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1 韓國開發硏究제 31 권제 2 호 ( 통권제 105 호 ) 이자율기간구조를이용한정책금리변경의효과분석 송준혁 ( 한국개발연구원부연구위원 ) Analyzing the Effect of Changes in the Benchmark Policy Interest Rate Using a Term Structure Model Joonhyuk Song (Associate Research Fellow, Korea Development Institute) * 송준혁 : ( ) jhsong@kdi.re.kr, (address) Korea Development Institute, Hoegiro 49, Dongdaemun-gu, Seoul, Korea Key Word: (Term Structure of Interest Rate), (No Arbitrage), (Monetary Policy) JEL code: E43, E52, E58 Received: Referee Process Started: Referee Reports Completed:

2 ABSTRACT This paper estimates the term structure of interest rates with the setup of 3-factor no arbitrage model and investigates the trend of term premia and the effectiveness of changes in policy interest rates. The term premia are found to be high in a three-year medium term objective, which can be interpreted as reflecting the recognition of investors who expect a higher uncertainty in real activities for the coming three years than for a longer term. Then, in order to look into the effect of policy interest rates after the recent change of benchmark interest rate, this paper analyzes the effects of the changes in short-term interest rates of the financial market on the yield curve of the bond market at time of change. Empirical results show that the discrepancy between call rate, short-term rate in money market, and instantaneous short rate, short-term rate in the bond market, is found to be significantly widened, comparing to the periods before the change in benchmark interest rate. It is not easy to conclude clearly for now whether such a widening gap is caused by the lack of experiences with managing new benchmark interest rate or is just an exceptional case due to the recent turmoil in the global financial market. However, monetary policy needs to be operated in a manner that could reduce the gap to enhance its effectiveness.

3 이자율기간구조를이용한정책금리변경의효과분석 17 Ⅰ. 서론.,..... (term structure of interest rates) (,, ),.,..,,.. Vasicek(1977)

4 18 韓國開發硏究 / Ⅱ., Cox, Ingersoll, and Ross(1985) (general equilibrium). Duffie and Kan(1996), Dai and Singleton(2000), Duarte(2004), Kim and Orphanides(2006),., Bekaert, Cho, and Moreno(2005), Ang, Piazzesi, and Wei (2006), Rudebusch and Wu(2008), Doh (2009) ,.. 7.,,.. (1991) McCulloch 3 1, (2002) Heath-Jarrow-Morton., (2000) CIR, (2001) -.. (2005) (2007). (2005) Nelson-

5 이자율기간구조를이용한정책금리변경의효과분석 19 Siegel 1, 3. (2007) 2,.,. (2007) 3, (signalling).. 3,..,. Ⅱ. 모형설정. Harrison and Kreps (1979), (riskneutral probability measure) (state price) (equivalent martingale measure)., (complete market). Duffie(2002), Dai and Singleton(2002), Duarte(2004) 3 (3-factor arbitrage-free term structure model), (affine model).

6 20 韓國開發硏究 / Ⅱ. 1 (zero-coupon bond),.. : (1),.. (2)., (stochastic discount factor). 1) (3) (3). log ( )., (4) (4). 2) (5). (expectations hypothesis) 1). (marginal rate of substitution) (level of marginal utility). Cochrane(2001). 2) Cochrane(2001).

7 이자율기간구조를이용한정책금리변경의효과분석 21. (risk premium hypothesis). Dai and Singleton(2000) (level), (slope) (curvature)....,,. 3). 4),. (latent factors)., (risk-neutral probability measure) Ornstein- Uhlenbeck., (5), (mean reversion), 3) Fama and Bliss(1987), Mishkin(1990), Fama(1990), Campbell and Shiller(1991), Cochrane and Piazzesi(2005), Hamilton and Kim(2002). 4) Ang and Piazzesi(2003), Diebold, Rudebusch, and Aruoba(2006), Rudebusch and Wu (2008), Bekaert, Cho, and Moreno(2005).

8 22 韓國開發硏究 / Ⅱ, (volatility).. (short rate). (6),.... (7) (7) 3, (market price of risk). Duffie and Kan(1996), (physical probability measure) ( ). (8),.. (9) 또는 또는,, (PDE). (10),.

9 이자율기간구조를이용한정책금리변경의효과분석 23, ( ) ( ). exp log (11). Dai and Singleton(2000). 5) (lower-triangular matrix), (diagonal matrix), (term premium).,. Ⅲ. 자료및추정 (12) (conditional expectations) 분석자료 KIS 3, 6, 9, 1, 2, 3, 5 1, ) Dai and Singleton(2000).

24 韓國開發硏究 / 2009. Ⅱ [Figure 1] Trends of Interest Rates(2000. 8. 2~2009. 8. 19) Source: KIS Ratings.

10 24 韓國開發硏究 / Ⅱ [Figure 1] Trends of Interest Rates( ~ ) Source: KIS Ratings.. 6),, 1.,. [Figure 1] , (curvature) 6) (2001) 1.

