Asia-Pacific Journal of Financial Studies (2009) v38 n1 pp109-132

Foreign Bond Investment and the Yield Curve* Sangwon Suh∗∗ Hanyang University, Ansan, Korea This is one of the seven accepted papers among 76 papers that were submitted to the solicitation by Asia-Pacific Journal of Financial Studies in the special “Call-for-Papers” event in 2008.

Abstract Market participants have argued that the yield curve in the Korean bond market has been increasingly flattened since 2007 caused partly by foreign investors’ rapidly growing investment in Korean bond market, motivated to take advantage of market imperfections seeking riskless profit making opportunities. To analyze how much foreign bond investments have affected the bond yields in Korea, in this paper I utilize a stylized affine term structure model that has an observable factor related with foreign bond investments as well as latent factors. I find supportive evidence for the argument by market participants that investment by foreigners has been an important factor behind the flattening of the yield curve since 2007. Taking out the effects of foreign bond investment on the yields, I observe much a weakened yield flattening phenomenon.

Keywords: Yield Curve; Affine Term Structure Model; Arbitrage Opportunity; Foreign Bond Investment; Korean Bond Market

*

I am grateful to the Editor-in-Chief and one anonymous referee for their helpful comments.

** Corresponding Author. Address: Department of Economics, College of Economics and Business Administration, Hanyang University, Ansan, Korea; E-mail: [email protected]; Tel: +82-31-400-5602; Fax: +82-31-436-8180.

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1. Introduction Even after the Korean bond market was opened to foreign investors in December 1997, foreigners’ bond investment remained small until 2006; their investment has increased dramatically since 2007. The phenomenon of rapidly increasing foreigners’ bond investment has several implications. Foreign investors have exerted a stronger influence on bond yields. If they make their investment decisions based upon factors other than economic fundamentals, arbitrage opportunities arising from market imperfections, for example (which turns out to be an important factor, as shown later), then market bond yields may also be affected by such non-fundamental factors. This means that the monetary transmission mechanism from the short-term policy interest rate to market interest rates may be weakened. It is also worthwhile to note that the trade channel and the stock market channel have been important in linking interest rates and the exchange rate in Korea; currently, the bond market channel has also become another important consideration. This fact suggests that the joint dynamics of interest rates and the exchange rate may now become more complicated. Figure 1 plots foreign investors’ Korean bond investments and term spreads, defined as the long maturity yields minus the short rate (the overnight call rate). As foreigners’ bond investment has increased since 2007, the term spreads of various maturities have fallen significantly, and the gaps between the spreads at different maturities have also narrowed, implying that the Korean yield curve has flattened. Therefore, market participants ascribe the increasing foreign bond investment to be one of the reasons for the yield curve flattening since 2007.1) In this paper, I investigate how much foreigners’ bond investment actually affects bond yields. Up to date, the influence of foreign investment on bond yields has been discussed among bond market participants, but this topic has not yet been rigorously investigated in academia, in which respect this paper has a contribution to make. I use a stylized affine term structure model, so that no-arbitrage conditions can be imposed among bonds of various maturities.2) In the model used in this paper, bond prices are exponential affine functions of underlying state variables: the observable variables related with for1) Because foreigners’ bond investment was small until 2006, it may not be attributable to several yield curve flattening phenomena occurring before 2007. 2) Refer, for example, to Ang and Piazzesi (2003) for the relative advantages of following structural factor model approaches over flexible but ad-hoc approaches such as VAR.

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eigners’ bond investment as well as latent variables. Figure 1. Foreigners’ bond investment and interest rate term spreads: 1, 3, 5 year(s) versus 1 day 6.0

12.0 Foreigners' bond investment (right, tn KRW) TB(1Y) - call(1D)

5.0

10.0

TB(3Y) - call(1D) TB(5Y) - call(1D)

