IR Futures Effective Asset Class ก Efficient Frontier

Interest Futures* ก * ก ก ก. ก ก 11 ก ก ก ก ก ( ) ก ก * Interest Futures ก ก ก ก ก ก ก ก ก ก (Synthetic Portfolio) ก * ก ก ก 2

กก IR Futures ก ก (Asset Class) IR Futures Supposedly Most Efficient and Effective Asset Class ก ก IR Futures Effective Asset Class ก Efficient Frontier ก IR Futures ก 20 ก.. 53 http://www.tfex.co.th/th/investor_corner/papers.html 3 ก ก ( ) ก ก ก ก ก ก Transaction Costs ก ก ก 4

กก ก กก ก ( ) = ( ) x = -1 x ( ) x ก (%) = ก 5 ก IR Futures กก Mark to Market Value ก 0.00 ก Value of IR Futures ก Initial Margin ก กก Initial Margin 6

Margins ก IR Futures Margin TCH ก * Initial Margin = 1.90 x TCH Margin 6M THBFIX Futures (TBF6) 9,000 17,100 5Y Gbond Futures (TGB5) 6,000 11,400 3M BIBOR Futures (BB3) 1,000 1,900 * ก TCH 12.. 53 7 ก Futures Prices ก กก ( ก ก ) Volatility ก ก ก ก ก Volatility ( ก ก ) %Price Change IR Futures Volatility ก Standard Deviation ( ) 3M BIBOR (Nearby) N.A. N.A. 6M THBFIX (Hypothetical Nearby) 0.0607% ก ก IR Futures 5Y Gbond (Hypothetical Nearby) 0.2568% TFEX SET 50 Index (Nearby) 1.9900% ก ก ก ก ก ( ก ก ) IR Futures Asset Class ก ก 8

ก ก ก R ก ก ก ก N (µ, σ) z ก N (0.00, 1.00) R z ก : R = µ + σz ก : R = σz µ 0.00 9 IR Futures ก ก ก SET 50 Futures ก V Multiplier F Futures Price ก ก ก Initial Margin TCH Margin = Initial Margin = ก 1. Volatility ก ก Standard Normal z 2. IR Futures SET 50 Futures ก ก ก ก 1. Multiplier ก Mark to Market 2. SF Safety Factor TCH Margin ก 10

ก ก IR Futures ก SET 50 Futures ก ก ก กก ก ก ก ก Regression R 2 t Statistics 3.. 50 11.. 53 6M THBFIX y t y t-1 5Y GBOND Log Return ThaiBMA 5YZRR Index SET50 Log Return SET50 Total Return Index 11 ก R 2 t Statistics * Lag 1 Lag 2 Lag 3 Lag 4 Lag 5 6MTHBFIX 11.25% -9.68-6.28-5.73-2.91-1.35 5Y GBOND 10.14% 9.62-0.03-0.82-0.34 0.72 SET 50 0.77% 1.24 1.90 0.36-0.74-1.05 * t 95% (2-Tail) t > 1.96 ก ก ก Underlying Variables ก ก ก กก IR Futures กก ก SET 50 Futures 12

ก ก IR Futures ( ) ก Underlying Variable ก Underlying Variable ก Futures Price Underlying Variable ก IR Futures Price ก The Cost of Carry Model 13 ก ก 6MTHBFIX Futures Interest Rate = Forward Interest Rate Simple Compounding. Period of 6 Months. No Arbitrage Condition ก ก 2 ก T+S ก 1 y T+S % S 0 T T T+S ก 2 T y T % ก Forward/Futures Interest T F S % 14

ก ก T F S % ก ก TFEX Futures S=1 6 ก T F 1 % I T = 100 - T F 1 100 yt+1 1+ ( T+1) 2 I T = 100- TF 100 1 = 100-2 -1 100 yt 1+ ( T) 2 ก ก ก I T ก ก THBFIX Rates T T+1 15 ก ก THBFIX Rate T Mean Reversion ก ก ก ก H 16

