Impact of Non-Traditional Monetary Policy on Cross-Currency
Basis Swap and Japanese Interest Rate Swap Markets☆
Meiji University, School of Commerce
Takayasu Ito

【Abstract】
The five-, 10-, and 20-year interest rate swap (IRS) rates co-move with the 6-month basis
swap rates under the quantitative and qualitative easing policy regime introduced by the
Bank of Japan (BOJ). The 10- and 20-year IRS rates co-move with the 12-month basis swap
rates under the quantitative and qualitative easing policy regime. The 10- and 20-year IRS
rates are in a one-to-one relationship with the six- and 12-month basis swap rates. A cheaper
yen gives foreign investors strong incentives to invest in 10- and 20-year IRS in thequantitative and qualitative easing policy regime. A cheaper yen gives foreign investors someincentives to invest in a 5-year IRS by funding yen in the six-month basis swap market. On
the other hand, the IRS rate does not co-move with the basis swap rate under the negativeinterest rate policy regime. A cheaper yen does not give foreign investors incentives to invest
in IRS. After the BOJ introduced the negative interest rate policy, the trend observed underthe quantitative and qualitative easing policy regime changed.

Keywords: Basis Swap, Japanese Interest Rate Swap, Non-traditional Monetary Policy☆
The original version of this paper was published as Ito (2018).
Meiji University, School of Commerce, Tokyo Japan1

1. Introduction
Not only Japanese government bonds (JGBs) but also the Japanese interest rate swap (IRS)
were traded on a very low yield after the Bank of Japan (BOJ) introduced a quantitative andqualitative easing policy. This trend became more apparent after the BOJ decided to introduce anegative interest rate policy on January 29, 2016. Under the phenomenon of low yield, overseas
investors capitalize on the brisk demand for dollars with highly profitable currency swaps.
Cross-currency basis swaps are often used as a tool for foreign-currency funding or
currency-risk hedging by banks and institutional investors. Foreign exchange (FX) swaps arecontracts in which one party simultaneously borrows one currency and lends another currency
to a second party. Hedge funds and other institutional investors often borrow dollars on theswap market to hedge against exchange-rate risk when investing in foreign bonds and otherinterest rate instruments.
A pickup in such trades would heighten demand for dollar swaps. With the spread on
dollar-yen basis swaps factored in, investing in IRS could be very attractive to overseas
investors. The 12-month dollar-yen basis swap rate was about minus 70 basis points in the
middle of July 2016. The five-year IRS rate was about minus 20 basis points in the same period.
Exchanging dollars for yen and investing the proceeds in five-year or five-year JGBs withnegative yields could produce an annual return of around 50 basis points for one year. Japanesebanks have a great demand for US dollar funding as US banks are hesitant to lend US dollars
because they are under the great pressure of downsizing the size of their balance sheet due totighter regulation (the Volcker rule).
The related literatures such as Arai et al. (2016), Baba et al. (2008), Baba et al. (2009),
Viviana (2016) and Wenxin et al. (2017) focus on cross currency markets. Ito (2017) showsthat a cheaper yen gives foreign investors strong incentives to buy 10- and 20-year JGBs in thequantitative and qualitative easing policy regime in Japan. A cheaper yen gives foreign
investors some incentives to buy 5-year JGBs in the same regime. On the other hand, the JGB
yield does not co-move with basis swap rate in the regime of negative interest rate policy. Afterthe BOJ introduced negative interest rate policy, the trend observed under the regime ofquantitative and qualitative easing policy has changed.
This study focuses on the cross-currency swap and IRS markets. It investigates whether acheaper yen gives foreign investors strong incentives to invest in IRS under the quantitativeand qualitative easing policy and negative interest rate policy regimes. None of the related
studies cited above analyzes the cross-currency swap and IRS markets. Thus, this paper
distinguishes itself from other previous works.
The remainder of this paper is organized as follows: Section 2 describes the data and provides

2

summary statistics, section 3 discusses the methodology, section 4 presents the results, andsection 5 concludes the paper.

