Yield Curve Construction and Medium-Term Hedging in Countries with Underdeveloped Financial Markets

Transcription

1 Local ineres rae risk approach Empirical resuls Supplemen Yield Curve Consrucion and Medium-Term Hedging in Counries wih Underdeveloped Financial Markes Model based pricing and valuaion M. Cincibuch 1 A. Remo 2 1 OGResearch 2 CERGE-EI June 4, 2010 M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

2 Objecive Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Pricing and valuaion of local currency fixed-rae deals, fixed-margin componen of floaing-rae conracs. on underdeveloped financial markes. Consruc he erm srucure of ineres raes (discoun facors) ha ake ino accoun risks involved and also compensaion for he risk. M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

3 Sofware: Iris Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Tools Yield Curve Consrucion Iris is a Malab oolbox developed by Jaromír Beneš ( Esimaion, inerpreaion of hisory, forecasing, forecas inegraion, decomposiions, and much more. I suppors: Solving raional expecaions models Boh sochasic and perfec-foresigh assumpions Idenificaion in boh ime and frequency domain Daabase and ime series handling M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

4 Forecasing ools Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Tools Yield Curve Consrucion Srucural medium-erm macroeconomic model model equaions Flexible NK model of moneary ransmission A sandard model adaped o EM phenomena Used in pracice by many EM cenral banks Near-erm forecasing ools Shor-erm models (ARIMA, VECMs, (B)VARs ec) Exper judgmen and secor specific analysis Daa driven (black-box) echniques inferior o exper judgmen in emerging markes M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

5 Local ineres rae risk approach Empirical resuls Supplemen Forecas based pricing Tools Yield Curve Consrucion Use medium-erm macroconomic projecion providing forecas of shor-erm ineres rae forecas of he exchange rae forecas of he oher variables esimae of he curren disequilibrium probabilisic disribuions for he forecass M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

6 Local ineres rae risk approach Empirical resuls Supplemen Tools Yield Curve Consrucion Condiional variance of RWF/USD (100*log) 1 Relaive conribuions ime period Absolue conribuions ime period shock_l_rwf_usd shock_dl_cpi_ar shock_i shock_dl_cpi_xf shock_dl_z_nd shock_dl_cpi_f ohers M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

7 Local ineres rae risk approach Empirical resuls Supplemen Tools Yield Curve Consrucion Condiional variance of zero-profi curve - Rwanda 1 Relaive conribuions Y 2Y 3Y 4Y mauriy Absolue conribuions Y 2Y 3Y 4Y mauriy shock_l_rwf_usd shock_i shock_dl_cpi_ar shock_dl_z_nd shock_prem shock_i_us ohers M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

8 Local ineres rae risk approach Empirical resuls Supplemen Projecion wih confidence bands Tools Yield Curve Consrucion Raios of domesic shock variances calibraed Toal variance of he model esimaed in wo seps: Variance of exernal schocks independenly Subsequenly he oal model variance by ML The cenral projecion independen of he band-widh Nominal NBR T bills Ineres Rae (per cen p.a.) 2 01:4 03:4 05:4 07:4 09:4 11:4 13: CPI Inflaion (y o y) 01:4 03:4 05:4 07:4 09:4 11:4 13: RWF/USD Nominal Exchange Rae :4 03:4 05:4 07:4 09:4 11:4 13: Real GDP Growh (per cen, y o y) 01:4 03:4 05:4 07:4 09:4 11:4 13:4 M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

9 Local ineres rae risk approach Empirical resuls Supplemen Differen approaches Tools Yield Curve Consrucion Two risk based (i.e. whole forecas disribuion maers) approaches: 1 Compensaes only for local ineres rae risk. Based on a local currency floa-o-fix swap (IRS). 2 Compensaes also for exchange rae risk, foreign erm premium. Based on cross-currency floa-o-floa and fix-o-fix or floa-o-fix swaps. M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

10 Local ineres rae risk approach Empirical resuls Supplemen Measure of he price of risk Tools Yield Curve Consrucion Trade-off beween risk and reurn of some zero-invesmen posiion measured by he raio of is expeced presen value o he sandard deviaion of his presen value. I is one possible generalizaion of he Sharpe raio (SR) for posiions involving cash flow in muliple poins of ime. For a single period posiion his coincides wih he Sharpe raio. M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

11 Local ineres rae risk approach Empirical resuls Supplemen Compensaing ineres rae risk The fixed leg rae of local floa-o-fix swap se o compensae he ineres rae risk. The ineres rae risk is calibraed on some exogenous reference value of he price of risk. Does no include he exchange rae risk direcly. M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