4.0

8.0

3.0

6.0

2.0

4.0

1.0

2.0

0.0

0.0

-1.0 2001/01

-2.0 2002/01

2003/01

2004/01

2005/01

2006/01

2007/01

2008/01

Many studies have been conducted on yield curve models and on the subclass of affine term structure models. Among them, the following works are most relevant to this paper: Ang and Piazzesi (2003), Ang, Dong, and Piazzesi (2007), Bikbov and Chernov (2006), Dewacher and Lyrio (2006), Dewacher, Lyrio, and Maes (2006), Duffee (2006, 2007), Hördahl, Tristani, and Vestin (2006, 2007), and Rudebusch and Wu (2004, 2007) all of which include macro factors as well as latent factors in their “macro-finance” affine term structure models. Kim (2007), meanwhile, discusses various challenges in the specification and implementation of “macro-finance” models. Rudebusch, Swanson, and Wu (2006) analyze the “conundrum” in U.S. long term bond yields by regressing the unusually large residuals during the “conundrum” periods on several potential explanatory variables. I find supportive evidence for the argument by market participants that investment by foreigners has been an important factor behind the flattening of the yield curve since 2007. Without the effects of foreign bond investment on the yields, the

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yield flattening phenomenon is considerably weakened. This paper is organized as follows: Section 2 explains developments in terms of foreign investment in the Korean bond market, and foreigners’ trading strategies in pursuing riskless profits. Section 3 describes the yield curve model belonging to the affine term structure class. I present the estimation results in Section 4 and conclusion in Section 5.

2. Foreigners’ investment in the Korean bond market The Korean bond market had beem gradually opened to foreign investors since July 1994 until December 1997 when all regulations against foreign entries were completely lifted. Yet, foreign investment in the bond market remained small until 2006. Its share in total listed bonds accounts for merely 0.6 percent at the end of 2006. However, foreign investment has increased dramatically since 2007, whose share rising to 4.5 percent by the end of 2007. Many market participants attribute the rapidly growing foreign bond investment to appealing arbitrage opportunities in the market during the one year period. Indeed, the Monetary Policy Report by the Bank of Korea (March 2008, p. 30) states that the great expansion of foreigners’ bond investments is mainly attributable to arbitrage transactions. When arbitrage opportunities exist, traders may employ appropriately-designed trading schemes to reap relatively riskless profits. When these opportunities are great, the trading volumes and the outstanding positions associated with arbitrage transactions also become large. Several types of transactions have been utilized for obtaining arbitrage opportunities in Korean financial markets. For instance, the FX swap rate, defined as the percentage deviation of the forward from the spot exchange rate, should be equal to the interest rate differential (i.e., the domestic minus the foreign interest rate) to eliminate arbitrage opportunities. In reality, however, discrepancies exist between the FX swap rate and the interest rate differential, creating arbitrage opportunities in the following steps: when the interest rate differential becomes much greater than the FX swap rate, which it has been since 2007, traders can earn profits with minimal risk by borrowing in a foreign currency (say, the US dollar, USD); converting it into Korean won (KRW) via FX swap transactions; investing the money in Korean bonds (or deposits) at a fixed rate; and settling at the maturity date.

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Other types of transactions seeking profits by exploiting market imperfections have also been made. As shown in Figure 2, an investor may earn profits by borrowing USD at Libor, converting it into KRW by entering a cross currency swap (CRS) contract as a payer promising to pay a fixed KRW interest rate in exchange for receiving Libor, and investing the funds in KRW bonds. If the KRW bond interest rate is greater than the fixed CRS rate, this trading scheme offers profits to the investor. Figure 3 shows another trading strategy which utilizes interest rate swaps (IRSs) and bonds. An investor may borrow KRW at a floating rate, switch it to a fixed rate by using an IRS, invest the KRW into a KRW bond, and receive a fixed rate interest on the bond investment. This trading strategy also allows the investor to make profit as long as the KRW bond interest rate is greater than the fixed IRS rate. An investor may also construct another trading scheme, in which a CRS and an IRS are utilized simultaneously as illustrated in Figure 4. This trading scheme is similar to that depicted in Figure 2, but the investor receives floating interest rate by depositing the KRW raised into a certificate of deposit (CD) and then converts the floating rate into a fixed rate by using an IRS contract. If the IRS fixed rate is greater than the CRS fixed rate, then the investor may realize profits from this trading. Figure 2. Bond trading associated with CRSs International financial market Libor

USD Borrowing Bond purchase

Bond market

USD

Investor Bond interest

KRW Libor

CRS market

KRW fixed rate

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Figure 3. Bond trading associated with IRSs Domestic financial market KRW Borrowing

KRW floating rate

Bond purchase

KRW fixed rate

Bond market

IRS market

Investor KRW floating rate

Bond interest

Figure 4. Investment associated with CRSs and IRSs International financial market Libor