2.DataBasis swap rates of six and 12 months and Japanese IRS rates of five, 10, and 20 years areused. The daily closing data are provided by Bloomberg. Basis swap rates moved in thenegative territory. The sample period is from March 1, 2013 to August 31, 2016. The entire
sample period is divided into two on the January 29, 2016, the date when the BOJ decided to
introduce a negative interest rate policy.
The sample period running from March 1, 2013 to January 28, 2016 is named Sample A; theBOJ introduced a quantitative and qualitative easing policy during this period. The BOJ
introduced a negative interest rate policy during the Sample B period. The Sample B period
finishes at the end of August 2016 because the BOJ introduced a yield curve control policy on
September 21, 2016. The yield curve control policy is as follows: The BOJ will apply anegative interest rate of minus 0.1 percent to the policy-rate balances in current accounts heldby financial institutions at the Bank. The Bank will purchase JGBs so that the 10-year JGB
yields will remain at around zero percent.
The movements of the 12-month basis swap rate and the yields of JGBs with maturities of three
and 12 months are shown in Figure 1, and the descriptive statistics are provided in Table 1.
%
1.5

M12

IY5

IY10

1

0.5

0

-0.5

Fig.1 The movement of 3 Series
Notes:
M12 = Basis Swap Rate, IY10 = IRS 10Y, IY20 = IRS20Y
Data Source : Bloomberg
Whole sample period is from March 1, 2013 to Augst 31, 2016.

3

08/04/2016

06/22/2016

05/11/2016

03/24/2016

02/09/2016

12/24/2015

11/10/2015

09/25/2015

08/11/2015

06/29/2015

05/18/2015

03/31/2015

02/17/2015

12/30/2014

11/14/2014

10/01/2014

08/18/2014

07/04/2014

05/23/2014

04/08/2014

02/24/2014

01/09/2014

11/21/2013

10/08/2013

08/23/2013

07/11/2013

05/30/2013

04/15/2013

03/01/2013-1

Table 1
Descriptive Statistics of Data for Analysis
Variable

Average

SD

Min

Max

MedianM6-0.2490.138-0.698-0.086-0.204M12-0.2920.140-0.733-0.117-0.229

IY5

0.299

0.094

0.133

0.589

0.281

IY10

0.688

0.171

0.375

1.101

0.661

IY20

1.385

0.234

0.935

1.835

1.404

Sample A

Sample B
M6-0.5690.108-0.776-0.410-0.530M12-0.6310.061-0.753-0.538-0.628IY5-0.0990.048-0.2140.033-0.092

IY10

0.079

0.083

-0.108

0.279

0.096

IY20

0.425

0.186

0.078

0.859

0.419

Notes:
Sample period from A is from March 1, 2013 to January 28, 2016.
Sample period from B is from January 29, 2016 to Augsut 31, 2016.

M is basis swap rate. IY is Japanese IRS rate.

3.Methodology
3.1 Unit Root Test
Because empirical analysis from the mid-1980s through to the mid-1990s shows that such data
as interest rates, foreign exchanges, and stocks are non-stationary, it is necessary to check
whether the data used in this paper contain unit roots. The augmented Dickey-Fuller (ADF) test
and the Kwiatowski-Phillips-Schmidt-Shin (KPSS) test are used. The ADF test defines the null
hypothesis as “unit roots exist” and the alternative hypothesis as “unit roots do not exist.” Fuller(1976) provides a table for the ADF test. The KPSS test defines the null hypothesis as “unit roots
do not exist” and the alternative hypothesis as “unit roots exist.” First, the original data arechecked to verify whether they contain unit roots. Next, the data with first difference are
analyzed to determine whether they have unit roots in order to confirm that they are I (1) process.

3.2 Cointegration Test and Theoretical BackgroundA cointegration framework is presented to analyze the relationship between IRS rate and basis
swap rate. Non-stationary time series wander widely with their own short-run dynamics, but alinear combination of these series can sometimes be stationary so that they show co-movementwith the long-run dynamics. Engle and Granger (1987) call this cointegration. In the test of theco-movement between IRS rate and basis swap rate by cointegration, equation (1) is estimatedby ordinary least squares (OLS) to find out whether the residual contains unit roots.

