Educational Note: Discounting

Front 1

1. What is the common practice for the valuation of policy liabilities?

Back 1

1) evaluate the policy liabilities on an undiscounted basis
2) consider the time value of money
3) Add a provision for adverse deviations (PfAD)

Front 2

2. What's the difference between the present value and the actuarial present value?

Back 2

The present value (PV) reflects only the time value of money

The actuarial present value (APV) = PV + PfAD

Front 3

3. What are the 3 fundamental elements of the discounting aspect of the valuation of policy liabilities?

Back 3

1) Selection of payment patterns
2) Selection of discount rates
3) Application of margins for adverse deviations

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4. What is the definition of Net?

Back 4

Net = Gross - Ceded

Front 5

5. What are the considerations for selection which two of gross, ceded and net are to be estimated directly?

Back 5

1) Data availability:
example: if there is a sparse or limited history of ceded data

2) Cash flow volatility:
Different lines of business may use a different approaches depending on the volatility and duration of cash flows by line

3) Reinsurance program:
Consider the type and consistency of a company's reinsurance programs.
May not be appropriate to use the net as a starting point if the company's net renteion level has changed significantly over the experience period.

4) Discount rate:
If the same discount rate is used to estimate the ceded present value and net present value, then any two of the three items would be estimated directly

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6. Undiscounted

Back 6

the sum of future payment

Front 7

7. Discount Rate

Back 7

The expected investment return rate used calculating the present value of a cash flow

Front 8

8. Payment Pattern

Back 8

The expected calendar period distribution of payments for a given period for a given accident, underwriting or report period

Front 9

9. Present Value (PV)

Back 9

The sum of expected future payments after recognizing the time value of money

Front 10

10. Margin for Adverse Deviations (MfAD)

Back 10

The Standards of Practice define margin for adverse deviations as “the difference between the assumption for a calculation and the corresponding best estimate assumption.” It is a factor applied to a present value or best estimate of a valuation variable to reflect the uncertainty in the variable.

Front 11

11. Provision for Adverse Deviations (PfAD)

Back 11

The Standards of Practice define provision for adverse deviations as “the difference between the actual result of a calculation and the corresponding result using best estimate assumptions.” It is the additional provision resulting from the application of a margin for adverse deviations

Front 12

12. Acturial Present Value

Back 12

The sum of the Present Value and the Provision for Adverse Deviations (i.e., APV = PV + PfAD)

Front 13

13. Claim liabilities

Back 13

The Standards of Practice define claim liabilities as “the portion of policy liabilities in respect of claims incurred on or before the balance sheet date.” Claim liabilities include indemnity amounts and allocated and unallocated claims adjustment expense amounts.

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14. Premium Liabilities

Back 14

The Standards of Practice define premium liabilities as “the portion of policy liabilities which are not claim liabilities.

Front 15

15. What is the first step in deriving the actuarial present value?

Back 15

Estimate the present value of expected claim and claim adjustment expense payments.

Front 16

16. How are the expected claim payments calculated?

Back 16

by applying an expected payment pattern to the undiscounted unpaid claims.

Front 17

17. What would the selected payment patterns reflect?

Back 17

The actuary’s best estimate with regard to the timing and amount of payments including both indemnity and claims adjustment expenses.

It may be appropriate to assume that the payment pattern for indemnity and/or allocated claims adjustment expenses also applies to unallocated claims adjustment expenses.

Front 18

18. What are the considerations to take into account when the claims are subdivided into reasonably homogeneous groups to select the payment patterns?

Back 18

1) groupings used for the valuation of the liabilities on an undiscounted basis,

2) payout period (i.e., the length of time over which payments are expected to be made for a group of claims), and

3) existence of a predetermined schedule of payments for a group of claims.

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19. Give few examples why the payment patterns may vary by year

Back 19

changes in legislation, mix of business, reinsurance or claims settlement practices

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20. Name ohter amounts that should be considered in the selection of payment patterns

Back 20

Timing of expected salvage, subrogation, and loss transfer amounts would be considered in the selection of payment patterns.

Timing of expected reinsurance recovery amounts would be considered in the selection of ceded or net payment patterns.

Front 21

21. When are the gross, ceded and net payment pattern likely to be the same for a given line of busines?

Back 21

When the reinsurance is quota-share

Front 22

22. The selected payment patterns would normally be consistent with assumptions used in the estimation of the undiscounted liabilities, subject to which considerations?

Back 22

1) if the undiscounted amounts are based on a paid development approach, then the claim payment pattern may be derived directly from the selected paid development factors

2)if the undiscounted amounts are based on other methodologies, then different methods of selecting the payment pattern may be used, such as historical ratios of paid losses at various maturity dates, to selected ultimate losses

Front 23

23. What are the type of payments associated with premium liabilities?

Back 23

1) future claims and claims adjustment expenses (consistent with the payment patterns associated with claim liabilities)
2) servicing or maintenance expenses
3) future reinsurance costs

Note: it would be appropriate to select different paymetn patterns for each types.