USD Borrowing CD purchase

CD market

USD

Investor CD interest

KRW fixed rate

CD interest

KRW fixed rate

IRS market

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KRW Libor

CRS market

Asia-Pacific Journal of Financial Studies (2009) v38 n1

If the bond maturity is matched with those of other associated contracts, for example FX swap, CRS, or IRS contracts as described above, and the investor keeps the bond and the contracts to maturity, then the investor can earn riskless profits.3) However, if the bond maturity is not matched with those of the associated contracts, then the profits do not become riskless any longer. On the other hand, if the investment portfolio is valued on a mark-to-market basis, then the profits may fluctuate in accordance with market price movements. The investor may be forced to unwind his/her portfolio due to possible trading loss limit constraints. Figure 5 shows foreigners’ bond investment, the interest rate differentials, and arbitrage opportunity proxies defined as the gaps between the interest rate differentials and FX swap rates for the maturities of three months and one year from January 2004 to February 2008. With a positive and large interest rate differential, foreigners may invest in domestic bonds in the form of a carry-trade in which they do not use any other instrument for hedging purposes. The monthly foreign investments seem to be most closely related with the arbitrage opportunity denoted by the gap between the three-month interest rate differential and FX swap rate. Figure 6 illustrates arbitrage opportunity proxies defined as the gaps between the bond yields and the IRS fixed interest rates and CRS fixed interest rates for the maturities of one and three year(s). Figure 7 shows the swap bases defined as the gaps between the IRS fixed interest rates and the CRS fixed interest rates for the same maturities. Among eight arbitrage opportunity proxies, the gap between the three-month interest rate differential and FX swap rate is most closely correlated with the monthly foreign investment. In the following sections, therefore, I investigate how much the proxy of the gap between the three-month interest rate differential and FX swap rate affects bond yields and whether the yield curve flattening since 2007 is actually attributable to the growing foreign bond investment influenced largely by arbitrage opportunities as has been claimed by market observers.4),

5)

3) Some other risks such as counter-party risk may be involved in, and so the profits may not be perfectly riskless. 4) Even though the amounts of foreigners’ bond investments could be directly used in this analysis, instead of arbitrage opportunity proxies, I investigate the relationship between the arbitrage opportunity proxy and the bond yields which, I think, is of more interest to us. In addition, the proxy is more observable than the amount of foreigners’ bond investment. 5) It is an on-going question why such arbitrage opportunities have persisted for such a long time on such a large scale, but it is beyond the scope of this paper.

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Figure 5. Foreigners’ bond investment, interest rate differentials, and arbitrage opportunities (interest rate differentials-FX swap rates) 12.0

6.0 Foreigners' bond investment (right, tn KRW) Interest rate differential (3M)

5.0

10.0

Interest rate differential (1Y) Interest rate differential - FX swap rate (3M) Interest rate differential - FX swap rate (1Y)

4.0

8.0

3.0

6.0

2.0

4.0

1.0

2.0

0.0

0.0

-2.0

-1.0 2004

2005

2006

2007

2008

Figure 6. Foreigners’ bond investment and arbitrage opportunities ((bond yields-CRS fixed rates) and (bond yields-IRS fixed rates)) 6.0

12.0 Foreigners' bond investment (right, tn KRW) KRW bond yield - IRS (3Y)

5.0

10.0

KRW bond yield - IRS (1Y) KRW bond yield - CRS (3Y) KRW bond yield - CRS (1Y)

4.0

8.0

3.0

6.0

2.0

4.0

1.0

2.0

0.0

0.0

-1.0

-2.0 2004

116

2005

2006

2007

2008

Asia-Pacific Journal of Financial Studies (2009) v38 n1

Figure 7. Foreigners’ bond investment and arbitrage opportunities (swap basis) 6.0

12.0 Foreigners' bond investment (right, tn KRW) swap basis (3Y)

5.0

10.0

swap basis (1Y) 4.0

8.0

3.0

6.0

2.0

4.0

1.0

2.0

0.0

0.0

-1.0

-2.0 2004

2005

2006

2007

2008

3. Model In this section, I describe the model employed in this paper, which is a stylized discrete time affine term structure model. The model is similar to that of Ang and Piazzesi (2003), but it is modified for the purposes of the research objectives and estimation efficiency. I assume that K1 observable factors fto follow a VAR(p) process, i.e.: fto = Φ 0o + Φ1o fto−1 + " + Φ op fto− p + Σouto ,