12 Local ineres rae risk approach Empirical resuls Supplemen Compensaing ineres rae risk (con) The hypoheical zero-invesmen posiion is o roll-over shor-erm borrowing for T periods in a local currency for r and o receive he fixed rae R T. The rae R T is deermined by condiion E( PV is) sd( PV = SR is) ref: ( 1+R T ) ( ( T E 1+ C ) ) T ( sd( 1+ C ) ) T = SR ref, where PV is = D(T) ( T 1+ C) = Π T =1 (1+ r ) ( N (1+R T) T ( N 1+ C ) T ). M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

13 Local ineres rae risk approach Empirical resuls Supplemen Compensaing exchange rae risk The long-erm rae se o compensae also for he exchange rae risk. Deermined from cross-currency swap s presen value disribuion and he price of risk. A reference value for he price of he risk derived from a similar conrac for which we have eiher observable or direcly modeled characerisics e.g. basis swap. Term premium compensaes for addiional volailiy of he fix-o-fix swap s PV comparing o basis swap. Co-movemens of he exchange rae and he ineres rae decrease he risk of he basis swap. Discoun facors can be derived from swap raes (boosrapping). M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

14 Local ineres rae risk approach Empirical resuls Supplemen Compensaing exchange rae risk (con.) Presen values of he basis swap and fix-o-fix swaps are: PV basis = PV fix2fix = T =1 T =1 ( N B ) ( S 0 r 1 () N S r N 1 +B S 0 (T) ( N B S 0 R T ) () N S R T +B (T) The rae R T of he enor T is deermined by condiion: ( ) ( ) E PVfix2fix E PVbasis ( ) = ( ). sd PVfix2fix sd PVbasis ) N S T ( N ) S 0 N S, T M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

15 Local ineres rae risk approach Empirical resuls Supplemen Presened prooype yield curves are based on he January 2010 Rwanda forecas: Projeced shor-erm rae was compounded o ge he base zero-profi curve - shown as viole line. The risk disribuions resul from all model shocks unresriced. The yield curve based on he local currency ineres rae swap compued wih he price of risk a 0.6. Swap raes of fix o 3M USD Libor used o compue foreign discoun facors and long-erm raes in consrucion of he yield curve based on cross-currency fix-o-fix swap. M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

16 Yield Curves, Rwanda baseline Local Currency Yield Curves (per cen p.a.) Y 2Y 3Y 4Y Cross Currency Fix o Fix SWAP Rae Zero Coupon Yield Curve (Sharpe raio=0.60) Zero Profi Curve

17 Demand Side Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions IS curve has backward and forward looking erms, moneary condiion index, and foreign demand ŷ = a 1 ŷ 1 +a 2 E[ŷ] +a 3 rmci 1 +a 4 (a 5 ŷ EZ 1 +(1 a 5 )ŷ EZ 1 )+εŷ Real moneary condiion index is a combinaion of real ineres rae gap and real exchange rae gap rmci = a 6 ( ẑ )+(1 a 6 )ˆr Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

18 Supply Side Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions CPI inflaion is a combinaion of food and ex-food inflaions π = c 5 π f +(1 c 5)π xf Ex-food Phillips curve: π xf =b 1 E[π xf ] +(1 b 1 b 2 b 3 )π 4xf 1 +b 2 π oil,im 2 +b 3 π im Food Phillips curve: +b 4 rmc xf +ε πxfood π f =b 5E[π f ] +(1 b 5 b 6 b 7 )π 4f 1 +b 6π food,im 1 Back o presenaion +b 7 π im +b 8 rmc f +ε πfood M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

19 Supply Side (con.) Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions Real marginal coss in ex-food producion: rmc xf = c 3 ŷ +(1 c 3 c 4 )ẑ +c 4 ˆ Real marginal coss in food producion: rp oil rmc f = c 1ŷ +(1 c 1 c 2 )ẑ +c 2 rp ˆ food Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

20 Moneary Policy Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions Policy rule: i = d 1 i 1 +(1 d 1 )(E[π ar ] + r +d 2ˆπ Inflaion forecas deviaion from he arge: +d 3 ŷ +d 4 ŝ RWF/USD )+ε i ˆπ = (π 4 +π π π 4 +3)/4 E[π ar ] Exchange rae depreciaion rae deviaion from is implied shor-erm arge: ŝ RWF/USD = s RWF/USD z +a 5 π US ss +(1 a 5 )(π EZ ss + sss USD/EUR ) π ar Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

21 Local ineres rae risk approach Empirical resuls Supplemen Model equaions Uncovered Ineres Rae Pariy Condiion Shor-erm UIP: s RWF/USD Long-erm UIP: = E[s RWF/USD ] (i i US r = r US + z prem )/4+ε srwf/usd +prem (π EZ ss π US ss + s USD/EUR ss )/4 Exchange Rae Expecaions parly backward looking: E[s RWF/USD ] =g 2 s RWF/USD +1 +(1 g 2 )(s RWF/USD 1 +2/4( z +π ar Back o presenaion a 5 πss US (1 a 5 )( sss USD/EUR +πss EZ ))) M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

