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Prepayment behaviors of Japanese residential mortgages
Japan and the World Economy 30 (2014) 1–9
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Prepayment behaviors of Japanese residential mortgages Naoki Kishimoto 1, Yong-Jin Kim * Faculty of Business Administration, Hosei University, 2-17-1 Fujimi, Chiyoda-ku, Tokyo 102-8160, Japan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 4 March 2013 Received in revised form 11 November 2013 Accepted 31 December 2013 Available online 15 January 2014
We investigate full prepayments of Japanese residential mortgages during a ten-year period from 1996 to 2005. This investigation is important because the amount of mortgages outstanding in Japan is huge, yet the study on their prepayments is very limited. This period from 1996 to 2005 was characterized by two distinct features of the evolution of interest rates that might have significant effects on mortgage refinancing. First, interest rate fluctuations were limited to a narrow range of a little over 1%. Surprisingly, full prepayments of Japanese mortgages were sensitive to small changes in interest rates. Second, long-term refinance rates did not fall well below the contract rates of most mortgages in our sample during the ten-year period, while short-term refinance rates did. With this interest rate relationship, if mortgagors ever refinanced, it was likely that they rolled over shortterm mortgage rates several times until they repaid mortgages completely. Hence, we examine the sensitivity of full prepayments to short-term vs. long-term interest rates, mortgagors’ expectation of future course of interest rates (by the slope of yield curve), and that of interest rate volatility. Our analysis shows that short-term interest rates have a slightly greater explanatory power for full prepayments than long-term interest rates. In addition, our analysis confirms that full prepayments are sensitive to both the slope of yield curve and interest rate volatility. Other issues we look into are the patterns of full prepayments in relation to loan age and seasonality. We find that the pattern of full prepayments relative to loan age is comparable to that of mortgages in the U.S., and that the seasonal pattern of full prepayments is attributable to relevant institutional arrangements in Japan. ß 2014 Elsevier B.V. All rights reserved.
JEL classification: D14 G21 G15 Keywords: Prepayment behavior Japanese residential mortgages Refinance
Prepayments of residential mortgages considerably alter the pattern of cash flows the holders of the mortgages receive. As a result, they pose major risk to the holders of mortgages, such as financial institutions (FIs) holding mortgages directly, and investors in mortgage-backed securities (MBSs). Hence, the questions such as how common prepayments are and how prepayments are related to interest rate movements are of critical importance to these mortgage investors with regard to their risk management as well as the pricing of mortgages and MBSs. It should be noted that the economic significance of this risk is substantial because massive amounts of residential mortgages are outstanding. For example, at the end of 2011, the amount of U.S.
home mortgages of the household sector was 9840 billion dollars, which was well above the corporate debt of 7800 billion dollars and a little below the Federal government debt of 10,453 billion dollars. Similarly, at the end of 2011, the total balance of Japanese residential mortgages was 207 trillion yen, which was approximately a half of the entire debt (402 trillion yen) of the private nonfinancial corporate sector and one fifth of national government debt (887 trillion yen).2 These facts warrant serious investigation into prepayments of residential mortgages. Indeed, many researchers have looked into prepayments of U.S. residential mortgages. A partial list of them includes Green and Shoven (1986), Schwartz and Torous (1989, 1993), Deng et al. (2000), and Dunsky and Ho (2007). By sharp contrast, such studies on Japanese residential mortgages are
* Corresponding author. Tel.: +81 3 3264 4562; fax: +81 3 3264 9698. E-mail addresses: [email protected] (N. Kishimoto), [email protected] (Y.-J. Kim). 1 Tel.: +81 3 3264 9733; fax: +81 3 3264 9698.
2 These numbers are based on Flow of Funds Accounts of the United States Fourth Quarter 2011, downloadable at http://www.federalreserve.gov/releases/z1/ 20120308/ and Japan’s Flow of Funds Accounts, downloadable at http://www.boj.or.jp/en/statistics/sj/index.htm/.
1. Introduction
0922-1425/$ – see front matter ß 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.japwor.2013.12.002
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N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
minimal. Specifically, to our best knowledge, publicly available studies on prepayments of Japanese residential mortgages are limited to only three academic papers: Sugimura (2002), Ichijo and Moridaira (2006), and Kutsuzawa (2007).3 Before we describe these studies on prepayments of Japanese residential mortgages, we point out a few distinct features of mortgage interest rates that are observed during the sample period from May 1996 to December 2005. Fig. 1 plots four interest rates in each month of the sample period. In this figure, WAC represents the weighted average coupon (WAC) of mortgages in our sample that started repayments in the same month. ARM rate stands for the average of interest rates on adjustable rate mortgages (ARMs) that are offered in the same month. 3-, 5- and 10-year rates are the averages of interest rates on mortgages which have fixed interest rates for the first 3, 5, and 10 years of mortgage terms, respectively, and which are offered in the same month. Incidentally, the ARM rates are compiled by the Bank of Japan, and the 3-, 5- and 10-year rates are compiled by Japan Financial News Co. Ltd. Also, in this paper, we refer to mortgages that have fixed interest rates for the first few years of mortgage terms as renegotiable mortgages. Fig. 1 reveals that interest rate movements during the sample period exhibited three features we ought to pay close attention to. First, all of the five time series showed little variation during this 10-year period. Specifically, the differences between the maximum and minimum values during this period of WAC, ARM, 3-year, 5year, and 10-year rates were 1.19%, 0.25%, 1.1%, 1.3%, and 1.32%, respectively. These changes are small compared to changes in mortgage interest rates in other developed countries. For example, according to Freddie Mac’s ‘‘Primary Mortgage Market Survey Archives,’’ the differences between the maximum and minimum values during our sample period of U.S. 1-year adjustable, 15-year fixed, and 30-year fixed rates were 3.875%, 3.55%, and 3.29%, respectively.4 Similarly, according to a Deutsche Bundesbank’s publication, the differences between the maximum and minimum values during our sample period of German variable, 5-year fixed, and 10-year fixed rates were 2.71%, 2.65%, and 3.53%, respectively.5 Second, the 10-year rate was above the concurrent WAC in every month of the sample period.6 Furthermore, the 10-year rate offered 3 Publicly available studies on prepayments of Japanese residential mortgages are rare mainly because Japanese FIs have been reluctant to give prepayment data to outsiders, including academicians. Sugimura (2002) and Ichijo and Moridaira (2006) could avoid this problem by obtaining in-house data from different FIs Sugimura and Ichijo worked for, while Kutsuzawa (2007) could do so by conducting an Internet survey of mortgage prepayments. We are fortunate that we could obtain Government Housing Loan Corporation (GHLC) prepayment data as recipients of a scholarship from GHLC’s affiliate, Housing Loan Progress Association, while GHLC had the policy to give the scholarship recipients access to its prepayment data. Note, however, that GHLC ended compiling prepayment data in the format that is amenable to our study shortly after we obtained the prepayment data. Currently, GHLC’s successor, Japan Housing Finance Agency, compiles aggregate prepayment data on its MBSs, each of which consist of mortgage loans with various contract rates and diverse stated maturities. 4 Freddie Mac’s Primary Mortgage Market Survey Archives are found at http:// www.freddiemac.com/pmms/pmms_archives.html. 5 This publication is published as a pdf file titled ‘‘Housing loans to households/ Mortgage loans secured by residential real estate,’’ which is downloadable at http:// www.bundesbank.de/Navigation/EN/Statistics/Money_and_capital_markets/Interest_rates_and_yields/Interest_rates_on_deposits_and_loans_nterest_rates_on_deposits_and_loans.html. 6 Newly originated GHLC mortgages typically had 20 years or longer until maturity and the yield curve based on Japanese government bonds was upward sloping throughout the sample period. Hence, the fact that the WAC was below the concurrent 10-year mortgage rate implies that GHLC mortgages were offered below the interest rates that would prevail in a competitive mortgage market. In fact, the financial statements of GHLC show that the GHLC could offer low rates due to the Japanese Government’s subsidy. For example, in the fiscal year ending in March 2005, GHLC received over 404 billion yen from the Japanese government, which helped fill the gap between GHLC’s interest expenses of 2073 billion yen and interest revenues of 1816 billion yen.