Front 24

24. What are the adjustements that may be required to do on the payment patterns for future claim costs?

Back 24

1) average accident date and average payment date underlying future claim costs

2) legislative or product changes

3) other considerations similar to those affecting the payment patterns associated with claim liabilities

Front 25

25. When are the Servicing or manintenance expenses paid?

Back 25

Paid over the earning period of the unexpired term of in-force policies and theime value of money would not be material.

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26. What are the considerations when determining the cash flow of future reinsurance costs?

Back 26

1) timing of the payment of applicable reinsurance premiums

2) earning period of the unexpired portion of in-force policies.

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27. What is the expected investment return rate for calculation of the present value of cash flow?

Back 27

It is the rate to be earned on the assets which support the policy liabilities.

Front 28

28. What does the expected investment return rate depend on?

Back 28

1) the method of valuing assets and reporting investment income

2) the allocation of those assets and that income among lines of business

3) the return on the assets at the balance sheet date

4) the yield on assets acquired after the balance sheet date

5) the capital gains and losses on assets sold after the balance sheet date

6) investment expenses, and losses from default (C1 risk).

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29. What does the paragraph 2240.02 of the Standards of Practice state?

Back 29

The actuary need not verify the existence and ownership of the assets at the balance sheet date, but would consider their quality.”

Front 30

30. What are the investment return rates (discount rate) used for?

Back 30

They are used to reduce expected future payment streams to their equivalent present value.

Front 31

31. How do the discount rate vary?

Back 31

The discount rates may vary from one claim grouping to the next, from one future calendar period to the next, or from one underlying accident or underwriting period to the next, although it is common to use a single rate for all years and product lines.

Front 32

32. What is the portfolio yield rate?

Back 32

A portfolio yield rate is the internal rate of return (IRR) which, when applied to the cash flows, produces the book value at a future date of the corresponding assets.

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33. What is the book value of an asset?

Back 33

The book value of an asset may be the market value, the amortized value, or such other value consistent with Canadian generally accepted accounting principles.

Front 34

34. What are the point to consider when calculating a portfolio yield rate?

Back 34

1) T-Bills are sold at a discount and mature at par value. T-Bill “coupon rates” are generally the nominal simple discount rate quoted in most publications

2) It is common for the yield on a bond portfolio to be quoted as a nominal yield, compounded semi-annually.The actuary may need to convert this rate to an equivalent annual effective interest rate. Some bonds have call features that result in redemption prior to maturity, and which may impact their valuation.

3) Early principal repayments are a feature of some securities and would be considered.

4) Accrued investment income is often held by a company in a separate account, but would be combined by the actuary with the book value of bonds.

5) Returns on equities are subject to volatility and care would be taken if equities are selected to support liabilities.For example, historical rates of return may not be indicative of future returns, especially in the short term. In addition, the quality of equities would be considered.

6) In some cases, an investment professional will provide the actuary with an estimate of the IRR

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35. What can actuary do when the actuary does not have enough detail to determine the asset cash flows?

Back 35

An approximation of IRR can be developed using the product of the duration and the book value to weight the yield rates of individual assets.

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36. What is the selection of discount rate for estimation of net present value?

Back 36

For the purposes of financial reporting, a portfolio yield rate would be used for estimating the net present value. The same discount rate would be used in the estimation of both premium and claim liabilities.

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37. How may the discount rate be estimated?

Back 37

The discount rate may be estimated on the basis of the entire investment portfolio or some categories of assets may be excluded.

Assets supporting net policy liabilities are sometimes segregated from assets supporting capital and surplus.it is common practice to assume that a subset of an insurance company’s assets would be matched to net policy liabilities

Consideration would also be given to the company’s policy regarding asset liability matching.

Front 38

38. What would the actuary consider if the asset cashflow is unconsistent with the liability cashflow?

Back 38

the actuary would consider the effect of reinvesting positive net cashflow, or the effect of the liquidation of assets to address negative net cashflow.

Front 39

39. What would the actuary consider if the reinvestment is required?

Back 39

the actuary would consider the expected future reinvestment rate for “new money” and the company’s investment strategy

Front 40

40. How would the actuary consider to determine whether it will be necessary to liquidate a portion of invested assets?

Back 40

He would determine whether or not the current or future asset portfolio has appropriately scheduled maturity dates and sufficient liquidity to cover the payments needed

Front 41

41. Name an alternative to liquidation of existing assets in the event of negative net cashflow

Back 41

the actuary might consider expected cashflow from future business (future renewals)

Such cashflow would be the net cashflow after consideration of the payout of expected claims and expenses, as well as the receipt of premiums and other revenue items.

Front 42

42. What would the selected discount rate be?

Back 42

The selected discount rate would be a blended rate based on the current portfolio yield rate, expected future reinvestment rates, as well as the expected capital gain or loss arising from premature liquidation.