11 이자율기간구조를이용한정책금리변경의효과분석 25 <Table 1> Summary Statistics for Interest Rates Mean Std. Dev Skewness Kurtosis Autocorrelation Jarque-Bera Normality Test Call Rate (0.1004) (0.1419) (0.1725) (0.5372) (0.0089) y 3M (0.1206) (0.2065) (0.2515) (0.5268) (0.0128) y 6M (0.1209) (0.2047) (0.2668) (0.4992) (0.0147) y 9M (0.1173) (0.1834) (0.2601) (0.4375) (0.0160) y 1Y (0.1163) (0.1718) (0.2417) (0.3928) (0.0166) y 2Y (0.1126) (0.1530) (0.2053) (0.4251) (0.0181) y 3Y (0.1154) (0.1632) (0.2143) (0.4740) (0.0180) y 5Y (0.1190) (0.1706) (0.2150) (0.4950) (0.0174) Note: Standard errors of summary statistics are estimated using GMM and presented in parentheses , 1 Vasicek CIR. <Table 1> (normality) Jarque-Bera 3.

12 26 韓國開發硏究 / Ⅱ [Figure 2] Sample Average Term Structure ,.,. [Figure 2] 1. <Table 1>. 7), 70%,. (principal component analysis). 7) (2001), (2007) 3, 2, 5.,

13 이자율기간구조를이용한정책금리변경의효과분석 27 [Figure 2] Cumulative Explanatory Power of Principal Components, (level), (slope), (curvature).. 8) 52 moving window (eigenvalue),. [Figure 2]. 1 60% 1. 8) Piazzesi(2003) 3 (level), (slope), (curvature), 2 (level) (slope), 1 (level)., Litterman and Scheinkman(1991) (curvature). Cochrane and Piazzesi(2005).

14 28 韓國開發硏究 / Ⅱ,. 2 98% , 모형추정과결과 Duffie and Stanton(2004), Kim and Orphanides(2006) - (state space model). - (Kalman filter).. (measurement equation) M 3, 3 3..,. (state equation). 9). -. <Table 2>. 9) James and Webber(2000), Kim and Orphanides(2006).

15 이자율기간구조를이용한정책금리변경의효과분석 29 <Table 2> Parameter Estimates Param. Est Std. Err Param. Est Std. Err e e e e e e e e e e e e e e-5 Log-likelihood , 4.02% (2007) %. (mean reversion).,. <Table 3> RMSE(Root Mean Squared Error) MAE(Mean Absolute Error). RMSE %, %, 1.645%

16 30 韓國開發硏究 / Ⅱ <Table 3> Root Mean Squared Error 3M 6M 9M 1Y 2Y 3Y 5Y All RMSE (%) MAE (%) Note: RMSE (%) =, MAE (%) =., MAE %, % 1.047%. RMSE MAE. [Figure 3] , ) , bp bp. [Figure 2] 1 ( ), 2008, % Lehman Brothers Merrill Lynch, 10) %p

17 이자율기간구조를이용한정책금리변경의효과분석 31 [Figure 3] Short Rate, Call Rate and Term Premium [Figure 4] Term Premium for All Maturities

18 32 韓國開發硏究 / Ⅱ. [Figure 4].,, 3. 1~3., 3.. Ⅳ. 정책금리변경의효과분석 % 25bp % 6 325bp % , , [Figure 5] , 1%p , %p

19 이자율기간구조를이용한정책금리변경의효과분석 33 [Figure 5] Yields and Term Premia, , ,. 2 12, , ,. 7

20 34 韓國開發硏究 / Ⅱ % 5.25%.,,.. [Figure 6] 0 10 (cumulative increments) , 25bp bp 3 17bp, 14bp., 12bp ). [Figure 6] <Table 4> 11bp. 11) % 7 5.9%.

21 이자율기간구조를이용한정책금리변경의효과분석 35 [Figure 6] Cumulative Increments of Call and Short Rates

22 36 韓國開發硏究 / Ⅱ <Table 4> Changes in Call Rates (unit: %) Date t Difference -3 (A) -2 (B) -1 (C) 0 (D) D-C C-B B-A Note: t = -k denotes k days prior to the decrease in policy rate., (autonomously).. 12) (2007),,, ).,

23 이자율기간구조를이용한정책금리변경의효과분석 ,. [Figure 7] 3 [Figure 6].... (market segmentation hypothesis).,,...,,.,

24 38 韓國開發硏究 / Ⅱ [Figure 7] Cumulative Increments of 3-Year Yields: Actual vs. Estimated

25 이자율기간구조를이용한정책금리변경의효과분석 RP. 13) RP.. [Figure 8] 2001~07, [Figure 9]. 20bp,., RP,. V. 결론..,.. 13), ( ).

26 40 韓國開發硏究 / Ⅱ [Figure 8] Cumulative Increments When Target Call is Decreased: 2001~2007

27 이자율기간구조를이용한정책금리변경의효과분석 41 [Figure 9] Cumulative Increments When Target Call is Increased: 2001~2007

28 42 韓國開發硏究 / Ⅱ. 2008, RP 7,. RP.,. (regime switching), ,..