in any month was never lower than the WAC of any mortgage pool that had been formed prior to that month by more than 35 basis points. Third, all of the 5-year, 3-year, and ARM rates were below the concurrent WAC of mortgage pools for most of the 10-year period, although none of the 5-year, 3-year, and ARM rates in any month of the sample period were lower than the WACs of mortgage pools that had been formed prior to that month by more than 135 basis points. According to Fabozzi and Modigliani (1992, p. 198), ‘‘historically, it has been observed that when mortgage rates fall to more than 200 bp below the contract rate, prepayment rates increase.’’ Given this historical fact, the observations made in Fig. 1 lead to a question: how sensitive mortgage refinancing was to interest rate movements during the sample period? Note that the prepayment data that are available to us do not distinguish prepayments due to refinancing from full prepayments due to other reasons, such as moving. Hence, we analyze full prepayments instead of refinancing. Note also that because full prepayments due to moving and default are less frequent than and not as closely related to interest rate movements as those due to refinancing, the effects of interest rates on full prepayments are likely to be found weaker than the effects of interest rates on refinancing. In this sense, it is not so bad to analyze full prepayments in order to obtain insights on the effects of interest rates on refinancing. In addition, our prepayment data are grouped data. Hence, we follow Schwartz and Torous (1993) in running Poisson regression, where the dependent variable is the number of occurrences of full prepayments in a month and the independent variables are a variety of interest-rate-related variables and other variables.7 We find that the coefficients of the interest rate variables are statistically significant and their values are fairly stable across various specifications of Poisson regression. The second and third observations in Fig. 1 imply that if a mortgage loan was prepaid due to refinancing, it is most likely that it was refinanced by an ARM or a renegotiable mortgage. This conjecture, in turn, implies that mortgagors who were considering refinancing were more concerned about short- and medium-term mortgage rates than long-term mortgage rates. To examine this hypothesis, we run various specifications of Poisson regression where a long-term mortgage rate is replaced by a short- or medium-term mortgage rate as an independent variable. The estimation results turn out to be in favor of this hypothesis. In addition, as we will see in detail in the next section, if a mortgagor refinances a mortgage loan by an ARM or a renegotiable mortgage, she is most likely to roll over a series of short- and/or medium-term rates in the future until she repays the mortgage completely. Hence, it is plausible that mortgagors’ expectation of both future course and volatility of interest rates has direct effects on mortgagors’ decision on refinancing. Therefore, we include the slope of Japanese government bond yield curve and the standard deviation of Japanese Treasury bill as additional independent variables of Poisson regression. It is confirmed that the estimation results are consistent with this hypothesis. Furthermore, it is well known that the age of a mortgage pool and dummy variables for months of the year exert strong influence on full prepayments. Hence, we include them as additional independent variables of Poisson regression to control the effects of them on prepayments. The estimation results indicate that the pattern of full prepayments relative to mortgage pool age is comparable to that for U.S. mortgages. In particular, the prepayment intensity increases consistently for the first seventy two months and declines gradually afterward. Furthermore, we have 7 In addition, we ran logit regression for grouped data and obtained results similar to the ones from Poisson regression, which are shown in Tables 2 and 3.
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
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Fig. 1. Residential mortgage rates. Sources: GHLC, Japan Financial News Co. Ltd., and The Bank of Japan.
identified several seasonal characteristics of full prepayments, which are attributable to various institutional arrangements in Japan. These arrangements include regularly paid bonuses, the tax saving effects of mortgage balances, and fiscal and academic years in Japan. Next, we briefly summarize the prior studies on the prepayments of Japanese residential mortgages and compare them with our study. First, Sugimura (2002) used data on individual mortgages to estimate Cox proportional hazards models where the time that passed from either origination or a prior partial prepayment, if any, to the next partial or full prepayment was examined with regard to a baseline hazard function, two interestrate-related variables, the time to maturity of a mortgage loan, and the age of a mortgagor. He estimated this model for each type of prepayments (full prepayments, partial prepayments, and defaults) separately, and found that the baseline hazard function ‘‘differs substantially depending on the prepayment type’’ and that ‘‘the fit of the model can be improved by distinguishing among prepayment types.’’ Ichijo and Moridaira (2006) estimated a Cox proportional hazards model with twenty nine covariates, which consisted of the ratio of a contract rate to a lagged 6-month interest rate, month dummies, and characteristics of a mortgage loan and a mortgagor. They ranked the covariates on the basis of Wald chi-square statistic, and found that loan age, number of prior partial prepayments, and the interest rate ratio were among the top of the list. Kutsuzawa (2007) estimated a Cox proportional hazards model, where he employed seventeen covariates, such as the ratio of a contract rate to the current ARM rate and the characteristics of a mortgage and a mortgagor. In this estimation, he divided data by mortgage types and estimated the model for each type of mortgages separately. Interestingly, he found that the coefficient estimate for the interest rate covariate was positive for fixed-rate mortgages (FRMs) granted by Government Housing Loan Corporation (GHLC), while it was negative for mortgages granted by private FIs.
Our study differs from these studies in two respects: data employed and issues addressed. First, our data are grouped data on pools of GHLC mortgages, while their data are on individual mortgages. In addition, our data are larger, more diversified geographically, and more homogeneous in mortgage types than the data the prior studies employed. In our view, however, it is the issues that make our study more distinct from the prior studies on Japanese mortgage prepayments than the data employed. Specifically, as discussed earlier in this introduction, during the sample period from 1996 to 2005, mortgage interest rates exhibited interesting patterns that might have major effects on full prepayments. Yet, none of the prior studies on Japanese residential mortgages addressed these patterns in relation to prepayments. Hence, we focus on them, especially paying close attention to how full prepayments were related to short- vs. long-term mortgage rates, the slope of yield curve, and the volatility of short-term interest rates. In the next section, we elaborate on the data we employ in this study. The following two sections discuss Poisson regression and its estimation results. In the last section, we conclude the paper. 2. Prepayment data Next, we turn to the prepayment data we analyze. These data are grouped data on 232 pools of FRMs, where each pool was formed by randomly sampling GHLC FRMs that started repayments in the same month (i.e., in a particular month from May 1996 to December 2005) and that had the same type of collaterals (i.e., either single-family homes or condominiums). The mortgages in the same pool have similar contract rates. This is because GHLC had the practice of offering mortgage loans at a narrow range of contract rates, as long as mortgage applicants and collaterals met the GHLC’s minimum requirements. For example, at the end of July 1995, with respect to which we have detailed information on contract rates, GHLC offered a mortgage at either 3.25% or 3.30% rate depending on the type of mortgage and collateral. Furthermore, there are no discount points on Japanese mortgage loans,
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
4 Table 1 Occurrences of full prepayments by year. Year payments started
Number of loans
Year full prepayments occurred
Total
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
17,656 18,396 17,108 24,968 22,126 16,206 8090 4260 2189 299
0
184 0
263 211 0
427 374 174 34
554 470 289 190 62
1329 1250 843 530 413 81
1687 1804 1346 815 836 345 43
1528 1933 1758 1333 1418 766 169 27
939 1210 1249 1288 1475 957 322 83 5
676 804 802 1171 1269 913 373 104 22 1
7587 8056 6461 5361 5473 3062 907 214 27 1
Total
131,298
0
184
474
1009
1565
4446
6876
8932
7528
6135
37,149
Note: Year in this exhibit starts in April and ends in March of the following year, except 1996, which starts in May and ends in March of 1997, and 2005, which starts in April and ends in December.