Theta Mu ก THBFIX Theta Mu 1M 0.0019 0.0316 3M 0.0010 0.0321 6M 0.0010 0.0341 9M 0.0010 0.0366 1.0 Y 0.0014 0.0377 1.5 Y 0.0015 0.0389 2.0 Y 0.0020 0.0406 ก ก ก Splined THBFIX Rates ก Thai BMA 17 ก ก THBFIX Futures Price ก ก Term Structure THBFIX Rates ก Spot THBFIX Swap THBFIX Rate Cubic Spline ก ก y (T), 0 y (T+1), 0 THBFIX Futures ก Spline Mu Theta ก ก Splined Mu s and Theta s ก y (T), 0 y (T+1), 0 ก y (T), H y (T+1), H ก ก THBFIX Futures Price 18

ก ก ก THBFIX6M Futures Price A Mean-Reversion Forecast of THBFIX Futures Price-- --Anya TU.xls : ก Estimate THBFIX Rates : ก ก 19 5Y GBOND Futures Interest Rate = Forward Interest Rate No Arbitrage Condition 5Y Gbond Futures T ก ก ก 5Y Gbond 5 (1) 1 (2) 5% ก 6 ก 2.50% ก ก F(T) 100 T F(T) t=0 20

ก 5Y Gbond 100 0 T T+1 T+2 T+8 T+9 T+10 0 : F(T) T : F(T) 5Y Gbond T+1: 2.50 T+2: 2.50 T+8: 2.50 T+9: 2.50 T+10: 102.50 Forward ก ก T ก ก Forward Interest Rate T f j ก T+j ก T ก ก Theoretical TFEX 5Y GBond Futures Price--Anya TU.xls ก ก ก F(T) ก ก Spot Rates T+j T+j+1 21 ก ก Term Structure Spot Interest Rates ก Single-Factor Interest Rate Models Vasicek Model ก Instantaneous Interest Rate Cox, Ingersoll and Ross Model ก Instantaneous Interest Rate ก กก 1. Instantaneous Interest Rate 2. Rate Driver Spot Rate 3. 5 ก ก ก 22

Vasicek Spot Interest Rates R(t, T) T ก ก Inst. Int. Rate r(t+h) 23 CIR Spot Interest Rates R(t, T) T ก ก Inst. Int. Rate r(t+h) 24

( ) ก ก ก ก Vasicek CIR Mu 1.3714e-3 1.3690e-3 Theta 6.9120e-5 3.1532e-5 Sigma 4.0900e-6 2.1215e-4 r(t) ก ก 25 ก ก ก 1 ก. 25 Spot Rates t Recover ก r(t) ก 2 ก Spot Rates t Recover Parameters ก r(t) ก A Vasicek Forecast of TFEX 5Y GBond Futures Price--Anya TU.xls ก A CIR Forecast of TFEX 5Y GBond Futures Price--Anya TU.xls ก ก CIR CIR ก Vasicek ก 26

ก A CIR Forecast of TFEX 5Y GBond Futures Price--Anya TU.xls 27 ก ก ก Asset Classes Enhanced Efficient Frontier ก Synthetic Bond Portfolio Duration 28

ก Asset Classes Statistical Properties : 11.. 2546 15 ก.. 52 factor = 250 THBFIX GBOND Statistics SET50 GOLD 3-7 yrs TRI T BILL index Futures Futures Annual Mean 7.23% 13.71% 4.06% 2.81% -12.62% -106.57 Annual STD 27.33% 21.16% 3.42% 0.17% 264.74% 376.22% Correlation SET50 1.0000 0.0618 0.0431-0.0387 0.0888 0.0434 GOLD 0.0618 1.0000 0.0102 0.0223 0.0718-0.0008 3-7 yrs TRI 0.0431 0.0102 1.0000 0.2306 0.3555 0.9027 T BILL index -0.0387 0.0223 0.2306 1.0000 0.1274 0.1793 THBFIX Futures 0.0888 0.0718 0.3555 0.1274 1.0000 0.3272 GBOND Futures 0.0434-0.0008 0.9027 0.1793 0.3272 1.0000 ก 1. Futures Short 2. ก ก Leverage { Return = (F1-F0) * Multiplier / IM)} 3. Correlations Futures ก Assets Improves Diversification 4. Futures Contract Value Initial Margin 29 ก Efficient Frontiers ก ก ก ก ก Constraints ก Long Only Basic Assets Long Short Futures ( Constraints ก ) ก ก 1.00 ก Absolute Value Margin Long Short ( ) ก ก 30

