การจ ดประช มทางว ชาการ ศาสตราจารย ส งเว ยน อ นทรว ช ย ด านตลาดการเง นไทย คร งท 17 ประจ าป 2552

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1 การจ ดประช มทางว ชาการ ศาสตราจารย ส งเว ยน อ นทรว ช ย ด านตลาดการเง นไทย คร งท 17 ประจ าป 2552 การบรรยายเร อง Active Fixed-Income Management with the Key Rate Duration Approach ผ บรรยาย ดร.ช ช ย ศร ศ นสน ย ว นศ กร ท 27 พฤศจ กายน 2552 เวลา 13:15 14:45 น. ห อง 201 คณะพาณ ชยศาสตร และการบ ญช มหาว ทยาล ยธรรมศาสตร ท าพระจ นทร

2 Active Fixed-Income Management with the Key Rate Duration Approach Chuchai Srisansanee, Ph.D. Consultant ThaiBMA & Director of FED-GMI GMI-KMUTT

3 Main Topics Key rate immunization Rationale Index replication Cashflow-matching Minimum risk Key rate attribution Treasury zero bond stripping Rationale Multi-tenor immunization Portfolio risk structures Leverage effects on setup costs and risk Portfolio value-at-risk 2

4 Key Rate Immunization 3

5 Rationale Immunization is a hedging method to protect a bond portfolio against risk due to interest rate movement Bond portfolio is constructed to replicate a value change of a target fixed-income portfolio. When interest rates change, P/L of both portfolio will offset. No risk! Zero yield curve is needed 4

6 Rationale Bond pricing is defined by If a hedging port has duration equal to that of the target port; then returns of both port will be equal. No interest rate risk The idea is used in the passive indexing If we match B D in, P/L will be equal. It is used in cashflow-matching Good idea for immunization but inefficient 5

7 Rationale Classical bond pricing is based on two implicit assumptions Flat yield curve Parallel shift Real yield curves (next slides) violate these assumptions Impact : possibly inefficient hedging 6

8 Rationale 8 ThaiBMA Cubic Spline Zero Curve (250 days) % d 1m3m6m 1y 2y 3y 4y 5y 6y 7y 8y 9y10y11y12y13y14y15y16y17y18y19y20y21y22y23y24y25y26y27y28y29y30y Date 7

9 Rationale 0.6 ThaiBMA Cubic Spline Zero Curve (250 days change) % d 1m3m6m 1y 2y 3y 4y 5y 6y 7y 8y 9y10y11y12y13y14y15y16y17y18y19y20y21y22y23y24y25y26y27y28y29y30y Date 8

10 Rationale In-depth analysis on spot rates in Thai bond market shows yield-shift pattern found in global markets (next slide) They are called (1) shift, (2) twist, and (3) butterfly Enhanced immunization should take advantages of shift amounts at each tenor 9

11 Rationale 100 Percentage Error Explained (corrrelation) Spot correlation: 3 patterns account for nearly 100% of risk % Loading on correlation of Zero Spot no latents % d 1m3m6m 1y 2y 3y 4y 5y 6y 7y 8y 9y10y11y12y13y14y15y16y17y18y19y20y21y22y23y24y25y26y27y28y29y30y Date Shift Twist Butterfly 10

12 Rationale Key rate approach works as follows Cashflow is mapped into two adjacent tenors Duration and convexity are computed for each key tenor; called key rate duration and key rate convexity resp. 1y 2y Point : attempt to capture yield curve shifts more realistically 11

13 Rationale Refined bond pricing is k is no. of key tenors D i is key rate duration at tenor i dy i is yield change at tenor i We are free to partially immunize to a horizon risky to our port Investing weight of bond n Time horizon Duration at tenor j due to bond n 12

14 Rationale By taking views on yield shifts on various tenors, traders are managing an active portfolio. The standard key rate model is Duration at tenor 1 due to bond n Investing weight of bond n Duration at tenor 1 Discussion 13

15 Index Replication 210 ThaiBMA Bond Index (1,820 days) Index Jan Aug Apr Nov Jul-2008 Date How to replicate this index? 14

16 Index Replication By bond pricing, ThaiBMA bond index is driven by ThaiBMA zero rates Obtain implied key rate durations Use 250 days (14-Nov-08 to12-may-09) Use regression; R 2 = 96.72% Residual analysis confirms the model validity Use LB bonds on 12-May-09; exclude T-Bill Immunize up to tenor 12y only 15

17 Index Replication Bonds on 12-May-09 16

18 Index Replication Implied key rate duration 0.9 No. of Days = Implied Key Rate Duration d 1m 3m 6m 1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y 21y 22y 23y 24y 25y 26y 27y 28y 29y 30y 17

19 Index Replication Residual plot Replicated bond index 0.5 Residual: value change 185 Bond Index = TBMA-GB Predicted Bond Index Bond Index 18

20 Index Replication 0.9 No. of Days = Unit Duration Implied Key Rate Duration d 1m 3m 6m 1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y 21y 22y 23y 24y 25y 26y 27y 28y 29y 30y KRD Approach Bond ID KRD Approach d 1m 3m 6m 1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y 21y 22y 23y 24y 25y 26y 27y 28y 29y 30y Time 19

