ASHK Appointed Actuaries Symposium Investment bank solutions to a Life Insurance Company George Coppens, CFA Head of ALM Solutions, Pensions and Insurance Team Derivatives Solutions Group, November 2006
About the speaker George Coppens, CFA Director Head of ALM Solutions, Pensions, and Insurance Team George Coppens started to work for ABN AMRO in 1996. Starting of in Asset & Liability Management, George gained extensive knowledge on the tasks and challenges of the analysis and management of the ABN AMRO balance sheet in terms of interest rate sensitivity, currency hedging and capital optimisation. Side-stepping to asset management firms AXA Investment Managers and SNS Asset Management being a senior relationship manager, George gained in-depth knowledge about implementation of ALM solutions and product development for insurance companies and pension funds. Currently he heads the ALM Solutions, Pensions, and Insurance Team for the Asian Region, within the Derivatives Solutions Group, responsible for structuring Asset and Liability Management Solutions for Financial Institutions and Corporates on the back of new product developments and regulatory changes (IFRS, RBC, Basle II). George is a CFA charterholder and holds a Msc-equivalent in Econometrics, University of Groningen, The Netherlands. George Coppens Director Head of ALM Solutions, Pensions and Insurance Team 38/F, Cheung Kong Center, 2 Queens Road Central, Hong Kong Tel: +852 2700 3015, Mob: +852 9483 0588 E-mail george.coppens@hk.abnamro.com 2
Shifting Accounting and Regulatory Policies Dramatic Change Book Value / Premium Based Framework Asset-Liability Framework Statutory Solvency Framework Risk-Based Solvency Economic Capital Framework Focus Liability only Static Minimum Capital Requirement Internally focused Focus Both Asset and Liability-based Targets based on changing business and economic conditions Market based measurement of risk Method of Risk Mgmt Passive Static Segmented Method of Risk Mgmt Active Dynamic Holistic Issues Easy to manage and administer Unresponsive to changing conditions Ignores investments and ALM Issues Cultural change Implementation expense Investor education 3
Two Asian Applications Economic Capital Optimisation Regulatory Capital Optimisation 4
Economic Capital Optimisation Issue Required How achieved Economic capital costs Risk transfer Option strategies Diversification Capital Protection Duration lengthening 5
Economic Capital Optimisation - Duration Lengthening Example: HKD denominated Note Assets Liabilities Coupon: MAX { [9%-Index], 1% } Underlying index: HKD10YR CMS Tenor: 15 years Zero Fixed Income Duration 100 15 92 8 25 Interest Sensitive Capital Duration Consider AFS: MtM thru equity No bifurcation Assets Inverse Floater 100 Liabilities 92 Interest Sensitive 8 Capital Duration 21.2 25 Duration Capital liberated dependent on internal model At Inception Capital reduction due to reduction in duration mismatch and risk transfer 6
Economic Capital Optimisation - Duration Lengthening Hong Kong Capital Markets Typically long term assets not available or very illiquid Extending the interest rate curve IBs taking on the spread risk 7
Which Duration Are We Talking About? Macaulay Duration is a weighted average measure of the life of a bond where the weight for each time points us the relative contribution of the present value of the cash flow at that time point to the price/value of the bond. Modified Duration is a measurement of the sensitivity of a bond s price to interest rates as interest rates change. Modified Duration is equal to Macaulay Duration when the bond pays coupon annually. What if the bond is option-embedded? Effective Duration is the duration for a bond with an embedded option when the value is calculated to include the expected change in cash flow caused by the option as interest rates change. This measures the responsiveness of a bond's price to interest rate changes, and illustrates the fact that the embedded option will also affect the bond's price. For option-embedded bonds, Effective Duration is a more accurate measurement of interest rate sensitivity. For option-free bonds, the Effective Duration is equal to Modified Duration. Thus they can be used inter-changeably in this case. How is the Duration being calculated? For vanilla bond illustration, Modified Duration is being calculated As a better reflection of price sensitivity, Effective Duration is being calculated for the HKD Inverse Floater. With each yield curve and maturity, the marginal value change with respect to 1 basis point change in the yield curve can be calculated. Effective Duration equals the marginal value change divided by the total value of the deposit. 8
