What is Matching and Duration?
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5. What is Matching and Duration?
If we consider that liabilities are a series of net cashflows
Cashflow Matching is whereby a set of assets is purchased such that their cashflows exactly offset the liability cashflows
If this could be achieved:
Value of liabilities exactly = MV of assets
The balance sheet is fully immune to changes in interest rates
However, in practice, perfect cashflow matching is not possible.
A more realistic aim is to match the Duration of assets and liabilities
If so the balance sheet is immune to small changes in interest rates
assuming a level change
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Duration
Average Mean Duration: PV of cashflows weighted by duration they are due
PV of cashflows
Modified Duration:
Derivative of change in price per small change in interest rates
Modified duration = v Mean duration Example:
If the 100m asset portfolio has a modified duration of 8 years:
If interest rates rise by 0.1 then the MV of the portfolio is:
100 1+8-0.1 = 99.2m, a reduction of 0.8m
Also assume that the portfolio belongs to a life insurance company:
Fair value liabilities of 80m
Modified duration of 15 years
If interest rates rise by 0.1 then the fair value of the liabilities is
80m1+15-0.1 = 78.8, a reduction of 1.2m
This change in interest rates produced a net gain of 0.4m due to AssetLiability mis-match
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Remember:
THERE IS NO SUCH
THING AS A FREE
LUNCH
22
Eg arbitrarily changing the Par dividend rate
should not create “instant” profits
Eg changing the assumed asset mix
should not create “instant” Profits
Remember:
THERE IS NO SUCH
THING AS A FREE
LUNCH
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AASB 1038 paragraph 10.2.2
Investments backing life insurance liabilities or life investment contract liabilities are permitted to be
measured at fair value through profit or loss under AASB 139. This is because the measurement of life insurance
liabilities under this Standard incorporates current information and measuring the financial assets backing
these life insurance liabilities at fair value eliminates or significantly reduces a potential measurement
inconsistency which would arise if the assets were classified as available for sale or measured at amortised
cost.
Example: Australian IFRS AASB 1038: Valuation of Assets
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AASB 1038: Discount Rates
1. To the extent that the benefits under life insurance contracts are not contractually linked to the performance of the assets held, the life insurance liabilities shall be discounted for
the time value of money using risk-free discount rates based on current observable, objective rates that relate to the nature, structure and term of the future obligations.
2. To the extent that the benefits under life insurance contracts are contractually linked to the performance of the assets held, the life insurance liabilities shall be discounted
using discount rates based on the market returns on assets backing life insurance liabilities.
3. In applying number 1 above, the discount rates adopted are not intended to reflect risks inherent in the liability cash flows, which might be allowed for by a reduction in the
discount rate in a fair value measurement, nor are they intended to reflect the insurance and other non-financial risks and uncertainties reflected in the life insurance liabilities.
The discount rates are not intended to include allowance for the cost of any options or guarantees that are separately measured as part of the life insurance liabilities.
4. In applying number 1 above, typically, government bond rates may be appropriate discount rates for the purposes of this Standard, or they may be an appropriate starting
point in determining such discount rates.
AASB 1038 paragraph 8.7, 8.8, 8.8.1, 8.8.2
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AASB 1038: Deposit Components
Some life insurance contracts contain both an insurance component and a deposit component. In some cases,
an insurer is permitted to unbundle those components
AASB 1038 paragraph 2.3.1
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Refresher: Fair Value
—
Assets
—
Liabilities
—
Duration
Discount Rates
Workshop using simple models of sample policies:
—
Term ROP
—
Participating
Aims:
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Discount Rates 13
This Section discusses the proposed GPV regulation to be implemented in Indonesia and especially on the topic of risk
discount rates to be employed in the valuation of reserves.
To be consistent with the development of IFRS and Fair Value Accounting, we are proposing that the expected future cashflows to
be discounted with risk free rates based observable, objective rates that relate to the nature, structure and term of future
obligation.
In Indonesia, this typically relates to the yield of bonds which is issued by the Government of Indonesia, including both IDR and
USD. We can used the yield-to-maturity of the Indonesian Government Bond to obtain the risk free forward yield at each of
the future term.
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Discount Rates 23
In this presentation, we defined the spot yield and forward yield as follows:
• Yield-to-maturity: is the internal rate of return IRR, overall interest rate earned by an investor who buys the bond today at the market
price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
• Spot Yield: is the reference to fixed-income securities reimbursed at maturity, without any intermediate payment of coupons andor
principal. For the purpose of this presentation, we assume the yield-to-maturity equals to spot yield.
• Forward Yield: is the implied yield from a spot yield curve of investment return of the instrument in the future, i.e. yield from end of
Year 1 to end of Year 2.
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Discount Rates 33
Why is forward yield used?
• The forward yield is used because it represent the expected yield of investment of that particular period. The methodology we have
employed in the projection is to project cashflows for a particular time period. We then discount those cashflows using the corresponding
yield at that particular period of time.
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Steps in getting risk free forward yield curve
1. Obtain yield-to-maturity yield curve
• Check against other source or previous period
2. Derive forward yield curve
3. Apply forward yield curve to discount projected cashflows
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