(1)

with uto ~ iid N (0, I ), and that K 2 latent factors ftu follow a VAR(1) process, i.e.: ftu = Φ1u ftu−1 + Σuutu ,

(2)

with utu ~ iid N (0, I ). The observable factor fto in this paper is the arbitrage opportunity proxy, defined as the three-month interest rate differential minus the FX swap

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rate, as explained in the previous section (i.e., K1 = 1). I will name the model with latent factors only as the Yield-Only model and the model with both observable and latent factors as the Arbitrage-Factor model. Defining ( K1 ⋅ p × 1) vector X to = ( fto , fto−1 , " , fto− p +1 ), X tu = ftu , and (K×1) vector X t = ( X tu , X tu ), where K = K1 · p+K2, I can concisely ex-

press Xt as a VAR(1) process, i.e.: (3)

X t = μ + ΦX t −1 + ∑ ε t ,

with ε t = (uto , 0, " , 0, utu ) and ⎛ Φ1o ⎛ Φ 0o ⎞ ⎜ ⎜ ⎟ ⎜ I ⎜ 0 ⎟ ⎜ μ = ⎜ " ⎟, Φ = ⎜ ⎜ ⎟ ⎜ 0 ⎜ 0 ⎟ ⎜ ⎜ ⎟ ⎜ 0 ⎝ 0 ⎠ ⎝

Φ 2o " Φ op 0

"

0

" 0

"

I

0

"

0

0 ⎞ ⎛ ∑0 ⎟ ⎜ 0 ⎟ ⎜ 0 ⎟ ⎜ ∑ = , ⎟ ⎜ ⎜ 0 0 ⎟ ⎟ ⎜ ' u⎟ Φ1 ⎠ ⎝ ∑ou

0 " 0 ∑ou ⎞ ⎟ 0 " 0 0 ⎟ ⎟. " ⎟ 0 " 0 0 ⎟ ⎟ 0 " 0 ∑u ⎠

(4)

Here, I allow for correlation between latent and observable factors, while they are independent of each other in Ang and Piazzesi (2003). I now assume that the riskless short-term interest rate rt set by the central bank is an affine function of the state vector, that is: rt = δ 0 + δ1 ' X t = δ 0 + δ1u ' X tu ,

(5)

where the observable factor X to related with foreign bond investments does not affect the central banks’ monetary policy, which is another difference from Ang and Piazzesi (2003). The reason for introducing this assumption is because there is no evidence yet that central banks take into account foreign bond investors when making their policy interest rate decisions. The pricing kernel mt is defined by 1 mt +1 = exp( − λt ' λt − δ 0 − δ1 ' X t − λt ' ε t +1 ), 2

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(6)

Asia-Pacific Journal of Financial Studies (2009) v38 n1

as in Ang and Piazzesi (2003). The market prices of risk λt are modeled as (7)

λt = λ0 + λ1 X t ,

where λ0 is (K×1), and λ1 is (K×K). The parameters in λ0 and λ1 that correspond to the lagged observable variables are set to zero. The observable factors X to associated with foreign bond investment affect bond yields through the market prices of risk. Another difference with Ang and Piazzesi (2003) lies in the assumption that the submatrix of λ1 corresponding to the latent factors is the identity matrix, i.e.: ⎛ λo ⎞ ⎛ λo ⎜ 0⎟ ⎜ 1 ⎜ 0 ⎟ ⎜ 0 λ0 = ⎜⎜ " ⎟⎟ , λ1 = ⎜ ⎜ ⎜ 0 ⎟ ⎜ 0 ⎜ u⎟ ⎜ ⎜λ ⎟ ⎝ 0 ⎝ 0⎠

0 " 0 0 " 0 " 0 " 0 0 " 0

0⎞ ⎟ 0⎟ ⎟. ⎟ 0⎟ ⎟ I⎠

(8)

Note that this assumption is innocuous and also employed in Duffee (2007). To see this, suppose that there exists an invertible matrix L such that λi1 = λ1 L, where ⎛ λo ⎜ 1 ⎜0 ⎜ i λ1 = ⎜ ⎜0 ⎜ ⎜0 ⎝