including GHLC loans. Hence, mortgages in the same pool are fairly homogeneous in terms of effective interest rate. GHLC mortgage loans typically had terms equal to or longer than 20 years at origination. Yet, as shown in Table 1, many of them were fully prepaid within the first few years. For instance, in the pool of single-family home mortgages that started repayment in May 1996, the number of mortgages dwindled from 1275 mortgages in May 1996 to 731 in December 2005. The GHLC prepayment data contain both the number of defaults and the number of full prepayments that were unrelated to default for each pool in each month after the pool was formed. In total, the data show that 1012 defaults and 37,149 full prepayments that were unrelated to default occurred among 131,298 mortgages that comprise the entire sample. Hence, it is safe to say that defaults were rare, but prepayments for other reasons were common among GHLC mortgages. In addition, as pointed out earlier regarding Fig. 1, the particular relationships among various mortgage rates that were observed during the sample period present interesting issues to address in relation to mortgage prepayments. Therefore, we focus our analysis on the effects of interest rates on full prepayments that were unrelated to default. As a final topic in this section, we elaborate on renegotiable mortgages. First, different FIs offer different sets of durations during which initial contract rates are fixed on renegotiable mortgages. But most, if not all, FIs offer renegotiable mortgages where initial contract rates are fixed for the first three, five, or ten years. Second, we illustrate renegotiable mortgages by a hypothetical example. Suppose that Ms. Smith took out a renegotiable mortgage that have a fixed contract rate for the first three years out of its 25year term (3-year renegotiable mortgage) in December 1996. Ms. Smith would pay the interest rate of 2.45% per annum, which was applicable to 3-year renegotiable mortgages in December 1996, over the next three years. Toward the end of the third year, Ms. Smith’s lender would ask Ms. Smith for how many years out of the remaining 22 years she would like to keep the interest rate on her mortgage fixed. Furthermore, the lender would add that Ms. Smith could switch to an ARM without incurring any fees. Suppose that Ms. Smith chose five years. Then, her lender would charge the interest rate of 2.65%, which was applicable to newly originated 5year renegotiable mortgages in December 1999, for the following five years. At the end of the ensuing five-year period, i.e., in December 2004, Ms. Smith would have to make the same decision as she had made in December 1999, and if she chose a relatively short duration during which her renegotiable mortgage has a fixed rate, she would need to make the same decision again in the near future. In short, if a mortgagor refinanced during the sample
period, it is likely that she rolled over short- or medium-term rates several times until she repaid the mortgage completely. 3. Poisson regression Following Schwartz and Torous (1993), we examine our prepayment data by Poisson regression. Namely, we assume that the number y of occurrences of full prepayments that are observed in a GHLC mortgage pool for a month has a Poisson distribution where the intensity of prepayment depends on a set of independent variables. In other words, the probability function of y is given by y
f ðyÞ ¼
el l y!
(1)
where l denotes the intensity parameter for the Poisson distribution. Note that the intensity parameter l can be interpreted as the expected number of prepayments during the month. Hence, it should depend on the number n of loans outstanding in a pool at the beginning of the month. We assume that the intensity parameter l is proportional to n. In addition, we assume that l has a log-linear relationship with a linear equation of independent variables, x0 b. Specifically, 0
l ¼ nex b
(2)
Our specification of Poisson regression yields the following loglikelihood function. k X 0 ðni exi b þ yi ln ni þ yi x0i b ln yi !Þ:
(3)
i¼1
In Eq. (3), i identifies an observation made for a particular pool in a particular month, and k denotes the total number of observations, which is 13,572 in our sample. We estimate a vector b of coefficients by maximizing this log-likelihood function with the Newton–Raphson method. The variance–covariance matrix of parameter estimators is based on the observed information matrix and therefore estimated by obtaining the negative inverse of the matrix of second derivatives of log-likelihood function. Next, we turn to independent variables for Poisson regression. The first independent variable is the ratio of the WAC of a pool to the mortgage rate prevailing in the market a month ago (interest rate ratio, hereafter), where the market mortgage rate is measured by one of the four interest rates illustrated in Fig. 1. We use this ratio as a proxy for the size of refinancing incentive for two reasons. First, as pointed out by Richard and Roll (1989), this ratio
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
approximates the ratio of the present value of mortgage payments to the mortgage balance fairly well if the mortgage has many years until its maturity. Second, if interest rates are very low, as in our sample period, a small change in mortgage rate leads to a nontrivial change in refinancing incentive. This relation is better captured by a ratio than by a difference. Note that because GHLC had the policy of extending mortgages only for newly built or purchased housing, GHLC mortgagors could refinance their mortgages only with private FIs. Furthermore, as pointed out earlier in the introduction, once a mortgagor refinanced her GHLC loan, it is very likely that she would roll over short- or medium-term rates several times before she repaid the mortgage loan completely. Hence, mortgagors who refinanced GHLC mortgages must have taken both future courses and volatilities of short- and medium-term interest rates into serious consideration. To test this hypothesis, we employ the slope of yield curve and the volatility of short-term interest rate as independent variables of Poisson regression. In particular, we measure the slope
5
of yield curve by the difference between 10-year Japanese government bond (JGB) yield and 3-month Treasury bill yield prevailing a month ago, and the volatility of short-term interest rate by the standard deviation of 3-month Treasury bill yield over the most recent six months. Given the expectations hypothesis, the bigger the difference between 10-year and 3-month yields is, the greater the anticipated increases in future short- and mediumterm interest rates are, and the lower the current prepayments are on GHLC loans. Hence, we expect a negative coefficient for the slope of yield curve. In addition, the higher the volatility of shortterm interest rates is, the more uncertain mortgagors feel about future short- and medium-term interest rates, and as a result, the lower the current prepayments are. Therefore, we expect a negative coefficient for the volatility of short-term interest rate. The refinancing decision mortgagors in our sample faced was a choice between keeping the current GHLC FRM and refinancing it with an ARM or a renegotiable mortgage. In this respect, Koijen et al. (2009) is relevant to our study because their finding based on
Table 2 Poisson regression without the volatility of interest rates. Variables
Model 1
Model 2
WAC/ARM
0.7037 (15.66)
0.7287 (16.06)
WAC/3 yr
Model 3
Model 4
Model 5
0.6377 (14.10) 0.5006 (12.75)
WAC/5 yr
0.4926 (12.12)
WAC/10 yr Slope
0.4191 (22.44)
0.4261 (22.76)
0.3282 (16.44)
0.5923 (10.53) 0.3324 (16.44)
BRP Age (10
Model 6
1
)
Age2 (103) Age3 (105) January February (101) March April May June July August September October November Condo
N LR chi-square AIC Adj. pseudo-R2
0.9314 (37.66) 0.7741 (15.93) 0.1451 (5.04) 0.2877 (11.52) 0.3428 (1.29) 0.2963 (12.00) 0.2045 (8.14) 0.1111 (4.35) 0.1064 (4.17) 0.1878 (7.55) 0.1347 (5.37) 0.1562 (6.28) 0.1268 (4.77) 0.2672 (9.71) 0.1287 (8.78)
0.9113 (36.69) 0.7763 (15.95) 0.1629 (5.66) 0.2631 (10.52) 0.0117 (0.04) 0.2725 (11.02) 0.1673 (6.64) 0.0727 (2.84) 0.0508 (1.98) 0.1352 (5.40) 0.1421 (5.66) 0.1925 (7.73) 0.1095 (4.12) 0.2441 (8.86) 0.1276 (8.71)
0.9107 (36.70) 0.7677 (15.80) 0.1598 (5.56) 0.2606 (10.42) 0.0419 (0.16) 0.2659 (10.75) 0.1589 (6.30) 0.0667 (2.60) 0.0453 (1.77) 0.1259 (5.02) 0.1379 (5.49) 0.1909 (7.66) 0.1084 (4.08) 0.2491 (9.04) 0.1187 (8.10)
0.9193 (37.09) 0.7800 (16.08) 0.1694 (5.91) 0.2618 (10.47) 0.0001 (0.00) 0.2715 (10.98) 0.1658 (6.58) 0.0748 (2.92) 0.0509 (1.98) 0.1283 (5.12) 0.1331 (5.30) 0.1786 (7.15) 0.1120 (4.21) 0.2473 (8.98) 0.1181 (8.05)
0.9220 (37.17) 0.7802 (16.07) 0.1661 (5.79) 0.2654 (10.61) 0.0180 (0.07) 0.2672 (10.79) 0.1583 (6.27) 0.0676 (2.63) 0.0432 (1.68) 0.1219 (4.85) 0.1233 (4.89) 0.1750 (7.00) 0.1122 (4.22) 0.2488 (9.03) 0.1133 (7.73)
0.3726 (20.65) 0.9291 (37.44) 0.7931 (16.31) 0.1701 (5.92) 0.2744 (10.98) 0.0758 (0.29) 0.2755 (11.14) 0.1672 (6.63) 0.0719 (2.80) 0.0495 (1.93) 0.1357 (5.42) 0.1393 (5.55) 0.1880 (7.55) 0.1108 (4.17) 0.2465 (8.95) 0.1296 (8.84)
13,572 22,466.3 42,677.8 0.3445
13,572 22,961.6 42,184.4 0.3521
13,572 22,862.3 42,283.8 0.3506
13,572 22,846.0 42,300.1 0.3503
13,572 22,809.9 42,336.2 0.3498
13,572 22,884.7 42,261.3 0.3509
Note: WAC/10 yr (WAC/5 yr, WAC/3 yr, WAC/ARM, respectively) denotes the ratio of WAC to 10-year (5-year, 3-year, ARM, respectively) rate. Slope and BRP denote the slope of yield curve and the bond risk premium, respectively. Age stands for the loan age in months, and Age2 and Age3 are Age squared and cubed, respectively. January to November are month dummies. Condo is the dummy variable for condominium. The values in parentheses are asymptotic t-statistics.