Why do Inverse Floaters have High Durations? Inverse Floater details: Nominal HKD 100mln Tenor 10YR Year Floater Cash Flows Inverse Floater Cash Flows Total Cash Flows Equivalent total cash flows Coupon [10% - 1YR Libor] 1 L0 10 L0 10 2 * 5 Consider a portfolio made up of 1 inverse floater mentioned above and the corresponding floater. 2 3 4 L1 L2 L3 10 - L1 10 - L2 10 - L3 10 10 10 2 * 5 2 * 5 2 * 5 Let s look at the net cash flows: 5 6 L4 L5 10 - L4 10 - L5 10 10 2 * 5 2 * 5 The cash flow profile essentially implies that the portfolio is equivalent to: 2 bonds with fixed coupon of 5 % 7 8 9 10 L6 L7 L8 100 + L9 10 - L6 10 - L7 10 - L8 100 + (10 L9) 10 10 10 200 + 10 2 * 5 2 * 5 2 * 5 2 * (100 + 5) 9
Why do Inverse Floaters have High Durations? The cash flow profile essentially implies that the portfolio is equivalent to 2 bonds paying a fixed coupon of 5 % Now by the law of one price: Price of Floater + Price of Inverse Floater = 2 * Price of 5% fixed coupon bond Hence, Duration of the Inverse Floater 2 * Duration of 5% fixed coupon bond Since the duration of the floater would be small compared to the duration of the fixed coupon bond 10
Why do Inverse Floaters have High Durations? Leveraged Inverse Floater details: Nominal HKD 100mln Tenor 10YR Year Floater Cash Flows Inverse Floater Cash Flows Total Cash Flows Equivalent total cash flows Coupon [15% - 2 *1YR Libor] 1 2 * L0 15 2 * L0 15 3 * 5 Consider a portfolio made up of 1 inverse floater mentioned above and two corresponding floaters. 2 3 4 2 * L1 2 * L2 2 * L3 15 2 * L1 15 2 * L2 15 2 * L3 15 15 15 3 * 5 3 * 5 3 * 5 Let s look at the net cash flows: 5 6 2 * L4 2 * L5 15 2 * L4 15 2 * L5 15 15 3 * 5 3 * 5 The cash flow profile essentially implies that the portfolio is equivalent to: 3 bonds with fixed coupon of 5 % 7 8 9 10 2 * L6 2 * L7 2 * L8 2 * (100 + L9) 15 2 * L6 15 2 * L7 15 2 * L8 100 + (15 2*L9) 15 15 15 300 + 15 3 * 5 3 * 5 3 * 5 3 * (100 + 5) 11
Why do Inverse Floaters have High Durations? The cash flow profile essentially implies that the portfolio is equivalent to 2 bonds paying a fixed coupon of 5 % Now by the law of one price: 2 * Price of Floater + Price of Inverse Floater = 3 * Price of 5% fixed coupon bond Hence, Duration of the Inverse Floater 3 * Duration of 5% fixed coupon bond Since the duration of the floater would be small compared to the duration of the fixed coupon bond 12
Explanation How do we explain this logically? If HKD interest rates changes, an inverse floater receives a double hit: Present value of future cash flow changes due to changing discount rates The future cash flows will change 100,000 Delta profile Inverse Floater 0-100,000-200,000-300,000-400,000-500,000 2D 1W2W 1M 2M3M 6M 9M1Y 2Y 3Y4Y 5Y 6Y7Y Delta per time bucket 8Y 9Y 10Y11Y12Y 13Y 14Y15Y 20Y 13
15 Year HKD Inverse Floater Investment (Structure 1) Deposit Taker: Maturity: Notional Amount: ABN AMRO Bank N.V. 15 Years HKD 1,000,000,000 30 Duration Change with Yield Curve Movement Deposit Amount: 100.00% of Par 25 Redemption Amount: 100.00% of Par 20 15 Client Receives: 9.00% - 10y CMS Quarterly 10 5 Minimum Coupon: Day Count: 1% Act/365 0-1.00% 0.00% 1.00% 2.00% 3.00% Initial duration: 21.2 Business Day: Modified Following Calculation Agent: ABN AMRO Bank N.V. Rule of Thumb: 2 * duration of 15YR bond @ 4.5% 14
Breakdown in Components explanation continued The inverse floater -Structure 1- consists of: Long investment in series of fixed rate payments @ 9% Leg 1 Long principal repayment of HKD 1bn Leg 4 Short series of HKDCMS 10YR Leg 3 Bought cap on HKDCMS 10YR Leg 2 Short initial cash payment of HKD 1bn Leg 5 ABH_-_HKD_-_INVERSE_FLOATER_-_OCT_23_1 Trade Leg 1 Leg 2 Leg 3 Leg 4 Leg 5 Instrument Total FXD CMSCAP CMS CASH CASH Currency HKD HKD HKD HKD HKD HKD HKD/ccy rate 1 1 1 1 1 1 Value -7,693,118 980,191,934 8,793,595-506,585,173 509,797,533-999,891,006 Basis point value -77 Value (HKD) -7,693,118 980,191,934 8,793,595-506,585,173 509,797,533-999,891,006 IR BS Delta (HKD) -2,118,998-659,923 100,074-800,060-759,364 274 Duration 21.19 6.60-1.00 8.00 7.59 0.00 Source: Pricing system ABN AMRO 15