ก Efficient Frontier-- --Anya TU.xls 2 Worksheets Constraints ก Efficient Frontier กก ก ก ก ก ก 31 Efficient Frontiers ก ก a. 4 Basic Assets b. 4 Basic Assets + 2 UNCONSTRAINED Futures 13% Expected Return 11% 9% 7% 5% 3% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Standard Deviation 4 Basic 4 Basic and 2 Futures Futures ก ก Efficient Frontier ก Asset Allocation ก SOLVER ก ก Converge Local Optimum 32

ก Synthetic Bonds ก seasoned ก กก ก Bid-Ask ก ก ก Adverse Price Pressure ก ก ก ก 5Y-Gbond ก กก Bid-Ask Spread ก ก ก ก ก ก ก ก 33 ก ก ก Synthetic Bond Portfolio ก Authentic Bond Portfolio ก ก Authentic Bond Portfolio ก Duration Portfolio กก ก Authentic Portfolio Synthetic Portfolio dy ก ก ก Duration Exposure 34

ก ก ก Synthetic Bond Portfolio ก Treasury Bill 5Y Bond Futures ก dy Synthetic Portfolio ก ก Authentic Bond Portfolio ก ก Synthetic Portfolio ก dy Target Duration ก ก ก GBOND Futures ก Hedging ก ก Synthetic Portfolio ก Cash T-Bill ก GBOND Futures ก ก Risky Bond Portfolio Futures Duration 35 ก ก ก ก GBOND Futures ก Initial Margin 11,400 ก Synthetic Portfolio Initial Margin ก 36

ก ก Synthetic Bond Portfolio ก Authentic Bond Portfolio Modified Duration D Target ก Synthetic Bond Portfolio ก W Treasury Bill Synthetic Portfolio Modified D TB 5Y GBOND Futures ( ) Modified Duration ก D F 37 2 Synthetic Bond Portfolio 1 ก dy ก TB = T-Bill h = Synthetic Portfolio EF = Exposure Bond Futures 1 2 ก Synthetic Portfolio ก W 11,400 = Initial Margin 1 38

Solution ก Synthetic Bond Portfolio ก 2 Unknowns Futures h T-Bill TB กก ก ก (1) (2). 38 39 2 EF = Exposure Position in Bonds ก 1 D F = Modified Duration 40

: Duration Bond ก ก ก n ก τ 1 0.5y B τ +n-2 ก ก 100+0.5y B τ+n-1 ก ก Durations 41 ก Duration Bond Duration ก ก Thai BMA Duration Bond Portfolio = Value-Weighted Average Duration Bond Portfolio 42

: Duration Bond Futures (1) Equivalent Assets ก Long Position 5Y GBond Futures T ก Long Position Riskless FCFs β 0 ก ก ก T ก β 0 Equivalent Asset Durations ก 43 : Duration Bond Futures (2) Underlying Bond Cash and Carry ก ก Value (VoBF 0 ) of Bond Futures Contract ก ก Duration Futures Contract ก B 0 D Mac ก Synthetic Bond Portfolio--Anya TU.xls 44

ก EF ก B 0 Underlying Bond ก ก ก EF ก 45 ก Synthetic Bond Portfolio--Anya TU.xls * 10,000,000 Bond Portfolio Modified Duration ก 5 ( ) Synthetic Bond Portfolio ก T Bill 5Y GBOND Futures ก 5Y GBOND Futures 1.75 6 Term Structure Duration ก 4.5039 ( ) Bond Exposure ก 105.9868 ก T Bill Duration ก 0.35 ( ) Initial Margin ก Broker ก 11,400 * ก ก ก Theoretical TFEX 5Y GBond Futures Price--Anya TU.xls ก 20 ก.. 53 46

Synthetic Bond Portfolio h ก 9.7493 T Bill ก 9,888,857.68 ก 9 10 47 Synthetic and Authentic Bond Portfolios ก... 48

ก ก ก 24 ก 2553 *. ก ก 11 ก ก ก ก ก ( ) ก * ก ก ก ก ก ก ก ก ก 49