4

IRS t     basist  ut
IRSt ＝ IRS rate(1)

basist = basis swap rate

When series IRSt and basist are both non-stationary I (1), they are said to be in a cointegration
relationship if their linear combination is stationary I (0). The cointegration relationshipbetween IRSt and basist implies that IRS rate and basis swap rate move together in the long-run
equilibrium. If IRS rate co-moves with basis swap rate, it is assumed that the IRS rate
decreases when the funding cost of Japanese yen gets lower. In other words, a cheaper yen
gives foreign investors incentives to invest in IRS.
In addition to testing whether IRS rate and basis swap rate are in a cointegration relationship,
the cointegration vector (1,-1), β in the equation (1), is checked using the dynamic OLS method
developed by Stock and Watson (1993). Equation (2) is used to test if β = 1 can be rejected. Δ
basist-j is the lead variable and the lag variable of basis swap rate. As for the number of leadand lag terms, 12 is used. Hirayama and Kasuya (1996) provide empirical analysis using Rats
procedure SWDYNAMIC.PRG. If β = 1 cannot be rejected, IRS rate changes to the same
degree as basis swap rate. The test of the cointegration vector is only conducted on a pair ofsamples when they are in a cointegration relationship.
p

IRS t     basist  b basis  u
t i

i

t

(2)

i  p

The methodology is summarized as follows: First, analyses are conducted on the pair-wise
relationship between IRS rate and basis swap rate, respectively. In other words, theco-movement of IRS rate with basis swap rate is investigated using the cointegration test. Next,
whether IRS rate and basis swap rate are in a one-to-one relationship is tested using thecointegration vector test. An interpretation of the results divided into three cases can be madein the following way:

Interpretation of cointegration analysis
Case

Cointegration

Cointegration Vector

Ⅰ

No

--

Ⅱ

Yes

β＝1 cannot be deniedⅢ

Yes

β＝1 can be denied

Ⅰ The IRS rate does not co-move with the basis swap rate. A cheaper yen does not giveforeign investors incentives to invest in IRS.

5

Ⅱ

The IRS rate co-moves with the basis swap rate. The IRS rate is in a one-to-one
relationship with the basis swap rate. A cheaper yen gives foreign investors strong
incentives to invest in IRS.

Ⅲ The IRS rate co-moves with the basis swap rate. The IRS rate is not in a one-to-one
relationship with the basis swap rate. A cheaper yen gives foreign investors someincentives to invest in IRS.

4. Results
4.1 Unit Root TestFirst, ADF and KPSS tests are conducted on the original series. All the results of the ADF andKPSS tests except for the ADF tests with a six-month basis swap trend and a 10-year IRS in
Sample A contain a unit root. The results do not eliminate the doubt that the original data haveunit roots because all the results of the KPSS test show that they contain unit roots. The KPSS
test is considered to have more statistical power than the ADF test. The results are shown in
Table 2 and Table 3.
Next, ADF and KPSS tests are conducted for the data with a first difference. The results showthat all the data with a first difference are stationary. Thus, it is appropriate to think that all of
the variables used for the analysis are non-stationary I (1) variables and to judge that
non-stationary time series can be used. The results are shown in Table 4 and Table 5.

4.2 Cointegration Test
Pair-wise analyses are conducted to check the relationships between the IRS rate and the basis
swap rate. The results of all the tests show that in Sample A, the IRS rate is in a cointegration
relationship with the six-month basis swap rate in the maturities of five, 10, and 20 years. The
IRS rate is in a cointegration relationship with the 12-month basis swap rate in the maturities of
10 and 20 years. On the other hand, the results of all the tests show that in Sample B, the IRS
rate is not in a cointegration relationship with the basis swap rate. The results are shown in
Table 6.
Next, the dynamic OLS method of Stock and Watson (1993) is used to check whether the βindicated in equation (2) equals 1 for Sample A. The results of tests show that β = 1 cannot berejected in the analysis of the swap rate in the maturities of 10 and 20 years, which means thata 1% increase in the basis swap rate leads to a 1% increase in the JGB yield. The results areshown in Table 7.

6

Table 2
ADF unit root test (Original Series)
Variable

Without Trend

With Trend

M6-0.137-3.476*

M12

0.763

-3.246IY5-1.049-2.987IY10-0.632-4.142*IY20-0.697-3.994M6

1.213-2.906M12

0.667-2.389IY5-0.969-2.091IY10-2.397-1.811IY20-2.273-1.829Sample A

Sample B

Notes:* indicates significance at the 5% level.
5% critical values are −2.864 (without trend) and −3.415 (with trend).
1% critical values are −3.437 (without trend) and −3.964 (with trend).