0 ⎞ ⎟ 0 ⎟ ⎟ " ⎟. 0 " 0 0 ⎟ ⎟ u 0 " 0 λi1 ⎟⎠ 0 " 0 0 " 0

(9)

By transforming eq. (7) into it , λt = λ0 + λi1 X

(10)

it = μ i +Φ iX i t −1 + ∑ iε , X t

(11)

i t = L−1 X , and eq. (3) into where X t

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Foreign Bond Investment and the Yield Curve

i ≡ L−1 ∑ , we obtain the same model as in Ang and Pii ≡ L−1ΦL , ∑ where μi ≡ L−1μ , Φ

azzesi (2003), without loss of generality. Assuming the trial solution form of the bond price of maturity n at time t ptn as ptn = exp( A n + B n ' X t ) ,

(12)

ptn +1 = Et exp(mt +1 ptn+1 ) ,

(13)

and from the pricing formula

we can obtain the following recursive relations for the coefficients:

A n +1 = A n + B n '( μ − ∑ λ0 ) +

1 B n ' ∑ ∑ ' B n − δ 0 , A1 = δ 0 , 2

B n +1 ' = B n '( Φ − ∑ λ1 ) − δ1 , B1 = −δ1 .

(14) (15)

The bond yields are simply expressed as

ytn = −

log ptn = An + Bn ' X t , n

(16)

An = − A n / n, Bn = − B n / n.

4. Estimation 4.1 Data Since the yield curve model is developed for discount bonds, I use the zero-coupon bond yield data provided by a bond pricing service provider.6) The data used consist of Korean treasury bond yields of 13 maturities (3, 6, 9, 12, 18, 24, 30, 36, 48, 60, 84, 6) The provider is KIS Pricing, Inc. (www.bond.co.kr). I tried another yield data provided by a different company (Korea Bond Pricing and KR Co., www.koreabp.com) as well, and found both data to be similar.

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108 and 120 months) and include the period from March 2001 to February 2008. We need a one-month riskless short-term interest rate which is not included in the yield data. I construct the one-month riskless rate by taking the averages of the overnight call rates between one Monetary Policy Committee (MPC) meeting date and the next meeting date, considering the fact that the MPC decides the policy interest rate (the overnight call rate) every month, and the call rate can be assumed as constant between the meeting dates. I use the MPC meeting periods instead of calendar months when I construct the monthly yield data, because of the consistency between the short rate and other yields. Figure 8 illustrates the monthly bond yields of selected 1, 12, 36, 60 months for the sample period. I choose the lag of the VAR process of the observable factor as three (i.e., p = 3 in eq. (1)), based on the information criteria AIC and SC. I use three latent factors (i.e., K2 = 3), as in Ang and Piazzesi (2003). Figure 8. Treasury bond yields of maturities of 1, 12, 36 and 60 month(s) 8 1M 12M

7

36M 60M

6

5

4

3

2 2001/3 2001/9 2002/3 2002/9 2003/3 2003/9 2004/3 2004/9 2005/3 2005/9 2006/3 2006/9 2007/3 2007/9

4.2 Estimation method Observable factor process (1) is estimated by the least squares method. The mean

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of the short rate process δ₀ in eq. (5) is taken as the sample mean of the short rate. There are 29 parameters ( Φ1u , ∑u , ∑ou , δ1u , λ0o , λ0u , λ1o ) to be estimated in the Arbitrage-Factor model and 24 parameters ( Φ1u , ∑u , δ1u , λ0u ) in the Yield-Only model. I use the maximum likelihood method to estimate the free parameters where the likelihood function is provided in Ang and Piazzesi (2003). To identify the latent factors, I assume as in Chen and Scott (1993) that three yields of maturities of 1, 12 and 36 month(s) are observed without measurement errors, but that the other yields are observed with measurement errors. Since there are many free parameters to be estimated, the estimation work is not easy. As suggested in Duffee (2007), I randomly choose one hundred initial points and run an optimization algorithm based on the Simplex method five times sequentially at each initial point. I next run a derivative-based optimization algorithm at each point. Finally, I choose as the estimate the point yielding the highest likelihood among the one hundred sets of estimates.