15 Year HKD Inverse Floater Investment (Structure 2) Deposit Taker: Maturity: Notional Amount: ABN AMRO Bank N.V. 15 Years HKD 1,000,000,000 40 35 Duration Change with Yield Curve Movement Deposit Amount: 100.00% of Par 30 25 Redemption Amount: Client Receives: 100.00% of Par 13.25% - 2 10y CMS Quarterly 20 15 10 5 Minimum Coupon: 1% 0-1.00% 0.00% 1.00% 2.00% 3.00% Day Count: Act/365 Initial duration: 28.1 Business Day: Modified Following Rule of Thumb: Calculation Agent: ABN AMRO Bank N.V. 2.9 * duration of 15YR bond @ 4.5% However CMS CAP impact 16
15 Year HKD Inverse Floater Investment (Structure 3) Deposit Taker: Maturity: Notional Amount: Deposit Amount: Redemption Amount: Client Receives: Minimum Coupon: Day Count: Business Day: ABN AMRO Bank N.V. 15 Years HKD 1,000,000,000 100.00% of Par 100.00% of Par 17.26% - 3 10y CMS Quarterly 1% Act/365 Modified Following 50 45 40 35 30 25 20 15 10 5 0 Duration Change with Yield Curve Movement -1.00% -0.50% 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% Initial duration: 32.9 Rule of Thumb: Calculation Agent: ABN AMRO Bank N.V. x * duration of 15YR bond @ 4.5% However CMS CAP impact 17
Duration Change of Three Structures As a more accurate measurement of price sensitivity, Effective Duration has been calculated for all three structures. Yield curve has been shifted under different scenarios, and Effective Duration is calculated by dividing the marginal value change by total value under each scenarios. The figure on the right plots the duration change of all three structures with respect to yield curve change in one graph. Duration change of structure 3 is the steepest among all, which means duration of structure 3 changes the fastest given the same yield curve shifting. This is because structure 3 has the highest gearing and the largest convexity. Duration change of structure 1 is flatter than the other two geared structures. This means structure 1 has smaller convexity which makes its duration changes more slowly. The larger the convexity, the faster the duration changes. And gearing increases the convexity of the structures. 50 45 40 35 30 25 20 15 10 5 0 Duration Change with Yield Curve Movement - 1 % + 1 % -1.00% 0.00% 1.00% 2.00% 3.00% Structure 1 Structure 2 Structure 3 Closing the duration mismatch: although long dated investments are not available in local currency 18
Inverse Floater Accounting Treatment 39.10 10. An embedded derivative is a component of a hybrid (combined) instrument that also includes a non-derivative host contract with the effect that some of the cash flows of the combined instrument vary in a way similar to a stand-alone derivative. [..] 11. An embedded derivative shall be separated from the host contract and accounted for as a derivative under this Standard if, and only if: 39.11 (a) the economic characteristics and risks of the embedded derivative are not closely related to the economic characteristics and risks of the host contract (see Appendix A paragraphs AG30 and AG33); AG33 AG33. The economic characteristics and risks of an embedded derivative are closely related to the economic characteristics and risks of the host contract in the following examples. In these examples, an entity does not account for the embedded derivative separately from the host contract. (a) An embedded derivative in which the underlying is an interest rate or interest rate index that can change [ ] closely related to the host instrument unless the [..] could at least double the holder s initial rate of return on the host contract Source: IASB 19
Conclusion Local currency investment Duration extension beyond available tenor No earnings volatility by MtM Hence, optimising Economic Capital 20
Two Asian Applications Economic Capital Optimisation Regulatory Capital Optimisation 21
New Singapore RBC rules Risk framework Total Risk Requirements = Insurance risks (C1) + Asset risks (C2) + Concentration risks (C3) Key points Key points include: Market discount rates instead of fixed (4%) discount factor on insurance liabilities Specific asset-related capital charges Implied charges for duration mismatches Specific Asset Charge Asset Class Type Specific Debt Sovereigns 0% Investment Grade 0.25% - 1.6% Others 8% Equity 16% Forex 8% Property 16% Source: Monetary Authority Singapore (MAS) 22
