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
5) Analyse results
22
11
Assumptions setting:
Economic
- Investment returns
- Inflation
- benefits
- expenses
- Actual Investments
- Target Investment
Strategy
- Market indices
- Expert analysis
Actuarial
- Mortality
- Morbidity
- Surrender
- Expenses
- acquisition
- maintenance
- investment
-Tax
experience
investigations
- Actual / Expected
- 3 yearly (often more)
- Industry experience
- Company experience
- Reinsurer
- Actuarial Investigations
- Activity based expense costings
- Analysis of past Earnings
23
- Actuarial
- Analysis of Earnings
- Monthly/Quarterly
Measure
Results
Assumption
Actuarial Control
Cycle
- Sensitivity Analysis
Implement
24
12
()
*
25
13
Experience in New Zealand
Australia
United Kingdom
Indonesia
Vietnam
Helped introduce actuarial standards for Australia:
Actuarial liabilities (Margin on Services, forrunner to IRFS)
Capital Adequacy
Solvency (mid 1990’s; forerunner for parts of Solvency II)
Tutoring and guest lecturer
2
1
Aims:
A refresher course on actuarial valuation.
To ensure everyone is up-to-speed for the more
technical training to follow
- Gross Premium Valuation:
What is it?
Why do it?
How does it work?
What needs to be done to implement it?
3
Before we start:
Remember:
Life insurance is
1) Intangible (not physical, it’s a “promise”)
2) Contingent (mortality, maturity, surrender,
lapse,..)
3) Long Term (could be a “life time”)
For each policy, we don’t know what the actual profit will be
until that individual policy finishes.
Reporting can be likened to posting an “interim” result.
4
2
Gross Premium Valuation:
Definition:Gross Premium Valuation
= liability equal to the discounted value of future net cashflows
Cashflows (CF):
- Premiums
- Expenses
- Commission
- Contingency
- Death
- Disablement
- Surrender
- Maturity
- Tax
GPV = - PV (CFt)
all t
CFt = total net cashflow
at time t
∞
= - Σ vt CFt
t=0
Does not include investment income.
- This is covered in the discount factors
5
Schematic:
Policy data
- premium
- cover
- age/sex
- term
Output:
Cashflow
1
Valuation Model
Assumptions
- economic
- actuarial
2
3
4
Premiums
Expenses
Commission
Death
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
6
3
Net Premium Valuation
Gross Premium Valuation
(using commutation factors)
- Artificial (eg Zilmer/Sprague)
+ Accurate
+can exactly model policy features
- Inflexible
- level premium stream
+multiple decrements
- fixed payment
+economic assumptions
- single decrement
+yield curves
- level interest rate
+Simple
- More Complex
+Doesn’t need computing power
- Computing Power
7
Why the need to change?
- Gives a truer picture of liabilities
In conjunction with fair valuation of assets gives a ‘realistic’
picture of balance sheet (and therefore earnings and value
creation)
International trends
• IFRS
• Fair value reporting
• Models can also be used for
•Embedded value
•Scenario analysis
•Solvency testing
8
4
As an aside:
IFRS Reporting
- Fair value assets
International Solvency
Regimes
- Fair value liabilities
- Margins / PADS
- Costing for guarantees
- Stochastic
The big difference is increased
disclosure
- Margins can be calculated as
“Liabilities” on conservative
assumptions
- Projection models also used for
Scenario testing
-Assumptions
-Sensitivities
- Analysis of earnings
9
Fun Facts!