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N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
U.S. data was that mortgagor’s choice between FRM and ARM at origination was explained by the ‘‘bond risk premium,’’ which is, according to Koijent et al. (2009, p. 293), ‘‘the premium earned on investing long in a long-term bond and rolling over a short position in short-term bonds.’’ Therefore, we run a Poisson regression with the bond risk premium added as an independent variable, where the bond risk premium is measured by the difference between 10year JGB yield prevailing a month ago and the average of 3-month Treasury bill yield over the last thirty six months. Incidentally, Koijen et al. (2009, p. 295) call this difference the ‘‘household decision rule’’ as a proxy for the bond risk premium. Note, however, that the mortgagors’ decision problem this paper addresses is not directly comparable to that Koijen et al. (2009) addressed, because, in this paper, mortgagors were to compare short- or medium-term rates with rates on their existing FRM, not with the prevailing rates on FRMs. Hence, we do not predict the sign of the coefficient for the bond risk premium. Additional independent variables for Poisson regression are the age of a mortgage pool, dummy variables for months from January to November to identify in which month of the calendar year prepayments were observed, and a dummy variable for pools of condominiums to distinguish them from pools of single-family homes. Furthermore, to capture nonlinear effects of pool age on prepayments, we add the pool age in months squared and the pool age in months cubed to independent variables. 4. Estimation results The estimation results are tabulated in Tables 2 and 3, where the coefficient estimates of independent variables are shown for twelve specifications (models) of Poisson regression. These models differ in interest-rate-related variables, but have pool age, dummy variables for months, and a dummy variable for condominium in common. All of the coefficients, except the one for the February dummy variable (in all models) and the one for June dummy variable (in Models 2–6), are statistically different from zero at the 1% significance level. Furthermore, as shown in the row titled ‘‘LR chi-square,’’ all models have very large values for the likelihood ratio chi-square, which implies the rejection of the null hypothesis that all coefficients are equal to zero. First, we examine the effects of the interest rate ratio on prepayments in general terms. Tables 2 and 3 show that the coefficient estimate of this variable is positive for all the rates we employ as the market mortgage rate in all specifications of Poisson regression. In other words, no matter which rate we employ as the market mortgage rate, and no matter which specification of Poisson regression we estimate, the lower the market mortgage rate is, the more often prepayments occur. Of course, this finding is consistent with prior studies on U.S. residential mortgages, such as Schwartz and Torous (1989, 1993), Richard and Roll (1989), Pavlov (2001), and Dunsky and Ho (2007). Next, we examine how the choice of the market mortgage rate affects the fit of the Poisson regression to the prepayment data. To this end, we compare Models 2–5 in terms of Akaike information criterion (AIC) and adjusted pseudo-R square (McFadden’s R square adjusted for the number of parameters as suggested by Ben-Akiva and Lerman (1985)). In addition, we compare Models 20 –50 in terms of AIC and adjusted pseudo-R square. These comparisons reveal that the ARM rate provides the best fit to the prepayment data than any of the longer-term interest rates, despite the fact that the ARM rate was stickier than the longer-term rates, as illustrated in Fig. 1. Incidentally, the stickiness of the ARM rate might be a reflection of the fact that the ARM rate is more directly affected by the Bank of Japan’s monetary policy than the longer-term rates. In addition, we examine the effects on prepayments of the slope of yield curve, the bond risk premium, and the interest rate
volatility. The comparison of Model 1 against Model 2 and that of Model 10 against Model 20 reveal that the addition of the slope of yield curve provides an improvement in goodness of fit.8 Similarly, the comparison of Model 6 against Model 2 and that of Model 60 against Model 20 uncover that the addition of the bond risk premium provides an improvement in goodness of fit that is almost comparable to the addition of the slope of yield curve. Yet, the most striking point about Tables 2 and 3 is that the interest rate volatility boost both AIC and adjusted pseudo-R square uniformly across all models. In short, the estimation results are consistent with our predictions about the effects on prepayments of the slope of yield curve and the interest rate volatility. Namely, the steeper the slope of yield curve is, the less often mortgage prepayments occur. The greater the interest rate volatility is, the less often mortgage prepayments occur. In addition, among all the specifications of Poisson regression, Model 20 in Table 3 has the best fit to the prepayment data. Therefore, we will employ Model 20 as a basis for our discussion. Before we turn to the next topic, we evaluate the economic significance of the interest rate ratio. For this purpose, we note that the intensity parameter l of Poisson regression gives the average number of occurrences of prepayments in a month. Furthermore, 0 by dividing Eq. (2) by n we have l/n being equal to ex b . Combining these facts, we see that the average prepayment rate, as measured 0 by l/n, is given by ex b . Based on this relationship, we can make some judgment about the economic significance of the interest rate ratio effects on prepayments. Specifically, let us take an example of the pool of single-family home mortgages that started repayments in May 1996. It had a WAC of 3.277% at the beginning of May 2003 when the ARM rate in the preceding month was 0 2.375%. Hence, the multiplicative factor of ex b attributable to the interest rate ratio is given by the exponential of 1.2963 3.277/ 2.375, where 1.2963 is the coefficient estimate of the interest rate ratio with the ARM rate being used as the market mortgage rate, as shown in Model 20 in Table 3. Now, assume that the ARM rate in April 2003 was higher than the actually observed rate by 50 basis points, that is, 2.375% +0.5 % =2.875 %. Then, the multiplicative 0 factor of ex b attributable to the interest rate ratio would have been given by the exponential of 1.2963 3.277/2.875, which is 21% less than 1.2963 3.277/2.375. In other words, other things being equal, the average prepayment rate, as measured by l/n, would have been 21% less if the ARM rate was higher than the actually observed rate by 50 basis points. Next, we turn to the effects of the age of a mortgage pool on prepayments. Fig. 2 draws the prepayment intensity as a function of the pool age in month, where all the other independent variables of Poisson regression are assumed to be zero, and the coefficient estimates of age-related variables are based on those of Model 20 . This figure indicates that the prepayment intensity increases initially, peaks in the seventy second month, and decreases gradually afterward. This pattern is roughly consistent with prior studies on U.S. residential mortgages. Note, however, that the month when the prepayment intensity peaks differs across studies; it is approximately seventy fifth month in Schwartz and Torous (1989), eighty fourth month in ‘‘Model 1’’ of Schwartz and Torous (1993), and approximately sixtieth month in Dunsky and Ho (2007). Considering that the peak month estimated by the U.S. studies cluster around the peak month we estimate for the Japanese mortgages, we can safely say that the pattern of prepayment intensity in relation to mortgage age is the same between U.S. and Japanese mortgages.
8 The addition of the slope of yield curve improves the goodness of fit in other specifications of Poisson regression where the ARM rate is replaced by 3-, 5-, or 10year rate.
