Actuarial Notes

Evaluation of the Runoff of P&C Claim Liabilities when the Liabilities are Discounted in Accordance with Accepted Actuarial Practice

By Canadian Institute of Actuaries · 2011 · 211064

Study guide: Exam 6C

A CIA educational note on evaluating the runoff of P&C claim liabilities when the liabilities are discounted in accordance with accepted actuarial practice. Revised by the Committee on Property and Casualty Insurance Financial Reporting as a minor amendment dated June 2011 (document 211064) and approved for distribution by the Practice Council on June 9, 2011, it is divided into three sections: the basic approaches to evaluating runoff, an accident year runoff model, and the allocation of investment income between liabilities and surplus.

On the syllabus

  • Exam 6C — objectives C1 and C5; the whole note.

Introduction

  • The note guides P&C actuaries who prepare a comprehensive report on the valuation of the policy liabilities and an evaluation of the runoff of the claim liabilities.
  • The usual undiscounted approaches — comparing estimated ultimate incurred amounts at successive valuation dates, or payments plus the change in outstanding amounts — must be modified or replaced when claim liabilities are discounted in accordance with accepted actuarial practice.
  • The guidance may be appropriate for the runoff of other liabilities, including self-insured retention.

1 Basic Approaches to the Evaluation of Runoff of Claim Liabilities

  • 1.1 Undiscounted Basis
    • The runoff, or calendar year emergence in t for accident years t−1 and prior, is computed in one of two ways that should produce the same result; either can be done on a policy or underwriting year basis with the portion of policy year t−1 earned in t excluded.

\text{(a)}\quad \text{Emergence}_t = \text{Ultimate estimated at } t-1 \;-\; \text{Ultimate estimated at } t \text{(b)}\quad \text{Emergence}_t = \text{Claim liabilities at } t-1 \;-\; \text{Paid during } t \;-\; \text{Claim liabilities at } t

  • 1.2 Discounted Basis
    • Comparing ultimates is not readily adjusted for the time value of money and the provision for adverse deviations; equation (b) is instead modified by discounting its second and third terms to t−1, or by subtracting the investment income earned during t on assets supporting the liabilities.
    • The two adjustments should produce equivalent results, but the second is simpler to calculate and present, and Sections 2 and 3 are based on it.
    • For the Appointed Actuary's report it is useful to identify the components of the runoff: the undiscounted claim liabilities, changes in the discount rate, and changes in the provision for adverse deviations.

2 Accident Year Runoff Model

  • Illustrated by a calendar-year example: the excess (deficiency) during CY 6 for each accident year is the discounted claim liabilities at the prior year-end plus the investment income on unpaid claims, less the losses paid and the discounted claim liabilities at the current year-end.
  • The investment income on unpaid claims is the annual yield times the average of the opening and closing discounted claim liabilities (for accident year 5, 6% × 36,500 = 2,190).
  • The model may be expanded to monitor the runoff over a period of time (Tables 5 and 6).

3 Allocation of Investment Income Between Liabilities and Surplus

  • The investment income attributable to policy liabilities should be determined, consistently with any allocation of assets, the company's investment policy and the basis used in discounting the policy liabilities, and the basis documented.
  • With no formal allocation, the default yield rate is the calculation used in exhibit 10.60 of the P&C-1 or P&C-2; the note refers to Educational Note 210079 (Discounting, November 2010) for approaches to selecting a discount rate.
  • The income is the selected yield times the average of the starting and ending net unpaid claims, net unearned premium, premium deficiency provisions and unearned commissions, less gross DPAC, agents', brokers' and policyholders' receivables and instalment premiums.
  • On the default yield, the investment income on policy liabilities is capped at the total investment income; if overall investment income is negative, the negative yield is used, so the runoff is penalized.
  • A simple approach for the assets backing net unpaid claims multiplies the investment yield by the mean net claim liabilities.

Exhibits

  • Table 1—Paid Losses During the Calendar Year (CY)
  • Table 2—Discounted Claim Liabilities
  • Table 3—Investment Income on Unpaid Claims
  • Table 4—Excess (Deficiency)
  • Table 5—Cumulative Excess
  • Table 6—Cumulative % Excess Ratio

Sources