- GPV Liabilities can be less than zero
- If assumptions hold true then reported profit will = exactly 0
- “Profit” at inception
-t = 0
-The moment just before the policy starts
- “Planned Profit”
- Release of margin in GPV liability
-Higher discount rate
-fixed %
- $ amount
- “re-run” GPV
-Set to make profit at inception = 0
10
5
Term Life
5 Years
50% ROP on Maturity
Annual premium: $10
Sum assured on Death: $5000
Surrender Value after 1 year
Projections:
Yearly
(best practice is monthly)
Cashflow assumed to occur at the end of each period
(best practice is some cashflow is at the beginning eg premiums)
11
Schematic:
Policy data
- premium
- cover
- age/sex
- term
Output:
Cashflow
1
Valuation Model
Assumptions
- economic
- actuarial
2
3
4
Premiums
Expenses
Commission
Death
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
12
6
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Net Cash Flow
Present Value
Cummulative
10
5
0%
0.0%
0%
nil
1.000
0
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Net Cash Flow
Present Value
Cummulative
Term Life
5,000
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
2
10.00
3
10.00
4
10.00
5
10.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(15.75)
(15.750)
(15.750)
(2.50)
(5.00)
(5.000)
16.250
10
5
0%
0.0%
10%
nil
1.000
0
9.25
9.250
21.250
9.25
9.250
12.000
9.25
9.250
2.750
9.25
9.250
(6.500)
(12.000)
(2.750)
6.500
15.750
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
Expenses
Product is profitable
therefore reserve at
time t =0 is negative
Term Life
5,000
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
2
10.00
3
10.00
4
10.00
5
10.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(15.75)
(9.780)
(9.780)
50% ROP
If no decrements then
that is needed is to
fund:
Expenses
Maturity
(2.50)
Gross Premium Valuation Reserve
(14.542)
If no decrements then
that is needed is to
fund:
13
(2.50)
(5.00)
(5.000)
14.542
50% ROP
Maturity
(2.50)
Gross Premium Valuation Reserve
(16.250)
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
9.25
8.409
19.542
9.25
7.645
11.133
9.25
6.950
3.488
9.25
6.318
(3.462)
(12.246)
(4.221)
4.607
14.318
Future cashflows are
discounted
14
7
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
10
5
10%
0.1%
10%
nil
lx
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
Net Cash Flow
Present Value
Cummulative
0.899
0
0.653
0.587
1
10.00
2
8.99
3
8.08
4
7.27
5
6.53
0.00
(5.00)
0.90
(4.50)
1.62
(4.04)
2.18
(3.63)
2.61
(3.27)
(14.68)
(0.50)
(0.45)
(0.40)
(0.36)
(0.33)
Premiums are needed is
to fund:
Expenses
Surrenders
(2.50)
!
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
0.727
Maturity
(0.25)
(0.22)
(0.20)
(0.18)
(0.16)
4.25
3.864
9.388
4.72
3.901
5.524
5.05
3.795
1.624
5.27
3.598
(2.171)
(9.29)
(5.769)
(5.769)
(6.077)
(1.965)
2.890
8.447
"
10
5
0%
0.0%
0%
nil
1.000
0
#
Future cashflows are
discounted
$ %&
Term Life
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
5,000
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
0.00
0.00
0.00
2
10.00
0.00
0.00
0.00
3
10.00
0.00
0.00
0.00
4
10.00
0.00
0.00
0.00
5
10.00
0.00
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(4.25)
0.00
(9.25)
0.00
(9.25)
0.00
(9.25)
0.00
15.75
0.00
(12.000)
(2.750)
6.500
(2.50)
50% ROP
If no decrements then
that is needed is to
fund:
Expenses
Maturity
(2.50)
Gross Premium Valuation Reserve
(16.250)
Death Claims
15
Gross Premium Valuation Reserve
(4.388)
lx
0.808
(2.50)
(5.00)
(5.000)
4.388
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
5 years
50% ROP
1.000
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Term Life
5,000
Change in reserves
matches cashflow
16
15.750
8
!
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
"
10
5
0%
0.0%
10%
nil
lx
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
1.000
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
0
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
5 years
1.000
1.000
1.000
1.000
1.000
1
10.00
(1.95)
0.00
0.00
2
10.00
(1.22)
0.00
0.00
3
10.00
(0.42)
0.00
0.00
4
10.00
0.46
0.00
0.00
5
10.00
1.43
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(2.30)
0.00
(8.03)
0.00
(8.83)
0.00
(9.71)
0.00
14.32
0.00
(12.246)
(4.221)
4.607
50% ROP
If no decrements then
that is needed is to
fund:
Expenses
Maturity
(2.50)
Change in reserve +
interest matches net
cashflow
17
!
lx
5,000
(2.50)
Gross Premium Valuation Reserve
(14.542)
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
Term Life
14.318
"
10
5
10%
0.1%
10%
nil
1.000
0
Term Life
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
5 years
5,000
50% ROP
0.899
0.808
0.727
0.653
0.587
1
10.00
(0.94)
0.00
(5.00)
2
8.99
(0.61)
0.90
(4.50)
3
8.08
(0.20)
1.62
(4.04)
4
7.27
0.29
2.18
(3.63)
5
6.53
0.84
2.61
(3.27)
(14.68)
(0.50)
(0.45)
(0.40)
(0.36)
(0.33)
Premiums are needed is
to fund:
Expenses
Maturity
(2.50)
Surrenders
(2.50)
Gross Premium Valuation Reserve
(4.388)
(0.25)
(0.22)
(0.20)
(0.18)
(0.16)
1.69
0.00
(4.11)
0.00
(4.85)
0.00
(5.56)
0.00
8.45
0.00
(6.077)
(1.965)
2.890
8.447
Death Claims
Future cashflows are
discounted
18
9
!