M is basis swap rate. IY is Japanese IRS rate.

Table 3
KPSS unit root test (Original Series)
Lag = 3
Variable

Lag = 12

Level Stationary

Trend Stationary

Level Stationary

Trend Stationary

M6

11.907*1.662*

4.654*

0.699*

M12

11.831*2.439*

4.614*

0.987*

IY5

10.939*1.208*

4.310*

0.507*

IY10

11.524*0.507*

4.524*

0.215*

IY20

12.253*0.546*

4.792*

0.230*

M6

2.368*

0.560*

0.976*

0.246*

M12

1.822*

0.593*

0.762*

0.258*

IY5

0.473*

0.228*

0.203*

0.118

IY10

1.900*

0.258*

0.818*

0.124

IY20

2.235*

0.390*

0.937*

0.178*

Sample A

Sample B

Notes:* indicates significance at the 5% level.
5% critical values are 0.463 ( level stationary) and 0.146 ( trend stationary).

M is basis swap rate. IY is Japanese IRS rate.

7

Table 4
ADF unit root test (first difference series)
Variable

Without Trend

With Trend

ΔM6-26.623*-26.378*

ΔM12-21.815*-21.635*ΔIY5-17.737*-19.295*

ΔIY10-17.537*-18.031*ΔIY20-17.608*-17.984*

ΔM6-10.251*-10.837*

ΔM12-13.079*-12.714*ΔIY5-10.240*-11.297*

ΔIY10-6.583*-6.404*ΔIY20-10.588*-11.025*

Sample A

Sample B

Notes:* indicates significance at the 5% level.
5% critical values are −2.864 (without trend) and −3.415 (with trend).

M is basis swap rate. IY is Japanese IRS rate.

Table 5KPSS unit root test (First Diffrenced Series)
Lag = 4
Variable

Lag = 12

Level Stationary

Trend Stationary

Level Stationary

Trend Stationary

ΔM6

0.057

0.048

0.06

0.05

ΔM12

0.14

0.035

0.153

0.038

ΔIY5

0.143

0.073

0.16

0.088

ΔIY10

0.256

0.116

0.26

0.115

ΔIY20

0.314

0.116

0.31

0.117

ΔM6

0.105

0.047

0.153

0.072

ΔM12

0.127

0.053

0.163

0.069

ΔIY5

0.145

0.044

0.204

0.066

ΔIY10

0.212

0.056

0.261

0.077

ΔIY20

0.417

0.057

0.340

0.068

Sample A

Sample B

Notes:* indicates significance at the 5% level.
5% critical values are 0.463 ( level stationary) and 0.146 ( trend stationary).

M is basis swap rate. IY is Japanese IRS rate.

8

Table 6
Cointegration test
Variable

Test Statistics

Variable

Sample A

Test Statistics

Sample B

M6,IY5-3.163**

M6,IY5-0.034

M6,IY10-3.466*

M6,IY10-0.593

M6,IY20-3.521**

M6,IY20-1.418

M12,IY5-2.614

M12,IY5-0.745

M12,IY10-3.049*

M12,IY10-1.291

M12,IY20-3.434*

M12,IY20-1.170Notes:*,** indicates significance at the 5% and 10% levels respectively ．
5% critical value is −3.3377 from MacKinnon (1991)．
10% critical value is −3.0462 from MacKinnon (1991)．

M is basis swap rate. IY is Japanese IRS rate.

Table 7
Cointegration vector testβModified SE

Modified t Value

M6,IY5

0.528

0.170

3.106

M6,IY10

1.046

0.260

0.176*

M6,IY20

1.503

0.332

1.515*

M12,IY10

0.974

0.305

0.085*

M12,IY20

1.445

0.349

1.275*

Variable

Sample A

Notes:* means that β = 1 cannot be rejected since modified t value is smaller than 5%
critical value (1.96).

M is basis swap rate. IY is Japanese IRS rate.