29 이자율기간구조를이용한정책금리변경의효과분석 43 참고문헌, :,, 13 2, 2000, pp.1~24., -,, 9 2, 2001, pp.265~286.,,, 12 2, 2007, pp.32~93.,,, 12 4, 2007, pp.121~166., :,, 2000, pp.1~47., Heath-Jarrow-Morton,, 8 2, 2002, pp.56~80.,,, 9, 1996, pp.411~424.,,, 11 2, 2005, pp.35~82.,,, 13, 1991, pp.327~355. Ang, Andrew and Monika Piazzesi, A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables, Journal of Monetary Economics 50, 2003, pp.745~787. Ang, Andrew, Monika Piazzesi and Min Wei, What Does the Yield Curve Tell Us about GDP Growth? Journal of Econometrics 131, 2006, pp.359~403. Bekaert, Geert, Seonghoon Cho, and Antonio Moreno, New-Keynesian Macroeconomics and the Term Structure, NBER WP No.11340, Campbell, John Y. and Robert J. Shiller, Yield Spreads and Interest Rate Movements: A Bird's Eye View, Review of Economic Studies 58(3), pp.195~228. Cochrane, John H., Asset Pricing, Princeton University Press, Cochrane, John H. and Monika Piazzesi, Bond Risk Premia, American Economic Review 95(1), 2005, pp.138~160. Cox, John, Jonathan Ingersoll, and Stephen Ross, A Theory of Term Structure of Interest Rates, Econometrica 53, 1985, pp.385~408. Dai, Qiang and Kenneth J. Singleton, Specification Analysis of Affine Term Structure Models, Journal of Finance 55, 2000, pp.531~552.

30 44 韓國開發硏究 / Ⅱ Dai, Qiang and Kenneth J. Singleton, Expectation Puzzles, Time-varying Risk Premia, and Affine Models of the Term Structure, Journal of Financial Economics 63, 2002, pp.415~441. Diebold, Francis X. and C. Li, Forecasting the Term Structure of Government Bond Yields, Penn Institute for Economic Research Working Paper No.02-26, Diebold, Francis X., Glenn D. Rudebusch, and Boragan S. Aruoba, The Macroeconomy and the Yield Curve, Journal of Econometrics 131, 2006, pp.309~339. Doh, Taeyoung, Yield Curve in an Estimated Nonlinear Macro Model, Federal Reserve Bank of Kansas City Working Paper, Duarte, Jefferson, Evaluating an Alternative Risk Preference in Affine Term Structure Models, Review of Financial Studies 17(2), 2004, pp.379~404. Duffie, Darrell and Rui Kan, A Yield-Factor Model of Interest Rates, Mathematical Finance 6(4), 1996, pp.379~406. Duffie, Darrell and Kenneth J. Singleton, An Econometric Model of the Term Structure of Interest Rate Swap Yields, Journal of Finance 52, 1997, pp.1287~1321. Estrella, Arturo and Frederic S. Mishkin, Predicting U.S. Recessions: Financial Variables as Leading Indicators, Review of Economics and Statistics 80, 1998, pp.45~61 Fama, Eugene F., Stock Returns, Expected Returns, and Real Activity, Journal of Finance 45(4), 1990, pp.1089~1108. Fama, Eugene F. and Robert R. Bliss, The Information in Long-Maturity Forward Rates, American Economic Review 77(4), 1987, pp.680~692. Hamilton, James and Dong Heon Kim, A Re-Examination of the Predictability of the Yield Spread for Real Economic Activity, Journal of Mone, Credit, and Banking 34, 2002, pp.340~360. Harrison, Michael J. and David Kreps, Martingales and Arbitrage in Multi-Period Securities Markets, Journal of Economic Theory 20, 1979, pp.381~408. Huang, Shirley J. and Jun Yu, On Stiffness in Affine Asset Pricing Models, Journal of Computational Finance 10(3), 2007, pp.99~123. Ilmanen, Antti, Overview of Forward Rate Analysis, Salomon Brothers, James, Jessica and Nick Webber, Interest Rate Modelling, John Wiley and Sons Ltd., Kim, Don H. and Athanasios Orphanides, Term Structure Estimation with Survey Data on Interest Rate Forecasts, Finance and Economic Discussion Paper, Federal Reserve Board, Litterman, Robert and Jose Scheinkman, Common Factors Affecting Bond Returns, Journal of Fixed Income 1, 1991, pp.54~61. Mishkin, Frederic S., The Information of the Longer Maturity Term Structure about Future Inflation, Quarterly Journal of Economics 55, 1990, pp.815~828. Piazzesi, Monika, Affine Term Structure Models, unpublished manuscript, Phillips, Peter C. B. and Jun Yu, Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance, Handbook of Financial Time-series, 2009, pp.497~530.

31 이자율기간구조를이용한정책금리변경의효과분석 45 Rudebusch, Glenn D. and Tau Wu, A Macro-Finance Model of the Term Structure, Monetary Policy, and the Economy, Economic Journal 118(530), 2008, pp.906~926. Vasicek, O., An Equilibrium Characterization of the Term Structure, Journal of Financial Economics 5, 1977, pp.177~188.

歯목차.PDF

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