Actuarial Notes

CAS Exam 6C Fall 2015, Question 14

Study guide: Exam 6C

The following information is available for a property and casualty insurance company that only writes auto insurance as at December 31, 2014. All amounts are in thousands of dollars ($000s).

Here is the composition of the bond portfolio of the company:

Description Bond #1 Bond #2 Bond #3 Bond #4
Classification Fair Value Option (FVO) Fair Value Option (FVO) Fair Value Option (FVO) Available for sale (AFS)
Maturity Date 31/12/2015 31/12/2016 31/12/2017 31/12/2017
Annual Coupon Rate 4.00% 4.50% 3.75% 3.75%
# of coupons per year 1 1 1 1
Par value $10,000 $10,000 $10,000 $10,000
Effective Yield 3.00% 3.00% 3.00% 3.00%
Market Value 10,097 10,287 10,212 10,212

The calendar year payout pattern of unpaid claims and ULAE is as follows:

Date % cumulative paid
31/12/2015 33.3%
31/12/2016 66.7%
31/12/2017 100.0%

The following additional information is also available:

  • Assume that unpaid claims and coupon payments are made exactly at the end of the year (December 31).
  • Net Undiscounted Unpaid Losses including ULAE = $31,000
  • The company matches its Fair Value Option (FVO) bond portfolio with its unpaid claims liabilities.
  • Assume that the market value of each bond corresponds to the present value of cash flows discounted at the effective yield.
  • There is no reinsurance.
  • Margin for Adverse Deviation (MfAD) Claims development: 10.0%
  • MfAD Investment return rates: 0.5%
  • Assume that there are no taxes.

A sudden change in interest rate occurs on December 31, 2014, which causes the effective yield on the bonds to increase from 3% to 3.5%

Calculate the impact on net income, other comprehensive income and equity due to the interest rate increase.

Part a (4.5 points)

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