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Page 1: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

"

* ** **

2005.11 2005

_________________________

* , . ** , il.gov.boi.www://http

, " 780 91007 Research Department, Bank of Israel, POB 780, 91007 Jerusalem, Israel

Page 2: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

1

" -12

1992 2002 . ,

-, .

,

; 2000 2002 ,

2000 ,

2002 .

. ,

", " ,

.

Page 3: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

2

1 .

" -12 1992 2002 ,

, .

, " ,

.

, "

.

" " ,

.

)expectations theory(,

, ,

' .1

., , ") "("pure" expectations theory ,

term premia) ( ) Lutz, 1940( ,

,Hicks)1939(.2

. ,

)Cook and Hahn ,1990( .

., ,

-Spot

) Fama ,1984; (3, , , ,

.", ,

) Fama ,1984; Mankiw and Summers ,1984; Mankiw and Miron ,1986,Campbell and Shiller ;

1991 ( . , ) , , , ( ,

) Mankiw, 1986; Hardouvelis ,1994; Bekaert, Hodrick and ,Marshall 1995(.4

1 . -12

6 , . 2 . , ]liquidity preference theory [ ; ,

. 3 rational expectations model of term structure (RETS) ,

-Spot . 4 Anderson et al. )1996 ( Cook and Hahn ) 1990 .(

Page 4: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

3

.

", , 1915 1979,

) ,Mankiw and Miron 1986( .

, .

. ,

. , Friedman) 1979(

-Froot) 1989(

.

,

. " "

.

. ,

- ) (/ - .

, .

. Kessel )1965(, , ,

, , )

( ) (.

Fama and French) 1989 ( . -Preferred Habitat Theory) Modigliani

and Sutch ,1966 ( .5

,

. - ARCH-M, Engle, Lilien and Robins) 1987( ,

; -Single Factor Estimation ,

6) ,Tzavalis and Wickens 1997; Gordon ,2003 ; "

) "Lower Bound Estimation (

) Excess Forward Return(7 )Startzs ,1982( .

5 .

. 6 , McCulloch) 1987 .( 7 - Spot .

Page 5: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

4

. ,

.

,

, , .

, Iyer) 1997(, " ;

Gravelle and Morley) 2004(,

, Gordon) 2003(,

-,

.

, " .

.

ARIMA Fama) 1984( .

Fama .

.

- , , :

Markov Switching Regime,

- / , -

. ,

- . ,

. " ", )

,Bekaert ,Hodrick ,Marshall 1995( . -

.

" -12

, , ,

. 2000 2002 , ,

2000 , 2002)

.(

, , -12

, " .

Page 6: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

5

:

" . .

ARIMA Fama.

, .

-

. .

- .

2. ,

, '

. )f( it,t

" )R( it :

)f1)........(f1)(f1)(r1()R1()1( it,t3t,t2t,t1t,ti

it,t ,

t it+

) t+i.(

)1 ( :

1)R1(

)R1(f)2( 1i

1it,t

iit,t

it,t .

t+i)f( it,t -Spot

])( itt rE[ , )i ( )

/( , :

iittit,t )r(Ef)3( .

,8 it,tu -Spot " " :

.),0(~)()4( 2,, uittittittit uurEr

8 -Rational Expectations Model of Term Structure . Elkayam and Ilek )2004 (

.

Page 7: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

6

3.

3.1

, ) .(

" ") EFR -

Excess Forward Return( , )f( it,t -Spot :

itit,tit,t rfEFR)5( .

, ,

) 4 ( . )3(, )4 (-)5(

:

ittiitt uEFR ,,)'5( .

)( i i .

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1 . )1 ( , )2 (-)3 (

, )4 (

EFR .

1 � ) FRE.(

: 2003:12-1993:01

ADFStd. DevMeanEFRt+i

3.528- 0.771 0.661- i=2

6.092- 0.999 0.536- i=3

4.440- 1.222 0.453- i=4

4.097- 1.561 0.259- i=5

3.944- 1.851 0.405- i=6

3.836- 2.049 0.367- i=7

4.353- 2.249 0.208- i=8

3.876- 2.365 0.329- i=9

4.450- 2.503 0.532- i=10

4.826- 2.633 0.533- i=11

4.069- 2.651 0.117- i=12 * )1 ( " .

** ) Schwartz Information

criteria .( 2.89-) 5% (-3.48-) 1% .(

Page 8: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

7

: " , -

1993.01 2003.12.9 ) , 9 ( 1992,

10,

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1 � .

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93 94 95 96 97 98 99 00 01 02 03

EFR12

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EFR9

9 -12 ,

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Page 9: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

8

, , . ,

EFR , ,

, -EFR .

)'5 ( ")

( . 1 ,

) (11,

.

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i

jjitjittittitt NeeeuucEFR

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2 ) Maximum Likelihood(.