21 Cashflow Matching Useful in ALM applications Example Corporate firm ABC is liable to pay a series of debts 500 in 3y, 1200 in year 5, and 800 in year 10 Treasurer constructs a hedging portfolio with a set of LB bonds (see index replication on 12-May-09) Key rate approach is employed 20

22 Cashflow Matching Immunization can be formed as follows Price of bond id 2 Debt at tenor 1 Remark In practice, we do not use this form of optimization. Hard to obtain a solution. 21

23 Cashflow Matching 1400 KRD Approach Cashflow d 1m 3m 6m 1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y 21y 22y 23y 24y 25y 26y 27y 28y 29y 30y Time KRD Approach 10 8 Duration d 1m 3m 6m 1y 2y 3y 4y 5y 6y 7y 8y 9y 10y 11y 12y 13y 14y 15y 16y 17y 18y 19y 20y 21y 22y 23y 24y 25y 26y 27y 28y 29y 30y Time 22

24 Cashflow Matching 2 KRD Approach Unit Bond ID 23

25 Minimum Risk Obj function below diversifies portfolio To minimize risk, change to 24

26 Minimum Risk 0.2 KRD Approach 0.15 Diversified Minimum Risk Unit Bond ID Both setups provide the same implied KRD structure Diversified cost is ; min risk cost is

27 Key Rate Attribution Table is excerpted from Quantitative Management of Bond Portfolios by Lev Dynkin ThaiBMA zero curve Underperform of 5-year wrt. parallel shift and benchmark ( )*0.83 ThaiBMA key rate duration From internal port or ThaiBMA index replication How do we interpret this number? 26

28 Treasury Zero Bond Stripping 27

29 Rationale Zero-coupon bonds are available for S/T bonds, e.g. T-Bill Modern applications need L/T zero-coupon bonds Simple solution : buy coupon bonds; then strip coupons and sell as zero bonds How to measure risk?(in accurate way) Efficient enough? 28

30 Rationale Real-world applications involve multi-tenor Classical immunization works on the average and single tenor Key rate approach can answer both business needs and technical difficulty Treasury zero bond stripping is just another application of key rate approach 29

31 Multi-Tenor Classical method is not good at multi-tenor immunization For a bullet portfolio, a weight is For a ladder portfolio, solve for weights For a barbell portfolio, how to allocate? A way out is to match the average duration of portfolio structure 30

32 Risk Strucuture Three common structures are ladder, bullet, and barbell Bullet : exposure is clustered around a single time horizon Ladder : exposure is spread out over time horizons Barbell : exposure is clustered on extreme sides of horizons 31

33 Risk Strucuture Data on 12-May-09 Bullet with a duration 8-year Ladder with equal investment Barbel with S/T duration 2-year and L/T duration 10-year Compare risk structures from classic method and key rate approach 32

34 Risk Strucuture Classical bullet Key rate bullet 33

35 Risk Strucuture Classical ladder Key rate ladder 34

36 Risk Strucuture Classical barbell Key rate barbell 35

37 Risk Structure Classical method generates risk structure in terms of bond units Key rate approach generates risk structure in terms of duration Which one makes more sense? 36

38 Leverage Duration can be interpreted as a risk sensitivity; hence, it can be used as a risk leverage We can vary duration in each portfolio structure until we satisfy with risk and setup cost Lessons learned here is important during the design of zero bond stripping 37

39 Leverage SDA : classical method KDA : key rate approach Observations : bullet - Key rate cost is more stable - Risk increases relatively linear - Classic cost and risk appear to increase at higher speed 38

40 Leverage FCFS : classical method KDA : key rate approach Observations : ladder - Risk is compared with fixed cost - Classic method has lower risk than that of key rate approach - This is not surprising! - As leverage increases, classical risk increases very slowly - Classical method outperforms in ladder 39

41 Leverage FCFS : classical method KDA : key rate approach Observations : barbell - Risk is compared with fixed cost - Classic method has lower risk but marginally negligible - Key rate approach generates the exact risk structure - At 1000% leverage, VaR gap is only 0.65% of setup cost VaR gap is a distance between classical and key rate VaRs 40

42 Value-at-Risk Value-at-Risk can be measured at each tenor and at portfolio level in contrast to the classical method in which VaR is calculated for a bond or a bond portfolio Some nonlinear value-at-risk is applicable to the statement above; calculation is not harder than delta value-at-risk (claim) 41

43 Stripping Previous slides show that barbell is the most complex structure but key rate approach performs well on this In index replication, implied key rate duration shows that risk structure is none of three common structures. Harder than basic ones Stripping is a series of bullets (complex) 42

44 Stripping Example We want to sell zero bonds with maturity 3y, 4y, 5y, 6y, 7y, 8y, 9y, and 10y Leverage is 3,,10 for tenors 3y,,10y Principal protection is 100 for each strip Key rate cost is allocated to these tenors Calculate discount prices, no. of units, and total amount for each strip In practice, cashflow-matching stripping is more realistic 43

45 Stripping 44

46 Stripping Sale profile obtained by the key rate approach 45

47 Q/A For further information, please contact Chuchai Srisansanee, Ph.D. Director of Financial Engineering Development and Research Center r (FED) Graduate School of Management and Innovation (GMI) King Mongkutt University Technology of Thonburi (KMUTT) fed.gmi@gmail.com 46