New Singapore RBC rules duration mismatch Value of Insurance Liabilities at different discount rates Market value of fixed income investment less (scaled) general debt risk charges Duration Risk Mismatch Requirement S$ 10,000 7,500 5,000 S$m 800 Decreasing Rate Environment Increasing Rate Environment 3.15% 3.45% 3.75% 4.05% 4.35% 4.65% L 1 L 0 L 2 D 1 D * - D 0 = General Debt Risk Requirement Value of zero duration investments D 0 D 2 L 0 - L * = Liability Adjustment Liability Adjustment 600 C 1 = LA 1 + DR 1 General Debt Risk Requirement 400 200 C 1 DR 1 LA 2 C 2 Duration risk charge: Higher of C1 and C2-200 -400-600 3.15% 3.45% 3.75% 4.05% 4.35% 4.65% Debt General Risk Charge Current long DR 2 interest rate > 3% < 3% Debt General From To From To Risk Charge 0.00 1.00 0.00 1.00 0.00 LA 2 1 1.00 3.00 1.00 3.00 0.20 3.00 6.00 3.00 6.00 0.40 6.00 12.00 6.00 12.00 0.70 1.00 2.00 1.00 1.90 1.25 2.00 3.00 1.90 2.80 1.75 3.00 4.00 2.80 3.60 2.25 4.00 5.00 3.60 4.30 2.75 5.00 7.00 4.30 5.70 3.25 7.00 10.00 5.70 7.30 3.75 10.00 15.00 7.30 9.30 4.50 15.00 20.00 9.30 10.60 5.25 20.00 10.60 12.00 6.00 12.00 20.00 8.00 20.00 12.50 23
Constant Proportion Portfolio Insurance (CPPI) CPPI typically consists of three underlying components Equity Component The Equity Component EC comprises a notional investment in the underlying physical portfolio the current equity holdings, assume MSCI World indexed. Cash Component Bond Component The Cash Component CC comprises either a notional loan extended by ABN AMRO to provide leveraged exposure to the Equity Component or a cash deposit (i.e. when a deleverage has occurred) in USD. The Bond Component BC comprises a notional investment in SGD zero coupon bonds to secure any guaranteed coupons over the life of the structure and to ensure that in a cash-out event a minimum of 100% is repaid at maturity in normal circumstances not used. 24
CPPI on an Equity Index current market CPPI is rules-based The fundamental drivers are: Yield, the equity component, and; Protection, the implicit bond floor Value (NAV) 100% Equity Gap ( EG ) Performance driven by return on (leveraged) exposure to equities Equity Component ( EC ) 0 Bond Floor ( BF ) Cash Maturity Change in bond floor value, driven by duration times interest rates movements -16% Component 25
CPPI on the MSCI World* current market Interest 3.56% Tenor 15.00 Index 1000.00 Multiplier 4.00 NAV 100.00 BF 73.97 EG 26.03 EC 104.14 Cash -4.14 CPPI is rules-based (cont d) The Equity Component (EC), the exposure to MSCI World equals MIN [ CAP, (EG*M) ], whereby the CAP is the maximum leverage allowed (typically 225% of notional), and EG the so-called equity-gap (NAV minus bond floor), and M the multiplier. At inception, in the current Singapore market** it can look like the following: Underlying exposure, MSCI World - index Agreed to pay back at least SGD 125 mln, in 15 years time. Present value of the bond floor is 125 / [(1 + 3.56%)^15] = 73.9 The Equity-gap (EG) equals [NAV bond floor] = [100 73.9] = SGD 26.0 mln Maximum CAP is 225% Multiplier is 4 Initial exposure to MSCI World equals MIN [ 225, 26 * 4 = 104.14 ] = SGD 104.14 mln, whereby SGD 4.14 mln is borrowed from cash component. Rebalancing during life is triggered by the implied multiplier 4.5 [EC / EG] 5.5, and the maximum CAP on the EC *) For illustration purposes. Can be any (liquid) equity index representing your current equity holdings **) Bloomberg, Nov 3, 2006 26
Risk Transfer historical analysis In order to illustrate the risk mitigating features of a CPPI structure, we have run stochastic simulations of 1-year historical rolling performances of a straight investment into equities and of an equity-linked CPPI structure, which are depicted in the graphs below. On both graphs the yellow line shows cumulative probability function of the 1-yr rolling average performance of the S&P 500 index since 1928. S&P 500 (1928 today) Performance of CPPI Note vs. pure equity investment 100% 120% cumul. prob. 80% 60% 40% 20% 0% -100% -50% 0% 50% 100% rolling 1y performance cumulative probability 100% 80% 60% 40% 20% 0% 0 50 100 150 200 S&P 500 rolling annual performance fitted Normal Distr. Risk transfer Equity Index Perform ance CPPI (NAV) The green line above shows cumulative probability function of a normal distribution that represents a good approximation of the actual equity performance. The green line above shows cumulative probability function of the 1-year rolling average performance of an S&P 500-linked CPPI note. The CPPI Note is a superior and safer investment in this part of the distribution, virtually eliminating market downside risk Source: Bloomberg, ABN AMRO 27