2 - 1993:1 2003:12

0c

)2( EFR

)1( 0.420-

)0.140( i=30.153-

)0.348( i=60.080-

)0.535( i=90.503

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) (

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6 -9 .( ,

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3.2 Fama

Fama) 1984 ( ) (

. Fama

11 : t . ) ( , t -11 t , .

) Gordon, M. (2003) ,Gravelle, T., Morley, J(2005).(

Page 10: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

9

)rr( tit , -Spot t t+i,

)3( :

.)rr()r(Ef)rr()6( titiittit,ttit

:

,itttittitit urfrr ,, )()()7(

ittu , .) 4 (.

i . , )7(

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.itttitttit urfrr ,, )()()8(

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5.0 .( )6 (

.

3 . ,

) (-1 . , ,

Page 11: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

10

3- amaF

itttitttit urfrr ,, )(

)1(

)2(

)3(

1

)4(

5.0

)5(

2R

)6(

i = 20.268 )0.075(

0.442 )0.071(

0.000 0.414 0.23

i = 30.452 )0.168(

0.864 )0.143(

0.343 0.012 0.26

i = 40.628 )0.241(

1.303 )0.184(

0.102 0.000 0.38

i = 50.317 )0.269(

1.138 )0.174(

0.430 0.004 0.28

i = 60.410 )0.389(

1.010 )0.230(

0.973 0.029 0.22

i = 70.309 )0.443(

0.903 )0.216(

0.654 0.064 0.21

i = 80.178 )0.469(

0.936 )0.219(

0.772 0.049 0.16

i = 90.256 )0.532(

0.883 )0.243(

0.632 0.116 0.15

i = 100.341 )0.661(

0.782 )0.278(

0.434 0.313 0.13

i = 110.233 )0.748(

0.669 )0.335(

0.325 0.615 0.11

i = 120.029- )0.635(

0.722 )0.261(

0.289 0.397 0.13

* Newey-West .

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Page 12: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

11

4 .

) kalman filter(;

,

.

-

:

ittititt uEFR ,,,)9( .

ti,1t10i,t ,

,),0(~, 21

1, eitit

i

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i,t t i .

, t t .

)( , ittu i-1.

) Fama( ,

" -12 . 4 2

. )

( .

4 � ,

, 1993:1 2003:12

Mean Squared Error1 0

1.187 0.945

)0.017(

0.007

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* .

2 - "

-12

-8

-4

0

4

8

93 94 95 96 97 98 99 00 01 02 03

1

01

Page 13: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

12

)Ex-ante(. , .

,12 ,

-Spot , ,

)Gravelle and Morley ,2004 ,Gordon; 2003 .( ,

" ") "Peso Problem(", -

. 13

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.

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., ,

) 1994 1996(,14 -

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1998) 1.5 ( 2001) 2 ( . ,

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12 : -preferred habitat theory , ,

. 13 " " - ,

-1976 .14 1994 . 15 single factor estimation , , ,

: , - . , , ,

, , ) . ,Tzavalis and Wickens1997 -,Gordon 2003( .

Page 14: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

13

,

. Engle et al) 1987 (-

. .

) - ( .

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, . ,

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2002 , ,

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.

- Markov-Switching Regime, :

.q]1SPr[,p]0SPr[,1,0S,)S1(

),0(~e,eeu,uEFR)10(

tttt10tS

2tS

1i

1jitjitjit,tit,ttSit,t

.0h,1Siff)hS1(

,0Siff

tt

202

1

t20

2tS

Page 15: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

14

00.10.20.30.40.50.60.70.80.9

1

-10-8-6-4-20246810

( ) 12-

10 - ) (

)S=0( , -0 - ) (

(S=1). , ,

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,

") (" , .

0 ,1 , - 21 , -h , 5

3:

5 � Markov-Switching Regime

0 1 21 h

0.134-

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0.123

)0.178(

3.908

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0.881-

)0.052(

* .

3 �

, -

. .

) - 3 .(

- . -

.

Page 16: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

15

.

, : ,- ,

, , ; .

5.2

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),,0(N~,),0(N~e,eeu

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t

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tS - )S=1 , .(

. ,

ARCH-M Engle, Lilien and Robins (1987),

Smith) 2002 .( , ,

)ittu , ( )MA(.

Page 17: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

16

, 6 4 , )

(, - -0.9 ,

. ) ( 0.7 ,

- .

6 - ,

1993:1 2003:12 ,

**1 s 1 0

0.909 )0.000(

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) ( S=1

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4 � " -12 ) .(

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2002 , , 1998

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Page 18: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

17

6 .

) ,

, ( ,

-Log-Likelihood , Wald .

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TSSRlog()2log(1(

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7 - " -12 ,1992:1 2002:12

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249.45 323.16 553.81 Sum Squared Residuals

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Page 19: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

18

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Page 20: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

19

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Page 21: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

20

8 .

" -12 1992

2002 , . ,

,

. -

.

, 0.7 . ,

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2000 2002

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Page 22: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

21

,. ,' ,) .1996 (." : " "

". 96.11 , , .

Andersen, N., et al. (1996). Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd,

West Sussex, England.

Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term Structure Anomalies", NBER Working Paper No. W6147

Campbell, J.Y, and Robert J. Shiller (1991)."Yield Spreads and Interest Rate Movements: A Bird's Eye View" ,Review of Economic Studies 58, 495-514.

Chib, S., and E. Greenberg (1996). "Markov Chain Monte-Carlo Simulation Methods in Econometrics" ,Econometric Theory 12, 409-431.

Cook, T. and T. Hahn (1990). "Interest Rate Expectations and the Slope of the Money Market Yield Curve" ,Federal Reserve Bank of Richmond Economic Review 76, 3-26.

Engle, R., D. Lilien and R.Robins (1987). "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model" ,Econometrica 55(2), 391-407.

Fama, E.F.(1984)."The Information in the Term Structure." Journal of Financial Economics 13, 509-528.

Fama, E.F. and K.R. French (1989). "Business Conditions and Expected Returns on Stocks and Bonds" ,Journal of Financial Economics 25, 23-49.

Friedman, B.M. (1979)."Substitution and Expectation Effects on Long-Term Borrowing Behavior and Long-Term Interest Rates" ,Journal of Money, Credit, and Banking II, No. 2, (May) ,131-150.

Froot K.A.(1989). “New Hope for the Expectations Hypothesis of the Term Structure of Interest Rates”, Journal of Finance, XLIV, No. 2, 283-305

Gordon, M.(2003). "Estimates of Time-Varying Term Premia for New Zealand and Australia", Reserve Bank of New Zealand, Discussion Paper No. 2003/06.

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Hardouvelis, G.A. (1994). "The term structure spread and future changes in long and short rates in the G-7 countries –Is there a puzzle ? "Journal of Monetary Economics 33, 255-283.

Hicks, J. (1939). Value and Capital ,London: Oxford University Press.

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Kessel, R. (1965). “The cyclical behavior of the term structure of interest rates”, occasional paper no.91, National Bureau of Economic Research, Cambridge, Mass.

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Kim, C.J. and C.R. Nelson (1999). State-Space Models with Regime Switching, Cambridge, Mass. and London: MIT Press.

Liviatan, N. and R. Melnick (1998). "Inflation and Disinflation by Steps in Israel." ResearchDepartment Discussion Paper No. 98.01, Bank of Israel.

Lutz, F.A. (1940). "The Structure of Interest Rates" ,Quarterly Journal of Economics 55, 36-63.

Mankiw, N.G.(1986)."The Term Structure of interest rates revisited", Brookings Papers on Economic Activity,1 ,61-96.

Mankiw, N.G. and J.A. Miron (1986). "The Changing Behavior of the Term Structure of Interest Rates" ,Quarterly journal of Economics, 101, 211-228.

Mankiw, N.G. and L.H. Summers (1984). "Do Long-Term Interest Rates Overreact to Short-Term Interest Rates ?", Brookings Papers on Economic Activity,1,61-96

McCulloch, J.(1987). "The Monotonicity of the Term Premium." Journal of Financial Economics 18, 185-192.

Modiligiani, F. and R. Sutch (1966)."Innovations in Interest rate policy", American Economic Review, 56, 178-97.

Newey ,Whitney K. and Kenneth .D. West, (1987). "Simple, Positive Semi-definite, Heterosckedasticity and Autocorrelation Consistent Covariance Matrix", Econometrica 55, 703-708

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Startz, R. (1982). "Do Forecast Error or Term Premia Really Make the Difference between Long and Short Rates ?" Journal of Financial Economics 10, 323-329.

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Page 24: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

23

1-': -

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Page 25: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

24

1-' . -ARIMA

lag

1 0.704 ** 0.466 **2 0.656 ** 0.238 **3 0.537 ** 0.145 **4 0.592 ** 0.143 **5 0.548 ** 0.182 **6 0.424 ** 0.107 *7 0.323 ** 0.0228 0.234 ** 0.0079 0.255 0.000

10 0.096 0.01011 0.074 0.000

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Page 26: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

25

),....,,(diag)var( 211tS

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Page 27: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

26

1 .2 )15 ( )16 ( , ,

. 1 .2 )15 (

pvalue -121 .

) 16(

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* - Newey-West .

1�' :

.1 � � .

-0.8

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0.0

0.4

0.8

1.2

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0.0

0.5

1.0

1.5

2.0

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93 94 95 96 97 98 99 00 01 02 03

Residual Actual Fitted

Page 28: Estimating and Interpreting the Yield Curve, John Wiley & Sons Ltd, West Sussex, England. Bekaert, G., R.J. Hodrick and D.A. Marshall (1995). "'Peso Problem' Explanations for Term

27

.2 � 12

-.1

.0

.1

.2

.3

.4

.5

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PAAR

.3 � -12

0.0

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3.0

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standard deviation of 12 month forward rate

.4 � )k( 12,t

-4

-3

-2

-1

0

1

2

3

93 94 95 96 97 98 99 00 01 02 03