4.3 Estimation results Table 1 reports the parameter estimates and their standard errors for both models. Table 2 shows the root mean squared errors (RMSE) and mean absolute errors (MAD) of both models, and also of the random-walk model for comparison. The YieldOnly model improves data fitting compared to the random-walk model for most maturities except the longer ones. For example, while the random-walk model offers errors of 24 (RMSE) and 18 (MAD) basis points for the yields of two-year maturity, the Yield-Only model gives much smaller errors of 5 (RMSE) and 4 (MAD) basis points. The Arbitrage-Factor model offers better fits than both the Yield-Only and the random-walk models, for all maturities. For example, the Arbitrage-Factor model fits the yields of seven-year maturity with errors of 19 (RMSE) and 13 (MAD) basis points, which is smaller than the 22 (RMSE) and 16 (MAD) basis points for the Yield-Only model, and the 26 (RMSE) and 20 (MAD) basis points for the random-walk model.

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Table 1. Parameter estimates Yield-Only

Arbitrage-Factor

Arbitrage-Factor

estimate

s.e.

estimate

s.e.

0.0427 ∑u,11

0.0067

0.0063

-0.8500

0.7321

-0.0658

0.1840 ∑u,21

0.4794

0.0084

0.5690

0.2494

0.0426

-0.0217

0.0321 ∑u,31

0.1312

0.0038

1.4980

0.0170

-0.0656

0.0232

-0.0606

0.1572 ∑u,12

0.5891

0.0240

-0.2694

0.1024

u Φ1,22

0.6354

0.0563

0.0156

0.1423 ∑u,22

0.2341

0.0317

-0.8741

0.5998

u Φ1,32

0.1978

0.0301

0.1353

0.0006 ∑u,32

-0.4431

0.0143

0.4401

0.2374

u Φ1,13

0.1936

0.0391

-0.0189

0.0200 ∑u,13

-0.4174

0.0647

0.0044

0.0877

u Φ1,23

0.2616

0.0496

0.0640

0.0893 ∑u,23

0.0475

0.0605

0.8071

0.3048

u Φ1,33

0.7506

0.0448

0.9714

0.0190 ∑u,33

0.6186

0.0758

0.1529

0.2225

u δ1,1

-5.0908

0.3257

0.2877

0.1972 ∑ou,1

-

-

-0.1914

0.0741

u δ1,2

2.1467

0.1635

-0.0105

0.0586 ∑ou,2

-

-

-0.1274

0.1821

u δ1,3

-4.1810

0.3841

0.1645

0.1401 ∑ou,3

-

-

0.3463

0.1330

λ0o

-

-

0.6969

0.3424

o λ0,1

-1.8564

0.1300

0.0875

0.1671

o λ0,2

0.9671

0.0660

-0.9017

0.3812

o λ0,3

1.6826

0.2113

-0.1051

0.0066

λ1o

-

-

0.1407

0.0755

estimate

s.e.

estimate

u Φ1,11

0.0853

0.0389

0.9345

u Φ1,21

-0.2957

0.0489

u Φ1,31

0.2616

u Φ1,12

s.e.

Yield-Only

Note) The estimates of ∑u ( ∑ou ) and their standard errors are multiplied by 104 for the Yield-Only model and by 102 for the Arbitrage-Factor model. The subscripts after the commas indicate the corresponding matrix or vector elements.

From eq. (16), the weight Bn represents the effect of each factor on the yield of maturity n and also the initial response of yields to shocks from the various factors. Figures 9 and 10 plot these weights as a function of yield maturity for the Yield-Only and the Arbitrage-Factor models, respectively. For the Arbitrage-Factor model, only the Bn weights corresponding to the contemporaneous arbitrage factor variable are plotted. The weights Bn have been scaled to movements of one standard deviation of the factors, and annualized by multiplying by 1200.

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Foreign Bond Investment and the Yield Curve

Table 2. RMSE and MAD of the models Maturity (month) 1 3 6 9 12 18 24 30 36 48 60 84 108 120

Random-Walk RMSE MAD 0.113 0.064 0.146 0.109 0.164 0.126 0.179 0.139 0.199 0.151 0.233 0.172 0.243 0.183 0.249 0.190 0.254 0.195 0.271 0.212 0.278 0.213 0.260 0.196 0.249 0.188 0.254 0.191

Yield-Only RMSE MAD 0 0 0.149 0.107 0.106 0.076 0.051 0.037 0 0 0.052 0.038 0.054 0.041 0.031 0.024 0 0 0.076 0.053 0.138 0.093 0.218 0.157 0.258 0.196 0.262 0.207

Arbitrage-Factor RMSE MAD 0 0 0.114 0.084 0.087 0.063 0.045 0.031 0 0 0.045 0.032 0.047 0.035 0.027 0.020 0 0 0.070 0.046 0.120 0.076 0.191 0.133 0.227 0.170 0.227 0.180

Note) RMSE and MAD are annualized by multiplying by 1200.