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
7
Table 3 Poisson regression with the volatility of interest rates. Variables
Model 10
Model 20
WAC/ARM
1.3034 (26.79)
1.2963 (26.46)
WAC/3 yr
Model 30
Model 40
Model 50
1.2191 (24.87) 1.0018 (23.60)
WAC/5 yr
1.0125 (23.16)
WAC/10 yr Slope
0.3509 (19.04)
0.3691 (20.00)
0.1661 (8.22)
1.5354 (24.24) 0.1262 (6.10)
BRP Volatility Age (101) Age2 (103) Age3 (105) January February (101) March April May June July August September October November Condo
N LR chi-square AIC Adj. pseudo-R2
Model 60
7.2219 (33.80) 0.8940 (35.90) 0.8373 (17.15) 0.1966 (6.80) 0.3028 (12.12) 0.3765 (1.42) 0.2958 (11.97) 0.2300 (9.15) 0.1573 (6.15) 0.1627 (6.38) 0.2115 (8.50) 0.1459 (5.81) 0.1221 (4.91) 0.1487 (5.59) 0.2787 (10.12) 0.0990 (6.75)
6.7782 (32.14) 0.8815 (35.26) 0.8409 (17.19) 0.2117 (7.32) 0.2796 (11.18) 0.0393 (0.15) 0.2721 (11.00) 0.1971 (7.82) 0.1195 (4.66) 0.1103 (4.30) 0.1671 (6.67) 0.1493 (5.95) 0.1526 (6.12) 0.1352 (5.08) 0.2583 (9.38) 0.0994 (6.77)
6.6523 (31.38) 0.8796 (35.23) 0.8220 (16.84) 0.2021 (7.01) 0.2724 (10.89) 0.0488 (0.18) 0.2593 (10.48) 0.1827 (7.25) 0.1081 (4.21) 0.0986 (3.84) 0.1488 (5.94) 0.1416 (5.64) 0.1507 (6.05) 0.1341 (5.04) 0.2684 (9.74) 0.0927 (6.32)
6.6388 (31.26) 0.8977 (36.05) 0.8488 (17.44) 0.2224 (7.74) 0.2739 (10.95) 0.0319 (0.12) 0.2699 (10.91) 0.1950 (7.74) 0.1251 (4.87) 0.1081 (4.21) 0.1514 (6.05) 0.1317 (5.25) 0.1235 (4.94) 0.1420 (5.34) 0.2653 (9.63) 0.0939 (6.39)
7.1383 (32.48) 0.9060 (36.33) 0.8636 (17.71) 0.2220 (7.72) 0.2756 (11.02) 0.0820 (0.31) 0.2497 (10.08) 0.1703 (6.75) 0.1009 (3.93) 0.0786 (3.05) 0.1222 (4.86) 0.0924 (3.66) 0.0969 (3.86) 0.1498 (5.63) 0.2732 (9.91) 0.0931 (6.35)
0.3001 (16.69) 6.7935 (32.05) 0.8943 (35.82) 0.8504 (17.41) 0.2150 (7.45) 0.2888 (11.56) 0.1298 (0.49) 0.2769 (11.20) 0.2009 (7.97) 0.1237 (4.82) 0.1153 (4.49) 0.1725 (6.89) 0.1496 (5.96) 0.1489 (5.98) 0.1369 (5.15) 0.2621 (9.52) 0.1015 (6.91)
13,572 23,810.5 41,335.5 0.3651
13,572 24,168.6 40,979.5 0.3706
13,572 24,010.0 41,138.1 0.3682
13,572 23,985.0 41,163.1 0.3678
13,572 24,041.5 41,106.6 0.3687
13,572 24,085.3 41,062.8 0.3693
Note: Volatility denotes the volatility of interest rates. The remaining variables are defined as in Table 2. The values in parentheses are asymptotic t-statistics.
Fig. 3 illustrates the coefficient estimates of dummy variables for months of the year based on the estimation results of Model 20 . It shows that mortgagors have the tendency to prepay more in January and March and less in February, October, November, and December than in other months. As seen in the Model 20 column of Table 3, this seasonal pattern is statistically significant except February. We can conjecture that several institutional arrangements in Japan are responsible for this pattern. First, a mortgagor is allowed to deduct a fixed percentage of her mortgage balance at the end of a calendar year from her income tax.9 Hence, mortgagors 9 The tax credit system for mortgage balances changed five times during our sample period. More specifically, the fixed percentage was changed within a range of 0.5–2% and the period during which the fixed percentage of the mortgage balance was deductible from income tax was changed within a range of the initial five to the initial fifteen years of the mortgage term. Therefore, in order to confirm the robustness of the seasonal pattern of prepayments, we run Model 20 in Table 3 for each of the six sub-periods of the sample period. We find that the seasonal pattern of prepayments is fairly stable under different tax credit systems and consistent with Fig. 3.
wishing to prepay would avoid prepaying in the last few months of the year and prepay in the first few months of the year. Second, academic years of practically all academic institutions as well as fiscal years of many corporations start at the beginning of April and end at the end of March. Hence, moving related to relocation, and as a result, prepayments due to moving, tend to occur in March. Third, it is a common practice in Japan that employers, both private and public, pay their full-time employees bonuses toward the ends of June and December, typically with December bonuses bigger than June bonuses. Hence, if the balance of a mortgage loan is small, probably because it was small at origination or because the mortgagor has prepaid a large proportion of the initial mortgage balance by prior partial prepayments, a full prepayment of the loan is more likely to occur after the mortgagor receives a bonus, i.e., in January and July than in other months. Finally, we make observations about the dummy variable for condos. As shown in Tables 2 and 3, the coefficient estimate for the condo dummy variable is statistically significant and fairly stable across all models. Generally speaking, mortgagors of condos are
8
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
Fig. 2. Baseline prepayment function.
Fig. 3. Coefficient estimates for month dummies.
younger and have smaller families than those of single-family homes. In addition, mortgagors of condos tend to live in big cities, while mortgagors of single-family homes are dispersed across Japan. Therefore, the former tends to be more mobile than the latter, which is consistent with our finding of a positive coefficient for the condo dummy. 5. Conclusions In this paper, we investigate full prepayments of Japanese residential mortgages granted by Government Housing Loan Corporation (GHLC) over a ten-year period from 1996 to 2005. This investigation is important because the amount of mortgages outstanding in Japan is huge, yet the study on their prepayments is scarce. In this study, we pay close attention to two features of interest rate relationships which were observed during the sample
period and which might be relevant to full prepayments of fixed rate mortgages. First, interest rates fluctuated within a narrow range of a little over 1%. Surprisingly, full prepayments of Japanese mortgages were sensitive to small changes in interest rates. Second, long-term refinance rates did not fall well below the contract rates of most mortgages in our sample throughout this ten-year period, while short- and medium-term refinance rates did. With this interest rate relationship, if mortgagors ever refinanced GHLC mortgages, they would refinance them by mortgages where initial interest rates were pegged to shorterterm rates. Hence, we examine the sensitivity of full prepayments to short- vs. long-term mortgage rates, slope of yield curve, bond risk premium, and interest rate volatility. We find that the shortterm mortgage rate provides a slightly better fit of Poisson model to the prepayment data than longer-term mortgage rates. Also, the addition of the slope of yield curve or the bond risk premium
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
improves the goodness of fit. Furthermore, the addition of the volatility of short-term interest rate improves the goodness of fit considerably across all models. In addition, the age of mortgage pool has a considerable power of explaining the occurrences of full prepayments. Specifically, the prepayment intensity increases initially as the pool ages, peaks in seventy two months after the origination of the pool, and decreases gradually afterward. Our estimation results provide convincing evidence that mortgagors in Japan have the tendency to prepay more in January and March and less in February, October, November, and December than in other months. We conjecture that several institutional arrangements in Japan may be responsible for this seasonal pattern. They include the prevalence of regularly paid bonuses, tax credit on mortgage balances, and the beginning and ending of typical fiscal and academic years of Japanese institutions. Acknowledgements We thank Housing Loan Progress Association, an affiliate of Government Housing Loan Corporation (GHLC), for providing us Housing and Finance Forum scholarship and GHLC prepayment data. In addition, we thank Stephen Brown, William Greene, Hideaki Hirata, Thomas Ho, and Mari Matsumoto for helpful discussion.
9
References Ben-Akiva, M., Lerman, S., 1985. Discrete Choice Analysis: Theory and Application to Travel Demand. MIT Press, Cambridge. Deng, Y., Quigley, J., Van Order, R., 2000. Mortgage terminations, heterogeneity and the exercise of mortgage options. Econometrica 68, 275–307. Dunsky, R., Ho, T., 2007. Valuing fixed rate mortgage loans with default and prepayment options. Journal of Fixed Income 16, 7–31. Fabozzi, F., Modigliani, F., 1992. Mortgage and Mortgage-Backed Securities Markets. Harvard Business School Press, Boston. Green, J., Shoven, J., 1986. The effects of interest rates on mortgage prepayments. Journal of Money, Credit, and Banking 18, 41–59. Ichijo, H., Moridaira, S., 2006. Analysis of prepayments of residential mortgage loans. Journal of Real Estate Financial Engineering 2006, 221–246 (in Japanese). Koijen, R., Van Hemert, O., Van Nieuwerburgh, S., 2009. Mortgage timing. Journal of Financial Economics 93, 292–324. Kutsuzawa, R., 2007. Analysis of mortgage prepayment, refinancing, and delay of payment. Urban Housing Sciences 58, 66–75 (in Japanese). Pavlov, A., 2001. Competing risks of mortgage termination: who refinances, who moves, and who defaults? Journal of Real Estate Finance and Economics 23, 185–211. Richard, S., Roll, R., 1989. Prepayments on fixed-rate mortgage-backed securities. Journal of Portfolio Management 15, 73–82. Schwartz, E., Torous, W., 1989. Prepayment and the valuation of mortgage-backed securities. Journal of Finance 44, 375–392. Schwartz, E., Torous, W., 1993. Mortgage prepayment and default decisions: a Poisson regression approach. Journal of the American Real Estate and Urban Economics Association 21, 431–449. Sugimura, T., 2002. A prepayment model for the Japanese mortgage loan market: prepayment-type-specific parametric model approach. Asia-Pacific Financial Markets 9, 305–335.