5. Concluding Remarks
This study focuses on the cross-currency swap and IRS markets. It investigates whether acheaper yen gives foreign investors strong incentives to invest in IRS under the regimes of thequantitative and qualitative easing and negative interest rate policies. Basis swap rates moved
in the negative territory. This indicates that foreign investors could fund Japanese yen on anegative basis. The five-, 10-, and 20-year IRS rates co-move with the six-month basis swap
rates under the quantitative and qualitative easing policy regime. The 10- and 20-year IRS rates
co-move with the 12-month basis swap rates under the quantitative and qualitative easing
policy regime.

9The 10- and 20-year IRS rates are in a one-to-one relationship with the six- and 12-month
basis swap rates. A cheaper yen gives foreign investors strong incentives to invest in 10- and20-year IRS under the quantitative and qualitative easing policy regime. A cheaper yen also
gives foreign investors some incentives to invest in 5-year IRS by funding yen in the six-month
basis swap market. On the other hand, the IRS rate does not co-move with the basis swap rate
under the negative interest rate policy regime. A cheaper yen does not give foreign investors
incentives to invest in IRS.
The BOJ introduced a quantitative and qualitative easing policy in April 2013. The yield
curve of IRS flattened sharply in the 10- and 20-year yields, declining from the beginning of2013 because market practitioners anticipated that the BOJ would introduce a large-scaleeasing policy. The investment in IRS by foreign investors using the cheaper yen funded on anegative basis in the cross-currency market contributed to the decline of long-term IRS rates.
After the BOJ introduced a negative interest rate policy, the trend observed under thequantitative and qualitative easing policy regime changed.

【Reference】
Arai, F., Makabe, Y., Okawara, Y. and Nagano, T. (2016), “Recent Trends in Cross-currency Basis,”
Bank of Japan Review, 2016-E-7.
Baba, N., McCauley, R.N. and Ramaswamy, S. (2009), “US Dollar Money Market Funds andnon-US Banks,” BIS Quarterly Review, pp. 65-81.
Baba, N., Packer, F. and Nagano, T. (2008), “The Spillover of Money Market Turbulence to FX Swap
and Cross-Currency Swap Markets,” BIS Quarterly Review, March, pp. 73-86.
Dickey, D.A. and Fuller, W.A. (1979), “Distribution of the Estimators for Autoregressive Time Series
with a Unit Root,” Journal of the American Statistical Association, Vol. 74, pp. 427-431．
Dickey, D.A. and Fuller, W.A. (1981), “Likelihood Ratio Statistics for Autoregressive Time Series
with a Unit Root,” Econometrica, Vol. 49, pp. 1057-1072.
Engle, R.F. and Granger, C.W.J. (1987), “Co-integration and Error Correction: Representation,
Estimation and Testing,” Econometrica, Vol. 55, pp. 51-276.
Fuller, W.A. (1976), Introduction to Statistical Time Series, John Wiley & Sons, Inc.
Hirayama, K. and Kasuya, M. (1996), “Financial Deregulation and Divisia Monetary Aggregates inJapan,” Mullineux, A. ed., Financial Innovation, Banking and Monetary Aggregates, Edward
Elgar, pp. 104-130.
Ito, T. (2017), “Impact of Cross Currency Basis Swap on Japanese Government Bond under
Non-Traditional Monetary Policy,” mimeo.

10

Ito, T. (2018), “Japanese Interest Rate Swap and Cross-Currency Basis Swap Markets under
Non-traditional Monetary Policy,” Macrotheme Review,Vol.7, pp1-11.
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, P. (1992), “Testing the Null Hypothesis of
Stationarity against the Alternative of a Unit Root,” Journal of Econometrics, Vol. 54, pp.
159-178.
MacKinnon, J. (1991), “Critical Values for Cointegration Tests,” Engle, R.F and C.W.J. Granger eds.,
Long-Run Economic Relationships: Readings in Cointegration, Oxford University Press, pp.
267-276.
Stock, J.H. and Watson, M.W. (1993), “A Simple Estimator of Cointegrating Vectors in Higher Order
Integrated Systems,’ Econometrica, Vol. 61, pp. 783-820.
Viviana, F. (2016), “A Defaultable HJM Modelling of the Libor Rate for Pricing Basis Swaps after theCredit Crunch,” European Journal of Operational Research, Vol. 249, pp. 238-244.
Wenxin, Du, Tepper, A. and Verdelhan, A. (2017), “Deviations from Covered Interest Rate Parity,”
NBER Working Paper No. 23170.

11