Figure 9. Bn yield weights for the Yield-Only model 0.4 Latent factor 1 Latent factor 2

0.2

Latent factor 3

0

-0.2

-0.4

-0.6

-0.8

-1 1

11

21

31

41

51

61 71 Yield Maturity n

81

91

101

111

Note) The Figure displays Bn yield weights as functions of maturity n for the Yield-Only model. The weights are scaled to correspond to one standard deviation movements in the factors and are annualized through multiplying by 1200.

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Figure 10. Bn yield weights for the Arbitrage-Factor model 5 Arbitrage factor Latent factor 1 Latent factor 2 Latent factor 3

4

3

2

1

0

-1 1

11

21

31

41

51

61

71

81

91

101

111

Yield Maturity n

Note) The Figure displays Bn yield weights as functions of maturity n for the Arbitrage-Factor model. The plots show only the Bn yield weights for contemporaneous state variables. The weights are scaled to correspond to one standard deviation movements in the factors and are annualized through multiplying by 1200.

Since the responses of market prices of risk to each latent factor are normalized to be one, we may not expect to have the typical interpretations of the identified latent factors as in Ang and Piazzesi (2003): the “level”, “slope”, and “curvature” factors. For the Yield-Only model, the second factor (Latent factor 2) looks like a “slope” factor since it is downward-sloping and moves the short-end of the yield curve more than the long-end. The first factor (Latent factor 1) and the third factor (Latent factor 3) are interpretable as “curvature” factors because they move the short-, middle-, and long-ends of the yield curve to different directions. Since the first and second factors move the yield curve to opposite directions, a linear combination of those factors would generate the missing “level” factor, which is a factor affecting yields of all maturities in the same way. For the Arbitrage-Factor model, the first and third latent factors play a role as the “slope” factor. The second latent factor looks to behave as a “level” factor, except at the very short-end of the yield curve. The additional arbitrage factor acts as a “slope” factor and moves the long-end of the yield curve more signifi-

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cantly in relative to that of the short-end. There are three “slope” factors with different slopes, and a combination of these “slope” factors might generate the missing “curvature” factor. While the weights Bn for the arbitrage factor depicted in Figure 10 represent the initial responses of yields to shocks from the arbitrage factor, Figure 11 shows the responses of yields to the arbitrage factor shock over time for some selected maturities: 1, 3 and 5 years. The yield of the 5-year maturity bond initially decreases by around 5 basis points in response to the arbitrage factor shock of a one percentage point increase, and the effect then gradually disappears. The yields of shorter maturities show similar patterns, but the responses to the shock are smaller: the yield of the 3-year maturity bond responds initially by 3 basis points, and that of the 1-year maturity by less than 1 basis point. Figure 11. Impulse response functions 0.00

-0.01

Percentage points

-0.02

-0.03

-0.04 Maturity of 1Y

-0.05

Maturity of 3Y Maturity of 5Y

-0.06 1

11

21

31

41

51

61

71

81

91

Months

Note) The plots represent the impulse responses of the 1-, 3-, and 5-year maturity yields to arbitrage shocks of one percentage point.

We can calculate the historical effects of the arbitrage factor on yields by combining the weights Bn for the arbitrage factor with the actual arbitrage factor movements. Figure 12 plots the historical effects of the arbitrage factor by artificially setting it to

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Figure 12. Effects of the arbitrage factor on yields 0.2

0

Percentage points

-0.2

-0.4

-0.6

Maturity of 1Y Maturity of 3Y Maturity of 5Y

-0.8

-1 2002

2003

2004

2005

2006

2007

2008

Figure 13. Interest rate term spreads after adjustment of the effects of the arbitrage factor: 1, 3, 5 year(s) versus 1 day 3.5 TB(1Y) - call(1D) TB(3Y) - call(1D) TB(5Y) - call(1D)