Contents lists available at ScienceDirect
Japan and the World Economy journal homepage: www.elsevier.com/locate/jwe
Prepayment behaviors of Japanese residential mortgages Naoki Kishimoto 1, Yong-Jin Kim * Faculty of Business Administration, Hosei University, 2-17-1 Fujimi, Chiyoda-ku, Tokyo 102-8160, Japan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 4 March 2013 Received in revised form 11 November 2013 Accepted 31 December 2013 Available online 15 January 2014
We investigate full prepayments of Japanese residential mortgages during a ten-year period from 1996 to 2005. This investigation is important because the amount of mortgages outstanding in Japan is huge, yet the study on their prepayments is very limited. This period from 1996 to 2005 was characterized by two distinct features of the evolution of interest rates that might have significant effects on mortgage refinancing. First, interest rate fluctuations were limited to a narrow range of a little over 1%. Surprisingly, full prepayments of Japanese mortgages were sensitive to small changes in interest rates. Second, long-term refinance rates did not fall well below the contract rates of most mortgages in our sample during the ten-year period, while short-term refinance rates did. With this interest rate relationship, if mortgagors ever refinanced, it was likely that they rolled over shortterm mortgage rates several times until they repaid mortgages completely. Hence, we examine the sensitivity of full prepayments to short-term vs. long-term interest rates, mortgagors’ expectation of future course of interest rates (by the slope of yield curve), and that of interest rate volatility. Our analysis shows that short-term interest rates have a slightly greater explanatory power for full prepayments than long-term interest rates. In addition, our analysis confirms that full prepayments are sensitive to both the slope of yield curve and interest rate volatility. Other issues we look into are the patterns of full prepayments in relation to loan age and seasonality. We find that the pattern of full prepayments relative to loan age is comparable to that of mortgages in the U.S., and that the seasonal pattern of full prepayments is attributable to relevant institutional arrangements in Japan. ß 2014 Elsevier B.V. All rights reserved.
JEL classification: D14 G21 G15 Keywords: Prepayment behavior Japanese residential mortgages Refinance
Prepayments of residential mortgages considerably alter the pattern of cash flows the holders of the mortgages receive. As a result, they pose major risk to the holders of mortgages, such as financial institutions (FIs) holding mortgages directly, and investors in mortgage-backed securities (MBSs). Hence, the questions such as how common prepayments are and how prepayments are related to interest rate movements are of critical importance to these mortgage investors with regard to their risk management as well as the pricing of mortgages and MBSs. It should be noted that the economic significance of this risk is substantial because massive amounts of residential mortgages are outstanding. For example, at the end of 2011, the amount of U.S.
home mortgages of the household sector was 9840 billion dollars, which was well above the corporate debt of 7800 billion dollars and a little below the Federal government debt of 10,453 billion dollars. Similarly, at the end of 2011, the total balance of Japanese residential mortgages was 207 trillion yen, which was approximately a half of the entire debt (402 trillion yen) of the private nonfinancial corporate sector and one fifth of national government debt (887 trillion yen).2 These facts warrant serious investigation into prepayments of residential mortgages. Indeed, many researchers have looked into prepayments of U.S. residential mortgages. A partial list of them includes Green and Shoven (1986), Schwartz and Torous (1989, 1993), Deng et al. (2000), and Dunsky and Ho (2007). By sharp contrast, such studies on Japanese residential mortgages are
* Corresponding author. Tel.: +81 3 3264 4562; fax: +81 3 3264 9698. E-mail addresses: [email protected] (N. Kishimoto), [email protected] (Y.-J. Kim). 1 Tel.: +81 3 3264 9733; fax: +81 3 3264 9698.
2 These numbers are based on Flow of Funds Accounts of the United States Fourth Quarter 2011, downloadable at http://www.federalreserve.gov/releases/z1/ 20120308/ and Japan’s Flow of Funds Accounts, downloadable at http://www.boj.or.jp/en/statistics/sj/index.htm/.
1. Introduction
0922-1425/$ – see front matter ß 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.japwor.2013.12.002
2
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
minimal. Specifically, to our best knowledge, publicly available studies on prepayments of Japanese residential mortgages are limited to only three academic papers: Sugimura (2002), Ichijo and Moridaira (2006), and Kutsuzawa (2007).3 Before we describe these studies on prepayments of Japanese residential mortgages, we point out a few distinct features of mortgage interest rates that are observed during the sample period from May 1996 to December 2005. Fig. 1 plots four interest rates in each month of the sample period. In this figure, WAC represents the weighted average coupon (WAC) of mortgages in our sample that started repayments in the same month. ARM rate stands for the average of interest rates on adjustable rate mortgages (ARMs) that are offered in the same month. 3-, 5- and 10-year rates are the averages of interest rates on mortgages which have fixed interest rates for the first 3, 5, and 10 years of mortgage terms, respectively, and which are offered in the same month. Incidentally, the ARM rates are compiled by the Bank of Japan, and the 3-, 5- and 10-year rates are compiled by Japan Financial News Co. Ltd. Also, in this paper, we refer to mortgages that have fixed interest rates for the first few years of mortgage terms as renegotiable mortgages. Fig. 1 reveals that interest rate movements during the sample period exhibited three features we ought to pay close attention to. First, all of the five time series showed little variation during this 10-year period. Specifically, the differences between the maximum and minimum values during this period of WAC, ARM, 3-year, 5year, and 10-year rates were 1.19%, 0.25%, 1.1%, 1.3%, and 1.32%, respectively. These changes are small compared to changes in mortgage interest rates in other developed countries. For example, according to Freddie Mac’s ‘‘Primary Mortgage Market Survey Archives,’’ the differences between the maximum and minimum values during our sample period of U.S. 1-year adjustable, 15-year fixed, and 30-year fixed rates were 3.875%, 3.55%, and 3.29%, respectively.4 Similarly, according to a Deutsche Bundesbank’s publication, the differences between the maximum and minimum values during our sample period of German variable, 5-year fixed, and 10-year fixed rates were 2.71%, 2.65%, and 3.53%, respectively.5 Second, the 10-year rate was above the concurrent WAC in every month of the sample period.6 Furthermore, the 10-year rate offered 3 Publicly available studies on prepayments of Japanese residential mortgages are rare mainly because Japanese FIs have been reluctant to give prepayment data to outsiders, including academicians. Sugimura (2002) and Ichijo and Moridaira (2006) could avoid this problem by obtaining in-house data from different FIs Sugimura and Ichijo worked for, while Kutsuzawa (2007) could do so by conducting an Internet survey of mortgage prepayments. We are fortunate that we could obtain Government Housing Loan Corporation (GHLC) prepayment data as recipients of a scholarship from GHLC’s affiliate, Housing Loan Progress Association, while GHLC had the policy to give the scholarship recipients access to its prepayment data. Note, however, that GHLC ended compiling prepayment data in the format that is amenable to our study shortly after we obtained the prepayment data. Currently, GHLC’s successor, Japan Housing Finance Agency, compiles aggregate prepayment data on its MBSs, each of which consist of mortgage loans with various contract rates and diverse stated maturities. 4 Freddie Mac’s Primary Mortgage Market Survey Archives are found at http:// www.freddiemac.com/pmms/pmms_archives.html. 5 This publication is published as a pdf file titled ‘‘Housing loans to households/ Mortgage loans secured by residential real estate,’’ which is downloadable at http:// www.bundesbank.de/Navigation/EN/Statistics/Money_and_capital_markets/Interest_rates_and_yields/Interest_rates_on_deposits_and_loans_nterest_rates_on_deposits_and_loans.html. 6 Newly originated GHLC mortgages typically had 20 years or longer until maturity and the yield curve based on Japanese government bonds was upward sloping throughout the sample period. Hence, the fact that the WAC was below the concurrent 10-year mortgage rate implies that GHLC mortgages were offered below the interest rates that would prevail in a competitive mortgage market. In fact, the financial statements of GHLC show that the GHLC could offer low rates due to the Japanese Government’s subsidy. For example, in the fiscal year ending in March 2005, GHLC received over 404 billion yen from the Japanese government, which helped fill the gap between GHLC’s interest expenses of 2073 billion yen and interest revenues of 1816 billion yen.
