Sources of Earnings: Tools for Managing Your LTC Business

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Sources of EarningsTools for Managing Your LTC
Business

• John K. Heins, FSA, MAAA
• PolySystems
• Robert J. LaLonde, FSA
• Insight Decision Solutions, Inc
• Mark A. Walker, FSA, MAAA
• Genworth Financial

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The Way It Was Meant To Be
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Earnings Include

• Percent of Premium
• Plus Gain on Interest
• Plus Gain on Persistency
• Plus Gain on Claim Experience
• Plus Expense Gain
• Plus Interest on Surplus (Capital,Equity)

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Sample Quarterly Statement
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Profit from Premium

• To quantify, you must have an idea of the
  valuation net premium(s)
• Should be able to obtain once a product is priced
• Best obtained from valuation system the more
  granular the better

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Gain From Interest

• (iActual iAssumed) x Net Liability
• Net liability for GAAP is all reserves less DAC
  (or VOBA for PGAAP blocks)
• Have to know assumptions, actual experience, and
  the exposure (net liability)

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Gain From Persistency

• (qActual qAssumed) x Net Liability
• q includes all forms of termination
• Net liability for GAAP is all reserves less DAC
  (or VOBA for PGAAP blocks)
• Gain could be split into pieces
• Have to know assumptions, actual experience, and
  the exposure

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Gain on Claim Experience

• Tabular Cost of Claims
• Less
• Incurred Claims
• If you dont know about tabular cost, it is not
  readily available
• If you know about tabular cost, it is probably
  not readily available

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• Paid Claims Chg in Reserves Interest
• (PaidCp PaidPp PaidOld )
• (CpV1 PpV1 OldV1 - V0 )
• (CpIBNR1 OldIBNR1 - IBNR0 )
• (IntIBNR IntV )
• (PaidCp CpV1 CpIBNR1 )(1)
• (IBNR0 IntIBNR - PaidPp - PpV1 - OldIBNR1)(2)
• (V0 IntV - PaidOld - OldV1 )(3)
• Estimated total claims for current period
• IBNR gain
• Case Reserve gain

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If you dont know where to begin

• start with DAC (fewer moving parts other than
  deferrals)
• DACReported (pActual/pAssumed) x DACSched.
• The Scheduled DAC is the amortized amount from
  the prior period if all assumptions are met

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• DACReported x pAssumed / pActual
• DACPrevious x (1 i)
• - NPDAC x (1 i)(1/2)
• You must know interest and net premium.
• Actual persistency (or termination) can be
  measured from premium, policy count, or other
  units in force.
• Assumed terminations are the unknown and will be
  used for

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Reserves

• VReported x pAssumed / pActual
• VPrevious x (1 i)
• - (NPBenefit Tabular Cost) x (1 i)(1/2)
• You must know interest and net premium.
• Tabular Cost is the unknown.

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Earnings by Source
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The more granular the better

• At the product level
• At the issue year level
• Formulae may be refined
• The more the assumptions are known and the more
  accurate actual is, the more accurate the
  calculations

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Sources of EarningsTools for Managing Your LTC
Business

• John K. Heins, FSA, MAAA
• PolySystems, Inc.

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Sources of EarningsTools for Managing Your LTC
Business

• The SOE Calculation

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The SOE Calculation

• Recall that Source of Earnings is all about the
  increase in reserves.

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Lets start with a traditional Fackler reserve
formula

• V(t1) (V(t) P(t)) (1 i(t)) - C(t)
• ? 1 - qd(t) -qw(t)

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Move the survivorship factor to the other side

• V(t1) (V(t) P(t)) (1 i(t)) - C(t)
• ? 1 - qd(t) -qw(t)

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Move the survivorship factor to the other side

• V(t1) 1 - qd(t) -qw(t)
• (V(t) P(t)) (1 i(t)) - C(t)

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Distribute the components of the survivorship
factor

• V(t1) V(t1) qd(t) V(t1) qw(t)
• (V(t) P(t)) (1 i(t)) - C(t)

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Then isolate V(t1)

• V(t1)
• (V(t) P(t)) (1 i(t)) - C(t)
• V(t1) qd(t) V(t1) qw(t)

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Multiply through by lives inforce lets call
this equation 1

• V(t1) l(t)
• l(t) V(t) P(t)) (1 i(t)
• - C(t) l(t)
• V(t1) qd(t) l(t)
• V(t1) qw(t) l(t)

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Now . . .

• V(t1) l(t1)
• V(t1) l(t1)
• V(t1) l(t) - l(t)

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And, rearranging a bit . . .