3

2.5

2

1.5

1

0.5

0

-0.5 2001/1

2002/1

2003/1

2004/1

2005/1

2006/1

2007/1

2008/1

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Foreign Bond Investment and the Yield Curve

Figure 14. Actual bond yield-model implied bond yield 0.8 0.7

Actual yield - Yield-Only model implied yield (5Y)

0.6

Actual yield - Arbitrage-Factor model implied yield (5Y)

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 2001/1

2002/1

2003/1

2004/1

2005/1

2006/1

2007/1

2008/1

be zero. Since the response of the yield to the arbitrage shock becomes larger as the maturity lengthens, the historical effects of the arbitrage factor become larger at a longer than a shorter maturity. The historical effects had risen to their highest levels of 66, 41 and 9 basis points for 5-, 3-, and 1-year maturities, respectively, in December 2007. These effects are not insignificant in 2007. Taking out these effects on the yields, the phenomenon of yield curve flattening in 2007 is considerably weakened as illustrated in Figure 13. This evidence supports market participants’ argument that the flattening has been partly due to the rapid increase in foreigners’ bond investment. Ever since foreign bond investment began to increase considerably, the arbitrage factor has been playing an important role in fitting the yield data. Figure 14 demonstrates that the Yield-Only model without including the arbitrage factor significantly overfits the actual yields of 5-year maturity from 2007. However, the ArbitrageFactor model fits well with the actual yields during that period. Lastly, I calculate and report in Table 3 the variances of the yields and those of the effects of the arbitrage factor on the yields in order to gauge the relative importance

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of the arbitrage factor to the yield movements.7) The relative importance of the arbitrage factor to the yield movements becomes higher as the maturity grows longer. The relative volatility reaches 53% for the yield on 5-year maturity bonds since 2007; however, it amounts to only 2% for the entire period. Table 3. Variances of the yields and the effects of the arbitrage factor Maturity (year)

2007/1-2008/2 Var. of yields Var. of AF effects

2001/3-2008/2 Ratio

Var. of yields

Var. of AF effects

Ratio

1

0.053

0.001

0.016

0.422

0.000

0.001

3

0.093

0.017

0.185

0.627

0.006

0.010

5

0.087

0.046

0.527

0.789

0.017

0.021

Note) “Var. of yields” denotes the variances of the yields for selected maturities of 1, 3 and 5 years, “Var. of AF effects” the variances of the effects of the arbitrage factor, and “Ratio” the ratios of “Var. of AF effects” to “Var. of yields.”

5. Conclusion In this paper, utilizing a stylized affine term structure model, I analyze whether the yield curve flattening in the Korean bond market since 2007 has been partly attributable to foreigners’ rapidly growing investment in Korean bonds, driven by foreign invenstors’ exploiting market imperfections and seeking riskless profits thereof. I find supportive evidence for the argument by market participants that investment by foreigners has been an important factor behind the flattening of the yield curve since 2007. Indeed, when leaving out the effects of foreign bond investment on yields, I find the yield flattening phenomenon considerably weakened. The issues of market imperfection and the effects of foreign investment on the bond yields here might be relevant to other emerging markets as well, and the analysis in this paper could be helpful for studying other countries’ cases. I use only one observable arbitrage factor along with three latent factors in the 7) Here, I do not use the variance decomposition technique, because we are interested in the subsample from 2007-the period of rapidly growing foreigners’ bond investment. The usual variance decomposition method is applied for the whole sample period. Note that the ratio of the variances of the yields to the variances of the effects of the arbitrage factor does not indicate the proportion of yield movements explained by the arbitrage factor, which is the usual interpretation from the variance decomposition technique.

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yield curve model. Since other countries have much evidence supporting that macro variables such as output and inflation can be significant factors relevant to determining bond yields, including those factors in the model will be beneficial. Here I employ the maximum likelihood estimation method, but it would be worthwhile trying a Bayesian estimation method as in Ang, Dong, and Piazzesi (2005), because the model has many parameters to be estimated.

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Rudebusch, Glenn D., Eric Swanson and Tao Wu, 2006, The bond yield “conundrum” from a macro-finance perspective, Monetary and Economic Studies 24(S-1), pp. 83128. Rudebusch, Glenn D. and Tao Wu, 2007, Accounting for a shift in term structure behavior with no-arbitrage and macro-finance models, Journal of Money, Credit, and Banking 39, pp. 395-422.

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