CIA. Duration

Question 1

which risk category under MCT does duration affect?

Answer 1

market rate risk
duration affects interest rate risk

Question 2

definition of duration

Answer 2

duration is a concept or a tool used to measure
- the average maturity of a series of fixed future cash flows
- the sensitivity that interest rate changes have on the present value of a series of future cash flows

Question 3

how is Macaulay duration computed?

Answer 3

as the weighted average of the time to each cash flow payment, using PV(future cash flow) as weights
- Macaulay duration is an intermediate step in calculation of interest rate sensitivity, NOT a measure of duration accepted by regulators

Question 4

3 types of duration measures

Answer 4

• Macaulay duration
• modified duration
• effective duration

Question 5

what is the formula relating Macaulay and modified duration?

Answer 5

modified duration = macaulay duration / (1+yield)

Question 6

what is the difference between modified and effective duration?

Answer 6

• effective duration accounts for situations where a change in interest rates changes cash flows (callable bonds, interest rate derivatives)
• modified does not

Question 7

what does modified duration measure?

Answer 7

it measures the sensitivity of the present value of a series of fixed future cash flows to changes in interest rates

Question 8

formula for effective duration

Answer 8

(fair value if yields decline - fair value if yields rise) /
(2 * initial price * change in yield in decimal)

Question 9

how can a more accurate approximation of impact of changes in interest rates on PV(future CF) be achieved?

Answer 9

through considering the curvature of price-yield relationship

Question 10

thing to consider in calculating duration for liabilities

Answer 10

• consistency of assumptions: assumptions for duration calculation should be consistent with discounting calculation from valuation
• duration calculation by LoB: use the same payout patterns as for discounting total duration, then total duration is a weighted average with weights = APV by LoB
• duration calculation on a combined basis: use effective duration
• when interest rate is small: modified duration and effective duration are approximately the same

Question 11

identify considerations of duration under GMA

Answer 11

FCF is interest sensitive, CSM is not

Question 12

identify considerations of duration under PAA

Answer 12

• LC is considered highly leveraged and extremely sensitive to i
• LRC excluding LC is not affected by changes in i

Question 13

can insurers use different methodologies to calculate duration of assets and liabilities?

Answer 13

no, also has to use the same methodology year to year

Question 14

is it permissible for the actuary to rely on an investment specialist for the calculation of asset duration? explain

Answer 14

Yes
- the actuary would be the enquiring professional, and the investment specialist would be the responding professional
- the actuary must review the investment specialist’s work for methodology and reasonableness

Question 15

examples of interest rate sensitive assets for insurers

Answer 15

• bonds
• preferred shares

Question 16

app A