CIA Discounting

Question 1

Give the fundamental elements of discounting

Answer 1

1 - Selecting payment patterns
2 - Selection of discount rates
3 - Application of MfAD

Question 2

Give considerations for which of gross, net, or ceded policy liabilities are estimated

Answer 2

• Data availability
• Cash flow volatility
• Re program - Type and consistency
• Discount rate - Ceded may differ from net

Question 3

Give factors to consider in the selection of the rate of return on assets underlying the discounting of policy liabilities

Answer 3

1 - Method of valuing assets and reporting investment income
2 - Allocation of income and assets among lines
3- Return on assets at balance sheet date
4 - Yield on assets after balance sheet date
5 - Capital gains/losses on assets sold after balance sheet date
6 - Investment expenses and losses from default

Question 4

What is the portfolio yield rate ?

Answer 4

IRR which, when applied to the cash flows, produces the book value at a future date of the corresponding assets

Question 5

What is the difference between PV and APV ?

Answer 5

Present Value (PV)
Sum of expected future payments after recognizing the time value of money 

Actuarial Present Value (APV)
APV = PV + PfAD

Question 6

Give considerations in selection of a discount rate for NPV

Answer 6

1 - Assets selected to support liabilities
2 - Reinvestment risk
-Reinvestment of positive net cash flows
-Company’s investment strategy
3 - Liquidation of assets
4 - Investment expenses

Question 7

Discount rate options for ceded PV

Answer 7

• Portfolio Yield Rate
Same discount rate used for NPV

• Risk-Free Rate
Reflects current or new money yield

• Assuming Company’s Discount Rate
Reflects evaluation from the Re’s point of view

Question 8

Assets supporting policy liabilities are sometimes segregated from assets supporting capital and surplus. Which assets are typically selected to match each of these segments ?

Answer 8

Common for a subset of an insurance companies assets, such as bonds, to be matched to policy liabilities while riskier assets, such as equities, are matched to capital and surplus

Question 9

Ceded APV =

Answer 9

Ceded PV + PfAD Ceded LDF + PfAD Ceded IR – PfAD Ceded RR

Question 10

Net APV =

Answer 10

Net PV + PfAD Net LDF + PfAD Net IR + PfAD Ceded RR

Question 11

Gross APV =

Answer 11

Gross PV + PfAD Gross LDF + PfAD Gross IR

Question 12

What are considerations an actuary should make in determining the cash flow of future Re costs with respect to discounting premium liabilities?

Answer 12

1 - Timing of the payment of applicable Re premiums

2 - Earning period of the unexpired portion of in-force policies

Question 13

Define MfAD and PfAD

Answer 13

MfAD
Difference between the assumption for a calculation and the corresponding best estimate assumption to reflect the uncertainty in the variable

PfAD
Difference between the actual result of a calculation and the corresponding result using best estimate assumptions additional provision resulting from application of a MfAD

Question 14

List considerations when claims would be subdivided into reasonably homogeneous groups for the selection of payment patterns

Answer 14

1 - Groupings used for the valuation of the liabilities on an undiscounted basis
2 - Payout period (splitting longer from shorter tailed)
3 - Existence of a predetermined schedule of payments for a group of claims.

Question 15

List types of payments associated with premium liabilities for which it may be appropriate to select different payment patterns

Answer 15

1 - Future claims and LAE
2 - Maintenance expenses
3 - Future Re costs

Question 16

List assumptions that would include MfADs

Answer 16

1 - Claims development
2 - Recovery from Re ceded
3 - IRR

Question 17

Briefly explain reasonable assumption related to the effect of the time value of money for Servicing expenses and future Re costs

Answer 17

Effect of the time value of money is normally insignificant on these items. Therefore, it is reasonable to assume that the undiscounted value is equal to APV

Question 18

Briefly discuss how investment expenses can affect discount rate

Answer 18

It may be reasonable, for example, to reduce the discount rate based on historical investment expenses

Question 19

When does the use of a rate based on the portfolio yield for ceded PV may be appropriate

Answer 19

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

Question 20

Discuss selection of discount rate for estimation of gross PV

Answer 20

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

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

Question 21

PfAD clm dev (gross)

Answer 21

PfAD clm dev (net) + PfAD clm dev (ceded)

Question 22

PfAD invest return (gross)

Answer 22

PfAD invest return (net) + PfAD invest return (ceded)