• V(t1) l(t1)
• V(t1) l(t)
• - V(t1) l(t) - l(t1)

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And

• V(t1) l(t1)
• V(t1) l(t)
• - V(t1) qd(t) qw(t)

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Now it gets just a little tricky

• V(t1) l(t1)
• V(t1) l(t)
• - V(t1) qd(t) qw(t)

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We replace the valuation lapse and mortality with
actual

• V(t1) l(t1)
• V(t1) l(t)
• - V(t1) qda(t) qwa(t)

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Replace the valuation lapse and mortality with
actual lets call this equation 2

• V(t1) l(t1)
• V(t1) l(t)
• - V(t1) qda(t) qwa(t)

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Now we insert equation 1 into equation 2

• Equation 1
• V(t1) l(t)
• l(t) V(t) P(t) 1 i(t)
• - C(t) l(t) V(t1) qd(t) l(t)
• V(t1) qw(t) l(t)
• Equation 2
• V(t1) l(t1)
• V(t1) l(t) - V(t1) qda(t) qwa(t)

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Now we insert equation 1 into equation 2

• V(t1) l(t1)
• l(t) ((V(t) P(t)) (1 i(t)) - l(t)
  C(t)
• l(t) V(t1) qw(t) - qwa(t)
• l(t) V(t1) qd(t) - qda(t)

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So, the formula for the actual change in reserves
at time t is

• DELTAV(t)
• V(t1) l(t1) - V(t) l(t)
• l(t) P(t) - l(t) C(t) l(t) i(t)
  (V(t)P(t))
• l(t) V(t1) qw(t) - qwa(t)
• l(t) V(t1) qd(t) - qda(t)

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Lets call this equation 3

• DELTAV(t)
• V(t1) l(t1) - V(t) l(t)
• l(t) P(t) - l(t) C(t) l(t) i(t)
  (V(t)P(t))
• l(t) V(t1) qw(t) - qwa(t)
• l(t) V(t1) qd(t) - qda(t)

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Now we can write an expression for earnings as

• E(t) l(t) G(t) - l(t) CA(t)
• ia(t) l(t) (V(t)P(t))
• - DELTAV(t)
• Where CA(t) actual claim rate at t, and
• ia(t) actual interest rate at t

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Lets call this equation 4

• E(t) l(t) G(t) - l(t) CA(t)
• ia(t) l(t) (V(t)P(t))
• - DELTAV(t)
• Where CA(t) actual claim rate at t, and
• ia(t) actual interest rate at t

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And finally, inserting equation 3 into equation
4

• E(t) l(t) G(t) - P(t)  
• - l(t) CA(t) - C(t)  
• l(t) ia(t) - i(t) (V(t) P(t))  
• l(t) V(t1) qda(t) - qd(t)
• l(t) V(t1) qwa(t) - qw(t)

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To include claim reserves for a block of disabled
lives, add

• li(t) ia(t) i(t) DV(t) B(t)
•  
• li(t) qca(t) qc(t) DV(t)

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Splitting claim terminations into recovery and
death . . .

• li(t) ia(t) i(t) DV(t) B(t)
•  
• li(t) qcda(t) qcd(t) DV(t)
•  
• li(t) qcra(t) qcr(t) DV(t)

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And finally, the equation for DAC SOE would be .
. .
?DAC(t) G(t) rdef 1-qw(t-1) i(t)
DAC(t-1) - G(t) rdef 1-qw(t-1)
DEXP(t) 1-qw(t-1) DEXP(t)
1-qw(t-1) DAC(t) qd(t-1)
1-qw(t-1) DAC(t) qw(t-1)

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Earnings by Source

• Robert LaLonde, FSA
• VP and Senior Account Mgr.
• Insight Decision Solutions, Inc.

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Classic Approach

• Profit CF Change in Accruals
• Change of Accruals
• Statutory
• GAAP
• Tax
• Embedded Value
• Management Basis

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The LTC Claim

• Disability model with incidence and continuance
  tables
• In this model can have multiple statuses
  transitions to and from statuses
• Alternatively, can have claim cost approach using
  lag factors for run-out
• Also, Case Reserves

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Two Approaches for LTC

• DI formulation
• Gain from Loading
• Gain from Interest
• Gain from Surrenders
• Gain from Incidence
• Gain from Termination
• Gain from Expenses

• Claim Cost
• Gain from Loading
• Gain from Interest
• Gain from Surrenders
• Gain from Claim Cost
• Schedule H Gain
• Gain from Expenses

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(/-)

• DI approach usually on a seriatim basis.
• Can identify reserve for each policy
• - Claim reserve approach often done on grouped
  basis, so lose individual policy association of
  reserves
• - This screws up any kind of product analysis
  unless you have a rule for reserve allocation at
  the policy level

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Gain From Termination Relative to Val assumptions
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Getting at Experience Gain

• EBS (CF - ? Accruals) for each component
• EBS CF - ? Valuation Assumptions
• EBS (CF Exp) (Exp - ? Val)
• EBS Experience Earnings Expected Earnings

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Gain From Termination Experience and Expected
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An Example
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Data Warehouse Solution
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EBS in a DW

• Better equipped to balance to actual earnings
• More costly but a lot more time spent on accuracy
  of data
• Robust analytical tools
• Slicing and Dicing period to period analysis
• Eliminates reruns

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EBS as an Enterprise Solution
AdminSystems
EBS
ValuationSystems
AccountingSystems
ManagementPlan
Management
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Slicing and Dicing

• Demonstration using a live application

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Typical EBS Format
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Actual to Expected
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Transition Report
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LTC Amounts Report
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LTC Claim Duration
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LTC Rate Analysis