Front 43

43. What would the selected discount rate be if the asset cashflow is consitent with the liability cashflow?

Back 43

the selected discount rate will be the same as the internal rate of return of the supporting assets

Front 44

44. What would the actuary consider regarding the investment expenses

Back 44

The actuary would consider the expected expenses.

It may be reasonable to reduce the discount rate based on historical investment expenses.

Front 45

45. How are the ceded liabilities shown in the balance sheet?

Back 45

Ceded liabilities are shown as recoverable amounts (assets) in the balance shee

Front 46

46. How are the ceded liabilities shown in the balance sheet?

Back 46

Ceded liabilities are shown as recoverable amounts (assets) in the balance sheet.

Front 47

47. Name an assumption regarding the liabilities ceded to another insurer?

Back 47

It is reasonable to assume that liabilities ceded to another insurer are supported by assets held by that insurer.

Front 48

48. What may the discount rate used to dermine ceded present value be selected from?

Back 48

1) the discount rate selected for net present value (i.e., a portfolio yield rate)

The use of a rate based on the portfolio yield for ceded present value may be appropriate if the company’s investments are sufficient to support its gross policy liabilities, or if the assets held by the assuming company to support its net policy liabilities are considered to be similar to the ceding company’s investment portfolio.


2) a risk-free rate

The use of a risk-free rate would reflect the current or “new money” investment return rate for a risk-free or other prudently invested portfolio of assets with appropriate duration. The risk-free rate may be determined using the average market yield on a series of government bonds that match the expected liability duration.

3) the discount rate used by the assuming company, such as in the case of cessions to an affiliated company

or a combination

Front 49

49. What would the actuary consider regarding the selection of discount rate for estimation of gross present value?

Back 49

If the same discount rate is used for estimating both the net and ceded present values, then the gross present value can be estimated directly using that same discount rate.

If ceded present value is estimated using a risk-free rate, or the assuming company’s discount rate, then the implied rate underlying the gross present value may not necessarily equal to the selected portfolio yield rate underlying the net present value.

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50. What are the assumptions an actuary would include a margin for adverse deviation for?

Back 50

1) claims development

2) recovery from reinsurance ceded

3) investment return rates

Front 51

51. What would the margin for adverse deviations for claims development be?

Back 51

The margin for adverse deviations for claims development would be a percentage of the claims liabilities excluding provision for adverse deviations.

the provision for adverse deviations is determined by applying a margin to the present value

The claims development margin may vary by year and by line of business, and may vary between gross, ceded and net liabilities (usually between 2.5% to 20%)

Front 52

52. What would the margin for adverse deviations for recovery from reinsurance be?

Back 52

The margin for adverse deviations for recovery from reinsurance ceded would be a percentage of the amount deducted on account of reinsurance ceded in calculating the premium liabilities or claim liabilities, as the case may be, excluding provision for adverse deviations.

the provision for adverse deviations is determined by applying a margin to the ceded present value. The provision for adverse deviations is deducted from the ceded present value and added to the net present value.

The margin for recovery from reinsurance ceded may vary by year and line of business (usually is between 0 to 15%)

Front 53

53. What would the margin for adverse deviations for investment return rate be?

Back 53

The margin for adverse deviations for investment return rate would be a deduction from the expected investment return rate per year.

the provision for adverse deviations is determined as the difference between present value calculations, before application of other margins, using two different discount rates:

1) the selected discount rate minus the investment return rate margin

2) the selected discount rate

The margin for investment return rate may vary by year and by line of business, and may vary between gross, ceded and net liabilities. (usually between 25 basis pts and 200 basis pts)

Front 54

54. Gross actuarial present value

Back 54

= Gross PV PfAD for claims + development (gross) PfAD for + investment return rate (gross)

Front 55

55. Ceded actuarial present value

Back 55

= Ceded PV +
PfAD for claims development (ceded) +
PfAD for investment return rate (ceded) -
PfAD for recovery from reinsurance ceded

Front 56

56. Net actuarial present value

Back 56

Net PV +
PfAD for claims development (net) +
PfAD for investment return rate (net) +
PfAD for recovery from reinsurance ceded

Front 57

57. Gross

Back 57

Gross = Net + Ceded

Front 58

58. PfAD for claims development (gross)

Back 58

PfAD for claims development (net) +
PfAD for claims development (ceded)

Front 59

59. PfAD for investment return rate (gross)

Back 59

PfAD for investment return rate (net) +
PfAD for investment return rate (ceded)

Front 60

60. How would the provision for adverse deviations be calculated?

Back 60

The provision for adverse deviations would be calculated by applying selected margins to the present value of the estimated future claim and claim adjustment expenses.(The calculation would be similar to the calculation of provision for adverse deviations associated with claim liabilities)

The margins may vary by line of business and/or year and may also differ from those associated with claim liabilities.

The effect of the time value of money is normally insignificant for servicing expenses and future reinsurance costs, and, therefore, it is reasonable in most cases to assume that the undiscounted value of these items is equal to the actuarial present value.