in any month was never lower than the WAC of any mortgage pool that had been formed prior to that month by more than 35 basis points. Third, all of the 5-year, 3-year, and ARM rates were below the concurrent WAC of mortgage pools for most of the 10-year period, although none of the 5-year, 3-year, and ARM rates in any month of the sample period were lower than the WACs of mortgage pools that had been formed prior to that month by more than 135 basis points. According to Fabozzi and Modigliani (1992, p. 198), ‘‘historically, it has been observed that when mortgage rates fall to more than 200 bp below the contract rate, prepayment rates increase.’’ Given this historical fact, the observations made in Fig. 1 lead to a question: how sensitive mortgage refinancing was to interest rate movements during the sample period? Note that the prepayment data that are available to us do not distinguish prepayments due to refinancing from full prepayments due to other reasons, such as moving. Hence, we analyze full prepayments instead of refinancing. Note also that because full prepayments due to moving and default are less frequent than and not as closely related to interest rate movements as those due to refinancing, the effects of interest rates on full prepayments are likely to be found weaker than the effects of interest rates on refinancing. In this sense, it is not so bad to analyze full prepayments in order to obtain insights on the effects of interest rates on refinancing. In addition, our prepayment data are grouped data. Hence, we follow Schwartz and Torous (1993) in running Poisson regression, where the dependent variable is the number of occurrences of full prepayments in a month and the independent variables are a variety of interest-rate-related variables and other variables.7 We find that the coefficients of the interest rate variables are statistically significant and their values are fairly stable across various specifications of Poisson regression. The second and third observations in Fig. 1 imply that if a mortgage loan was prepaid due to refinancing, it is most likely that it was refinanced by an ARM or a renegotiable mortgage. This conjecture, in turn, implies that mortgagors who were considering refinancing were more concerned about short- and medium-term mortgage rates than long-term mortgage rates. To examine this hypothesis, we run various specifications of Poisson regression where a long-term mortgage rate is replaced by a short- or medium-term mortgage rate as an independent variable. The estimation results turn out to be in favor of this hypothesis. In addition, as we will see in detail in the next section, if a mortgagor refinances a mortgage loan by an ARM or a renegotiable mortgage, she is most likely to roll over a series of short- and/or medium-term rates in the future until she repays the mortgage completely. Hence, it is plausible that mortgagors’ expectation of both future course and volatility of interest rates has direct effects on mortgagors’ decision on refinancing. Therefore, we include the slope of Japanese government bond yield curve and the standard deviation of Japanese Treasury bill as additional independent variables of Poisson regression. It is confirmed that the estimation results are consistent with this hypothesis. Furthermore, it is well known that the age of a mortgage pool and dummy variables for months of the year exert strong influence on full prepayments. Hence, we include them as additional independent variables of Poisson regression to control the effects of them on prepayments. The estimation results indicate that the pattern of full prepayments relative to mortgage pool age is comparable to that for U.S. mortgages. In particular, the prepayment intensity increases consistently for the first seventy two months and declines gradually afterward. Furthermore, we have 7 In addition, we ran logit regression for grouped data and obtained results similar to the ones from Poisson regression, which are shown in Tables 2 and 3.
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3
Fig. 1. Residential mortgage rates. Sources: GHLC, Japan Financial News Co. Ltd., and The Bank of Japan.
identified several seasonal characteristics of full prepayments, which are attributable to various institutional arrangements in Japan. These arrangements include regularly paid bonuses, the tax saving effects of mortgage balances, and fiscal and academic years in Japan. Next, we briefly summarize the prior studies on the prepayments of Japanese residential mortgages and compare them with our study. First, Sugimura (2002) used data on individual mortgages to estimate Cox proportional hazards models where the time that passed from either origination or a prior partial prepayment, if any, to the next partial or full prepayment was examined with regard to a baseline hazard function, two interestrate-related variables, the time to maturity of a mortgage loan, and the age of a mortgagor. He estimated this model for each type of prepayments (full prepayments, partial prepayments, and defaults) separately, and found that the baseline hazard function ‘‘differs substantially depending on the prepayment type’’ and that ‘‘the fit of the model can be improved by distinguishing among prepayment types.’’ Ichijo and Moridaira (2006) estimated a Cox proportional hazards model with twenty nine covariates, which consisted of the ratio of a contract rate to a lagged 6-month interest rate, month dummies, and characteristics of a mortgage loan and a mortgagor. They ranked the covariates on the basis of Wald chi-square statistic, and found that loan age, number of prior partial prepayments, and the interest rate ratio were among the top of the list. Kutsuzawa (2007) estimated a Cox proportional hazards model, where he employed seventeen covariates, such as the ratio of a contract rate to the current ARM rate and the characteristics of a mortgage and a mortgagor. In this estimation, he divided data by mortgage types and estimated the model for each type of mortgages separately. Interestingly, he found that the coefficient estimate for the interest rate covariate was positive for fixed-rate mortgages (FRMs) granted by Government Housing Loan Corporation (GHLC), while it was negative for mortgages granted by private FIs.
Our study differs from these studies in two respects: data employed and issues addressed. First, our data are grouped data on pools of GHLC mortgages, while their data are on individual mortgages. In addition, our data are larger, more diversified geographically, and more homogeneous in mortgage types than the data the prior studies employed. In our view, however, it is the issues that make our study more distinct from the prior studies on Japanese mortgage prepayments than the data employed. Specifically, as discussed earlier in this introduction, during the sample period from 1996 to 2005, mortgage interest rates exhibited interesting patterns that might have major effects on full prepayments. Yet, none of the prior studies on Japanese residential mortgages addressed these patterns in relation to prepayments. Hence, we focus on them, especially paying close attention to how full prepayments were related to short- vs. long-term mortgage rates, the slope of yield curve, and the volatility of short-term interest rates. In the next section, we elaborate on the data we employ in this study. The following two sections discuss Poisson regression and its estimation results. In the last section, we conclude the paper. 2. Prepayment data Next, we turn to the prepayment data we analyze. These data are grouped data on 232 pools of FRMs, where each pool was formed by randomly sampling GHLC FRMs that started repayments in the same month (i.e., in a particular month from May 1996 to December 2005) and that had the same type of collaterals (i.e., either single-family homes or condominiums). The mortgages in the same pool have similar contract rates. This is because GHLC had the practice of offering mortgage loans at a narrow range of contract rates, as long as mortgage applicants and collaterals met the GHLC’s minimum requirements. For example, at the end of July 1995, with respect to which we have detailed information on contract rates, GHLC offered a mortgage at either 3.25% or 3.30% rate depending on the type of mortgage and collateral. Furthermore, there are no discount points on Japanese mortgage loans,
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
4 Table 1 Occurrences of full prepayments by year. Year payments started
Number of loans
Year full prepayments occurred
Total
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
17,656 18,396 17,108 24,968 22,126 16,206 8090 4260 2189 299
0
184 0
263 211 0
427 374 174 34
554 470 289 190 62
1329 1250 843 530 413 81
1687 1804 1346 815 836 345 43
1528 1933 1758 1333 1418 766 169 27
939 1210 1249 1288 1475 957 322 83 5
676 804 802 1171 1269 913 373 104 22 1
7587 8056 6461 5361 5473 3062 907 214 27 1
Total
131,298
0
184
474
1009
1565
4446
6876
8932
7528
6135
37,149
Note: Year in this exhibit starts in April and ends in March of the following year, except 1996, which starts in May and ends in March of 1997, and 2005, which starts in April and ends in December.