Risk Transfer stochastic simulation Return distributions 15 years, 125%, multiplier 4, MSCI World - linked 1000 900 800 700 600 500 Assumptions: 400 Equity premium 4% over short term rate 300 Equity index lognormal distributed 200 Short term rate HW model 100 Equity volatility 15% 0 Last year s correlation input -50% -30% -10% 10% 30% 50% 70% 90% 110% 130% 150% Risk transfer Equities - 1YR% Note - 1YR% Equities - 5YR% Note - 5YR% The CPPI Note is a superior and safer investment in this part of the distribution, virtually eliminating market downside risk Source: Bloomberg, ABN AMRO 28
An Alternative to Equities regulatory capital treatment Example: SGD denominated Note Underlying index: MSCI World index Tenor: 15 years 125% protection Leverage: [0, 4] At Inception Ratio Amount Equity Gap 26% 26.0 Bond Floor 74% 74.0 NAV 100% 100.0 Specific 16.00% 4.2 1.60% 1.2 5.35% 5.3 General Debt -8.00% -5.9-0.57% -0.6 Capital liberated = 24 5.3 + 5.9 = 24.6 mln per SGD100 mln Assets Equities Assets AAB Note At Inception 100 XX 24 YY ZZ 100 XX 5.3 YY 6 ZZ Liabilities C1 Capital C2 Asset Charge Capital C2 Duration MM Capital C3 Capital Liabilities C1 Capital C2 Asset Charge Capital C2 Duration MM Capital C3 Capital Capital reduction of almost all of the original C2 Asset Charge Capital Please note that approval from the Monetary Authorities of Singapore (MAS) is required. The savings shown is to be considered as preliminary result subject to MAS approval. 29
CPPI on an Equity Index alternatives comparison Strategy Protection Level Participation in equity Index Duration extension Buy put options on Index At a 100 Less than 100 None Buying a zero coupon bond, plus investing the remainder into equity Index At a 100 Less than 100 Highest Buying zero coupon bond, plus buying series of call options on equity Index At a 100 Less than 100 Highest Investment in CPPI note linked to the equity Index At a 100 Equal to or above 100 Highest 30
CPPI on an Equity Index accounting treatment According to IFRS, the Note would be valued as a combination of the host (a fixed coupon paying bond), o can be classified as HtM, L&R, AFS, or HfT the value of the so-called embedded derivative o classified as HfT, fair value changes through P&L The net asset value (NAV) can be decomposed into the two Note components: Bond floor; o Value equals the discounted guaranteed payouts to the valuation date; Equity gap; o Value equals the difference between NAV of the Note and the Value of Bond component; The decomposition of the Note into two components Is required for accounting purposes Will help to determine the appropriate regulatory 31
Conclusion Risk transfer of current risky assets Duration extension Hence, optimising Regulatory Capital 32
A1 Duration in detail 33
Macaulay Duration Literally, Duration is a measure of the maturity of a bond which is calculated in relation to the present value of cash flows due on the bond. It is measured in time (usually years), and is essentially a weighted average of the number of years to maturity. The weights used are the present values of the cash flows in each year. This measure adjusts the maturity of a bond to allow for the timing of individual cash flow payments. It is also called Macaulay s Duration. Mathematically, duration is calculated by the formula: Duration = n t i i = 1 PV (Ci ) Pr ice An alternative representation of duration is to place imaginary buckets on a see-saw. The size of the buckets and their placement represents the timing and size of the cashflows. The diagram below illustrates the duration of an assumed 3-year bond with annual 6% coupon and priced at par. This balancing point in the middle of the see saw is the Duration. 34
