Duration Gap Assumptions. The duration of assets and liabilities must be known precisely. The market value of assets must be known

Transcription

1 Duration Analysis

2 Duration Gap Assumptions The duration of assets and liabilities must be known precisely The market value of assets must be known The change in interest rates can only be a parallel shift Convexity is not expected to influence valuation Term structure of interest rate is flat

3 Duration Gap Duration Gap Asset Duration (Liabilities Duration x Weight) D (D x W ) A L L W L Total Liabilities Total Assets D Duration of assets; D Duration of liabilities A L

4 Duration Gap analysis focuses on the market value of equity Goal of Duration Analysis Duration computes weighted average of the cash flows (interest and principal payments) of the instrument, discounted to the present time

5 Computation of Duration Analysis Net Worth Total Assets Where : ( Modified Duration x R) (1 R) Duration Gap Asset Duration (Liability Duration x W ) W L E E Modified Duration Gap Total Liabilities Total Assets ( Modified Duration x R ) Duration Gap E: Market value of equity; R : Change in interest rate L

6 Computation of Duration 0 C :D N P R :Cashflows;Discountrate.:Numberofyearstomaturityoftheinstrument.:Presentvalueoftheinstrument.:Interestrateattimet. Modified Duration (MD) = Macauley Duration (D) = D 1 R1122NN0Nttt=1Nttt=1CxDx1+CxDx2+.CxDxN=PCxDxtCxD

7 Duration of Assets and Liabilities for Banks Duration of assets and liabilities : A A A A n n D X D X D... X L L L L n n D X D X D...X D D X : Weights; D : Duration. A : Assets; L : Liabilities. n : Time to maturity.

8 Example Assets T Bill Investment Liabilities Certificate of Deposit 1 year 7% 30 1 year 6% 50 Loan 2 year 10% 70 3 Year Time Deposit 9% 40 Capital RSA < RSL = 30 < 50 RSA - RSL = = -20 (Negative gap) Rate sensitive assets less than rate sensitive liabilities Bank strategy: Borrowing short and lending long

9 Rates Rise by 2% - Rate Shock of 200 basis point Assets Discounted Cash Flows T Bill : ( ) Loan: 7.00 = 6.25 ( ) = ( ) Asset Value 97.63

10 Rates Rise by 2% - Rate Shock of 200 basis point Liabilities 1 Year CD = ( ) Discounted Cash Flows Year TD = 3.60 = 3.24 ( ) = 3.60 = 2.92 ( ) 2 = = ( ) Total Liabilities Market Value of Bank Capital ( ) 9.59 Additional Income - (-20 x 0.02) 0.40 Decline in Capital Value of Bank ( ) 0.01 Book Value of Bank Capital 10.00

11 Duration Gap Assets Duration T Bill : Loan : D A DA x (1) 77.00x (2) + 2 ( ) (1+0.12) Weighted Average duration 0.30 x x

12 CD: TD: DL 2 D L 1 Liabilities 54.00x (1) (1 0.08) 50 Duration Gap 3.6x (1) 3.6x (2) 43.6x (3) (1.11) (1.11) (1.11) Duration Weighted Average duration x x Duration DA < DL : < Duration Gap= Leverage-adjusted Duration Gap = ( 0.9 x ) 0.034

13 W L Impact on Equity Equity R VE( DAWL DL)xAx 1 R L 90 A 100 R 0.02 V E [0.034]x100x 1.10 Value x100x Decline in Equity Value (Duration Gap) Macauley s Duration 0.057

14 Duration Gap and Financial Risk Exposure Equity Value E A L E A L R R DA x A DL x L 1R 1 R R R L DA x A DL x xa 1R 1 R A R DA WL x DL x A x 1 R L WL A

15 Impact on Equity Change Value Elasticity Instantaneous rate of change E E 0 R R de 1 dr (1 R) (ExD) This can be rewritten as de E dr (1 R) D Hence a change in equity value is indiated by duration gap times change in interest rate

16 Duration Gap Exposure - Example Base Case : Assets Liabilities Equity Capital / Assets Assumptions: D 5 D 3 A R 0.10 W 0.90 L R 1% L

17 Rates Fall by 1% R V E (DA WL xd L)xAx( ) 1 R 0.01 (50.9 x3) x 100 x ( ) R 0.01 A DA x A 5 x x (100) R R 0.01 L DL x L 3 x x 90 1 R (90)

18 Rates Fall by 1% New Balance Sheet Assets Liabilities Equity Capital / Assets * % *

19 Rates Raise by 1% R V E (DA WL xd L)xAx( ) 1 R 0.01 (50.9 x3 ) x 100 x ( ) R 0.01 A DA x A 5 x x (100) R R 0.01 L DL x L 3 x x (90) R

20 New Balance Sheet Rates Rise by 1% Assets Liabilities Equity 7.91* Capital / Assets = 8.29 % *

21 Adjustment for Zero Duration: Duration Gap Exposure - Example Assets Liabilities Equity Capital / Assets % Assumptions: D 2.7 D 3 A R 0.10 W 0.90 L R 1% L

22 Duration Gap and Financial Risk Exposure Duration gap = (2.7 (3 x 0.9)) 0 Modified duration = 1/1.1 0 V [D W D ]A( R/(1R)) E A L L [2.7 (0.9 x3)]x100 x(0.01/(10.10)) 0 In terms of changes in asset and liabilities : VA 2.46 [ 2.7 x(0.01/ (10.10))] V 2.73 [ 3 x(0.01/ (10.10))] L VL x WL 2.73 x(90/100) 2.46 VA V L V E 10 Capital / Total Asset Value %

23 Duration Gap = 0 ( R) E 0,i.e.(DA WL xd L)x 1 R Three methods : 1. Reduce D A shorten the maturity of assets 2. Increase D L lengthen the maturity of liabilities 3. Increase W increase leverage L

24 Implication of Duration GAP Analysis Positive Duration GAP - Assets are more price sensitive than liabilities When interest rates rise (fall), assets will fall proportionately more (less) in value than liabilities and value of equity will fall (rise). Negative Duration GAP - Weighted liabilities are more price sensitive than weighted assets When interest rates rise (fall), assets will fall proportionately less (more) in value than liabilities and the equity value will rise (fall).

25 Duration Gap Analysis Duration Gap Interest Rate Change Assets Liabilities Equity Positive Increase Decrease > Decrease Decrease Positive Decrease Increase > Increase Increase Negative Increase Decrease < Decrease Increase Negative Decrease Increase < Increase Decrease Zero Increase Decrease = Decrease No change Zero Decrease Increase = Increase No change

26 Immunization of Bank Portfolio Immunization target on (Capital/ Asset ) 0 Require : DA DL x WL Example: Computation Value D 4.5 A DL 5 WL 0.90 R V E ( x 5 ) x (100 ) x % A 4.5 x % L 5 x

27 Immunization of Bank Portfolio Computation Value EVE Ex AAAx (100) LLLx (100) ( Capital / Assests) x

28 Immunization of Bank Portfolio Immunization of bank portfolio is when the gain from the higher (lower) reinvestment rate is offset by the capital loss. Change in capital is insensitive to changes in interest rate fluctuations.

29 Immunization of Bank Portfolio Duration matching alone will not immunize a bank s statement of interest rate sensitive condition. Duration matching and comparable value gap impact on income are required. Asset and liability cash flow patterns, amount and timing must match exactly.