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
"
10
5
10%
0.2%
10%
nil
1.000
0
p.a
Sum Insured
years (50% ROP)
p.a.
p.a.
Actual
Term Life
5000
5 years
0.898
0.806
0.724
0.650
0.584
1
10.00
(0.94)
0.00
(10.00)
2
8.98
(0.61)
0.90
(8.98)
3
8.06
(0.20)
1.61
(8.06)
4
7.24
0.29
2.17
(7.24)
5
6.50
0.84
2.60
(6.50)
(14.60)
(0.50)
(0.45)
(0.40)
(0.36)
(0.33)
(2.50)
(2.50)
Gross Premium Valuation Reserve
Per policy
(4.388)
(0.25)
(0.22)
(0.20)
(0.18)
(0.16)
1.68
(5.01)
(4.11)
(4.49)
(4.84)
(4.03)
(5.53)
(3.61)
8.41
(3.24)
(6.759)
(2.431)
3.978
50% ROP
If actual experience
valuation assumptions
experience profits or
losses occur
Therefore valuations
often include explicit
margins of PAD’s
19
12.932
'
Annual Premium
Term Life
Surrender Rate
Mortality
Discount rate
Tax
lx
End of year:
Premiums
Interest Income
Surrenders
Mortality
Maturity
Expenses
Acquisition
Maintenance
Investment
Commission
Initial
Renewal
Tax
Change in reserves
Profit
10
5
0%
0.0%
10%
nil
1.000
0
Term Life
p.a
years (50% ROP)
p.a.
p.a.
Sum Insured
5 years
5,000
50% ROP
1.000
1.000
1.000
1.000
1.000
1
10.00
(0.95)
0.00
0.00
2
10.00
(0.42)
0.00
0.00
3
10.00
0.18
0.00
0.00
4
10.00
0.86
0.00
0.00
5
10.00
1.63
0.00
0.00
(25.00)
(0.50)
(0.50)
(0.50)
(0.50)
(0.50)
(0.25)
(0.25)
(0.25)
(0.25)
(0.25)
(0.30)
3.00
(6.03)
2.80
(6.83)
2.60
(7.71)
2.40
16.32
2.20
(4.246)
1.779
8.607
Expenses
Maturity
(2.50)
(2.50)
Gross Premium Valuation Reserve
(4.542)
If no decrements then
that is needed is to fund:
Extra Margin 10 , 8 , 6 ,
4, 2
Profit = Release of
Margin (+ interest)
20
16.318
10
Schematic: Next Steps
Policy data
- premium
- cover
- age/sex
- term
1) Will need policy
inforce data
Output:
Cashflow
2) Build a model to
project cashflowsPremiums
Valuation Model
Assumptions
- economic
- actuarial
3) Need best estimate
actuarial assumptions
4) Set economic
assumptions
1
2
3
4
Expenses
Commission
Death
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
5) Analyse results
21
Schematic: Next Steps
Policy data
- premium
- cover
- age/sex
- term
Output:
Start
practicing
Cashflow
1) Build
a model toby
1
building
your
own
Premiums
project
cashflows
1) Will need policy Valuation Model
Expenses
Commission
examples
inforce data
Death
Assumptions
- economic
- actuarial
3) Need best estimate
actuarial assumptions
4) Set economic
assumptions
2
3
4
Disablement
Surrender
Maturity
Tax
Gross Premium Valuation
5) Analyse results
22
11
Assumptions setting:
Economic
- Investment returns
- Inflation
- benefits
- expenses
- Actual Investments
- Target Investment
Strategy
- Market indices
- Expert analysis
Actuarial
- Mortality
- Morbidity
- Surrender
- Expenses
- acquisition
- maintenance
- investment
-Tax
experience
investigations
- Actual / Expected
- 3 yearly (often more)
- Industry experience
- Company experience
- Reinsurer
- Actuarial Investigations
- Activity based expense costings
- Analysis of past Earnings
23
- Actuarial
- Analysis of Earnings
- Monthly/Quarterly
Measure
Results
Assumption
Actuarial Control
Cycle
- Sensitivity Analysis
Implement
24
12
()
*
25
13