Macaulay Duration Duration is usually less than the tenor of the bond because of the cash flow during the life of the bond. The only case in which a bond's duration would equal its maturity would be the case of a zero-coupon bond. In these cases the only cash flow which occurs is at the final maturity date. Given the market rate, two factors of a bond, or extensively speaking, fixed income securities, affect the duration of a couponbearing instrument. They are Maturity and Coupon. Normally, the longer the maturity, the larger the duration. For bonds of the same maturity, coupon plays an important role in affecting duration. Example: Coupon Matters (!"#! $% $%!#! $%!% %!%"!! "" $!#!#% "!% #!#"!# " $! %" $"!!! %#!"#! %"# %"# %!# %$!"%!!$ % %$!%"! %%#!" "% $!#!# %"% #!#"! "$" $%#% #$$ $""! &' &' The second deposit pays more coupon in early years, adding more weight to the shorter tenor of cash flows, which makes its duration less than the first deposit with regular coupon payment. 35
Modified Duration Another measure of duration is called Modified Duration. This measure of duration is used to immunise a portfolio against interest rate risk, what bondholders usually want to know is by how much the price/value of the bond will be affected by interest rate changes. Put in math, the relationship is shown as: Percentage change in bond price/value = - Modified Duration Change in yield (in absolute percentage point) Modified Duration is nothing more than the Macaulay Duration divided by (1+yield/coupon frequency) Taking the two deposits in the previous example, Modified Duration is equal to Macaulay Duration since the coupon payment is annual. In two cases, for every 1% change in the yield, the price/value of the deposits will change by 4.79% and 4.68% respectively in the opposite direction. This is not only useful in assessing the change in value of the investment if the investor thinks interest rates are likely to rise, but will also help decide the size of any hedging transaction the investor may want to undertake. Yield change will not affect the value of the floating part of a floating rate bond. Only the nearest interest payment whose coupon rate has been pre-set is subject to interest rate risk. Hence the Modified Duration of a floating rate bond is equal to the length of the interest payment interval. 36
Which Duration Are We Talking? Macaulay Duration is a weighted average measure of the life of a bond where the weight for each time points us the relative contribution of the present value of the cash flow at that time point to the price/value of the bond. Modified Duration is a measurement of the sensitivity of a bond s price to interest rates as interest rates change. Modified Duration is equal to Macaulay Duration when the bond pays coupon annually. What if the bond is option-embedded? Effective Duration is the duration for a bond with an embedded option when the value is calculated to include the expected change in cash flow caused by the option as interest rates change. This measures the responsiveness of a bond's price to interest rate changes, and illustrates the fact that the embedded option will also affect the bond's price. For option-embedded bonds, Effective Duration is a more accurate measurement of interest rate sensitivity. For option-free bonds, the Effective Duration is equal to Modified Duration. Thus they can be used inter-changeably in this case. How is the Duration being calculated? For vanilla bond illustration, Modified Duration is being calculated As a better reflection of price sensitivity, Effective Duration is being calculated for the TWD Inverse Floater. With each yield curve and maturity, the marginal value change with respect to 1 basis point change in the yield curve can be calculated. Effective Duration equals the marginal value change divided by the total value of the deposit. 37
Duration Change The value change based on duration is valid for small changes in interest rates, but will not be wholly accurate for large changes. The reason for this is that duration changes with the interest rate movement, thus causing deposit values do not change by proportionately the same amount at all interest levels. The change of duration shows a concave shape. This is driven by the Convexity. Convexity is the measurement of the change in Duration as interest rates change. The diagram below takes a 10-year bond as an example. Graphs on the right illustrate the relationship between duration change and yield change and maturity change. Since the bond is a vanilla one, Modified Duration is calculated. 9.20 9.15 9.10 9.05 9.00 8.95 8.90 8.85 Duration Change with Yield Change 8.80 1.00% 1.25% 1.50% 1.75% 2.25% 3.25% 4.25% 5.25%!"#! $% $ %!%$ $" %$ $!$# #$ #%% #!$" % #"!## ## " ##! %$"#$ # #%! ##% $!! ## #$" " # ## ##! " 10 9 8 7 6 5 4 3 Duration Change with Maturity Change &'! 2 1 0 10 9 8 7 6 5 4 3 2 1 38