22 Expecaions Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions E[π f ] = π f +1 E[π xf ] = (π +1 c 5 π f +1 )/(1 c 5) E[ŷ] = ŷ +1 E[π4] = g 1 π+1 4 +(1 g 1)π 1 4 E[π ar ] = (π ar +π+1 ar +π+2 ar +π+3)/4 ar Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

23 Food Prices Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions π food,im rp food rp food rp food rp ˆ food π food = π food = p food = rp food + s RWF/USD p = j 7 rp food = j 9ˆ rp food = 4(p food rp food = 4( + rp ˆ food 1 +ε rpfood +εˆ rpfood 1 rp food p food 1 ) rp food 1) z rp food Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

24 Oil Prices Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions π oil,im = π oil rp oil = p oil p rp oil rp oil + s RWF/USD rp oil = + ˆ π qoil = j 8 π qoil 1 +(1 j 8 ) rp ˆ oil = j 10 ˆ π oil rp oil 1 +εˆ rpoil = 4(p oil p oil 1 ) π qoil = 4( rp oil rp oil 1) z π qoil rp oil +ε rpoil ss Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

25 Local ineres rae risk approach Empirical resuls Supplemen Exogenous Processes for Trends Model equaions z = h 2 z 1 +(1 h 2 ) z ss +ε z ȳ = h 1 ȳ 1 +(1 h 1 ) ȳ ss +ε ȳ z = 4( z z 1 ) ȳ = 4(ȳ ȳ 1 ) prem = h 3 prem 1 +(1 h 3 ) r ss + +ε prem Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

26 Local ineres rae risk approach Empirical resuls Supplemen Exogenous Variables Model equaions π US π EZ π US π EZ π 4US π 4EZ π im = 4(p US = 4(p EZ p US 1 ) p EZ 1 ) = j 1 π 1 US +(1 j 1 )πss US +ε πus = j 2 π 1 EZ +(1 j 2)πss EZ +ε πez +π 1 US +π US 2 +π US 3 )/4 = (π US = (π EZ +π EZ 1 +π EZ 2 +π EZ 3)/4 = π + s RWF/USD z Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

27 Local ineres rae risk approach Empirical resuls Supplemen Exogenous Variables (con.) Model equaions p = a 5p US +(1 a 5 )(p EZ π = 4(p p 1) π ar = h 5 π ar 1 +(1 h 5)π ar ss +ε πar r US i US s USD/EUR s USD/EUR ŷ EZ ŷ EZ = j 6 r US 1 +(1 j 6) r US ss +ε rus +s USD/EUR ) = j 3 i 1 US +(1 j 3 )( r ss US +πss US )+ε ius = s USD/EUR ss = s USD/EUR 1 = j 5 ŷ 1 EZ +εŷez = j 4 ŷ 1 EZ +εŷus +ε susd/eur + s USD/EUR /4 M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

28 Real Ideniies Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions r = i E[π4] r = r +ˆr z = 4(z z 1 ) z = s RWF/USD p +p z = z +ẑ y = 4(y y 1 ) y = ȳ +ŷ y year = (y +y 1 +y 2 +y 3 )/4 4y = ( y + y 1 + y 2 + y 3 )/4 Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

29 Nominal Ideniies Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions π 4 = (π +π 1 +π 2 +π 3 )/4 π 4f = (π f +π f 1 +π f 2 +π f 3)/4 π 4xf = (π xf +π 1 xf +π 2 xf +π 3)/4 xf π = 4(p p 1 ) π f = 4(pf pf 1 ) π xf = 4(p xf p xf 1) Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

30 Local ineres rae risk approach Empirical resuls Supplemen Compounded Ineres Raes Model equaions i 4 = (i +i 1 +i 2 +i 3 )/4 i 8 = (i 4 +i 4 4)/2 i 12 = (2i 8 +i4 8 )/3 i 16 = (3i 12 +i 12 4 )/4 i 4 US i 8 US i 12 US i 16 US = (i US = (i 4 US = (2i 8 US = (3i 12 US +i US 1 +i US 2 +i US 3 )/4 +i 4 US 4 )/2 +i 4 US 8 )/3 +i 4 US 12 )/4 Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes

31 Excess Reurn Brief Overview Local ineres rae risk approach Empirical resuls Supplemen Model equaions er 4 = srwf/usd 4 er 8 = (srwf/usd 8 s RWF/USD +i 4 1 i4 US 1 s RWF/USD )/2+i 1 8 i8 US 1 er 12 = (s RWF/USD 12 s RWF/USD )/3+i 1 12 i12 US 1 er 16 = (s RWF/USD 16 s RWF/USD )/4+i 1 16 i 1 16 US Back o presenaion M. Cincibuch, A. Remo YC Consrucion On Underdeveloped Financial Markes