A2 Accounting in detail 39
Inverse Floater Accounting Treatment IAS 39 10. An embedded derivative is a component of a hybrid (combined) instrument that also includes a non-derivative host contract with the effect that some of the cash flows of the combined instrument vary in a way similar to a stand-alone derivative. An embedded derivative causes some or all of the cash flows that otherwise would be required by the contract to be modified according to a specified interest rate, financial instrument price, commodity price, foreign exchange rate, index of prices or rates or other variable. A derivative that is attached to a financial instrument but is contractually transferable independently of that instrument, or has a different counterparty from that instrument, is not an embedded derivative, but a separate financial instrument. 40
Inverse Floater Accounting Treatment IAS 39 11. An embedded derivative shall be separated from the host contract and accounted for as a derivative under this Standard if, and only if: (a) the economic characteristics and risks of the embedded derivative are not closely related to the economic characteristics and risks of the host contract (see Appendix A paragraphs AG30 and AG33); (b) a separate instrument with the same terms as the embedded derivative would meet the definition of a derivative; and (c) the hybrid (combined) instrument is not measured at fair value with changes in fair value recognised in profit or loss (ie a derivative that is embedded in a financial asset or financial liability at fair value through profit or loss is not separated). If an embedded derivative is separated, the host contract shall be accounted for under this Standard if it is a financial instrument, and in accordance with other appropriate Standards if it is not a financial instrument. This Standard does not address whether an embedded derivative shall be presented separately on the face of the financial statements. 41
Inverse Floater Accounting Treatment IAS 39 AG33. The economic characteristics and risks of an embedded derivative are closely related to the economic characteristics and risks of the host contract in the following examples. In these examples, an entity does not account for the embedded derivative separately from the host contract. (a) An embedded derivative in which the underlying is an interest rate or interest rate index that can change the amount of interest that would otherwise be paid or received on an interest-bearing host debt instrument is closely related to the host instrument unless the combined instrument can be settled in such a way that the holder would not recover substantially all of its recognised investment or the embedded derivative could at least double the holder s initial rate of return on the host contract and could result in a rate of return that is at least twice what the market return would be for a contract with the same terms as the host contract. 42
Disclaimer: ABN AMRO Bank N.V. ( ABN AMRO ) and its affiliates (the ABN AMRO Group ) puts forward the following in good faith. However, you should be aware that: The ABN AMRO Group is not, and does not hold itself out to be, an adviser as to legal, taxation, accounting or regulatory matters in any jurisdiction. You shall be responsible for making your own independent investigation and appraisal of the risks, benefits and suitability of the information described above (the Information ), and ABN AMRO shall incur no responsibility or liability whatsoever to you in respect thereof. No action, omission, recommendation or comment made by the ABN AMRO Group nor any of its directors, officers, employees or agents (each, a Relevant Person ) in relation to the Information (as defined herein) shall constitute, or be deemed to constitute a representation, warranty or undertaking of or by the ABN AMRO Group or any Relevant Person. This document does not constitute an offer of, or an invitation to subscribe for or purchase, any security. 43