including GHLC loans. Hence, mortgages in the same pool are fairly homogeneous in terms of effective interest rate. GHLC mortgage loans typically had terms equal to or longer than 20 years at origination. Yet, as shown in Table 1, many of them were fully prepaid within the first few years. For instance, in the pool of single-family home mortgages that started repayment in May 1996, the number of mortgages dwindled from 1275 mortgages in May 1996 to 731 in December 2005. The GHLC prepayment data contain both the number of defaults and the number of full prepayments that were unrelated to default for each pool in each month after the pool was formed. In total, the data show that 1012 defaults and 37,149 full prepayments that were unrelated to default occurred among 131,298 mortgages that comprise the entire sample. Hence, it is safe to say that defaults were rare, but prepayments for other reasons were common among GHLC mortgages. In addition, as pointed out earlier regarding Fig. 1, the particular relationships among various mortgage rates that were observed during the sample period present interesting issues to address in relation to mortgage prepayments. Therefore, we focus our analysis on the effects of interest rates on full prepayments that were unrelated to default. As a final topic in this section, we elaborate on renegotiable mortgages. First, different FIs offer different sets of durations during which initial contract rates are fixed on renegotiable mortgages. But most, if not all, FIs offer renegotiable mortgages where initial contract rates are fixed for the first three, five, or ten years. Second, we illustrate renegotiable mortgages by a hypothetical example. Suppose that Ms. Smith took out a renegotiable mortgage that have a fixed contract rate for the first three years out of its 25year term (3-year renegotiable mortgage) in December 1996. Ms. Smith would pay the interest rate of 2.45% per annum, which was applicable to 3-year renegotiable mortgages in December 1996, over the next three years. Toward the end of the third year, Ms. Smith’s lender would ask Ms. Smith for how many years out of the remaining 22 years she would like to keep the interest rate on her mortgage fixed. Furthermore, the lender would add that Ms. Smith could switch to an ARM without incurring any fees. Suppose that Ms. Smith chose five years. Then, her lender would charge the interest rate of 2.65%, which was applicable to newly originated 5year renegotiable mortgages in December 1999, for the following five years. At the end of the ensuing five-year period, i.e., in December 2004, Ms. Smith would have to make the same decision as she had made in December 1999, and if she chose a relatively short duration during which her renegotiable mortgage has a fixed rate, she would need to make the same decision again in the near future. In short, if a mortgagor refinanced during the sample
period, it is likely that she rolled over short- or medium-term rates several times until she repaid the mortgage completely. 3. Poisson regression Following Schwartz and Torous (1993), we examine our prepayment data by Poisson regression. Namely, we assume that the number y of occurrences of full prepayments that are observed in a GHLC mortgage pool for a month has a Poisson distribution where the intensity of prepayment depends on a set of independent variables. In other words, the probability function of y is given by y
f ðyÞ ¼
el l y!
(1)
where l denotes the intensity parameter for the Poisson distribution. Note that the intensity parameter l can be interpreted as the expected number of prepayments during the month. Hence, it should depend on the number n of loans outstanding in a pool at the beginning of the month. We assume that the intensity parameter l is proportional to n. In addition, we assume that l has a log-linear relationship with a linear equation of independent variables, x0 b. Specifically, 0
l ¼ nex b
(2)
Our specification of Poisson regression yields the following loglikelihood function. k X 0 ðni exi b þ yi ln ni þ yi x0i b ln yi !Þ:
(3)
i¼1
In Eq. (3), i identifies an observation made for a particular pool in a particular month, and k denotes the total number of observations, which is 13,572 in our sample. We estimate a vector b of coefficients by maximizing this log-likelihood function with the Newton–Raphson method. The variance–covariance matrix of parameter estimators is based on the observed information matrix and therefore estimated by obtaining the negative inverse of the matrix of second derivatives of log-likelihood function. Next, we turn to independent variables for Poisson regression. The first independent variable is the ratio of the WAC of a pool to the mortgage rate prevailing in the market a month ago (interest rate ratio, hereafter), where the market mortgage rate is measured by one of the four interest rates illustrated in Fig. 1. We use this ratio as a proxy for the size of refinancing incentive for two reasons. First, as pointed out by Richard and Roll (1989), this ratio
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
approximates the ratio of the present value of mortgage payments to the mortgage balance fairly well if the mortgage has many years until its maturity. Second, if interest rates are very low, as in our sample period, a small change in mortgage rate leads to a nontrivial change in refinancing incentive. This relation is better captured by a ratio than by a difference. Note that because GHLC had the policy of extending mortgages only for newly built or purchased housing, GHLC mortgagors could refinance their mortgages only with private FIs. Furthermore, as pointed out earlier in the introduction, once a mortgagor refinanced her GHLC loan, it is very likely that she would roll over short- or medium-term rates several times before she repaid the mortgage loan completely. Hence, mortgagors who refinanced GHLC mortgages must have taken both future courses and volatilities of short- and medium-term interest rates into serious consideration. To test this hypothesis, we employ the slope of yield curve and the volatility of short-term interest rate as independent variables of Poisson regression. In particular, we measure the slope
5
of yield curve by the difference between 10-year Japanese government bond (JGB) yield and 3-month Treasury bill yield prevailing a month ago, and the volatility of short-term interest rate by the standard deviation of 3-month Treasury bill yield over the most recent six months. Given the expectations hypothesis, the bigger the difference between 10-year and 3-month yields is, the greater the anticipated increases in future short- and mediumterm interest rates are, and the lower the current prepayments are on GHLC loans. Hence, we expect a negative coefficient for the slope of yield curve. In addition, the higher the volatility of shortterm interest rates is, the more uncertain mortgagors feel about future short- and medium-term interest rates, and as a result, the lower the current prepayments are. Therefore, we expect a negative coefficient for the volatility of short-term interest rate. The refinancing decision mortgagors in our sample faced was a choice between keeping the current GHLC FRM and refinancing it with an ARM or a renegotiable mortgage. In this respect, Koijen et al. (2009) is relevant to our study because their finding based on
Table 2 Poisson regression without the volatility of interest rates. Variables
Model 1
Model 2
WAC/ARM
0.7037 (15.66)
0.7287 (16.06)
WAC/3 yr
Model 3
Model 4
Model 5
0.6377 (14.10) 0.5006 (12.75)
WAC/5 yr
0.4926 (12.12)
WAC/10 yr Slope
0.4191 (22.44)
0.4261 (22.76)
0.3282 (16.44)
0.5923 (10.53) 0.3324 (16.44)
BRP Age (10
Model 6
1
)
Age2 (103) Age3 (105) January February (101) March April May June July August September October November Condo
N LR chi-square AIC Adj. pseudo-R2
0.9314 (37.66) 0.7741 (15.93) 0.1451 (5.04) 0.2877 (11.52) 0.3428 (1.29) 0.2963 (12.00) 0.2045 (8.14) 0.1111 (4.35) 0.1064 (4.17) 0.1878 (7.55) 0.1347 (5.37) 0.1562 (6.28) 0.1268 (4.77) 0.2672 (9.71) 0.1287 (8.78)
0.9113 (36.69) 0.7763 (15.95) 0.1629 (5.66) 0.2631 (10.52) 0.0117 (0.04) 0.2725 (11.02) 0.1673 (6.64) 0.0727 (2.84) 0.0508 (1.98) 0.1352 (5.40) 0.1421 (5.66) 0.1925 (7.73) 0.1095 (4.12) 0.2441 (8.86) 0.1276 (8.71)
0.9107 (36.70) 0.7677 (15.80) 0.1598 (5.56) 0.2606 (10.42) 0.0419 (0.16) 0.2659 (10.75) 0.1589 (6.30) 0.0667 (2.60) 0.0453 (1.77) 0.1259 (5.02) 0.1379 (5.49) 0.1909 (7.66) 0.1084 (4.08) 0.2491 (9.04) 0.1187 (8.10)
0.9193 (37.09) 0.7800 (16.08) 0.1694 (5.91) 0.2618 (10.47) 0.0001 (0.00) 0.2715 (10.98) 0.1658 (6.58) 0.0748 (2.92) 0.0509 (1.98) 0.1283 (5.12) 0.1331 (5.30) 0.1786 (7.15) 0.1120 (4.21) 0.2473 (8.98) 0.1181 (8.05)
0.9220 (37.17) 0.7802 (16.07) 0.1661 (5.79) 0.2654 (10.61) 0.0180 (0.07) 0.2672 (10.79) 0.1583 (6.27) 0.0676 (2.63) 0.0432 (1.68) 0.1219 (4.85) 0.1233 (4.89) 0.1750 (7.00) 0.1122 (4.22) 0.2488 (9.03) 0.1133 (7.73)
0.3726 (20.65) 0.9291 (37.44) 0.7931 (16.31) 0.1701 (5.92) 0.2744 (10.98) 0.0758 (0.29) 0.2755 (11.14) 0.1672 (6.63) 0.0719 (2.80) 0.0495 (1.93) 0.1357 (5.42) 0.1393 (5.55) 0.1880 (7.55) 0.1108 (4.17) 0.2465 (8.95) 0.1296 (8.84)
13,572 22,466.3 42,677.8 0.3445
13,572 22,961.6 42,184.4 0.3521
13,572 22,862.3 42,283.8 0.3506
13,572 22,846.0 42,300.1 0.3503
13,572 22,809.9 42,336.2 0.3498
13,572 22,884.7 42,261.3 0.3509
Note: WAC/10 yr (WAC/5 yr, WAC/3 yr, WAC/ARM, respectively) denotes the ratio of WAC to 10-year (5-year, 3-year, ARM, respectively) rate. Slope and BRP denote the slope of yield curve and the bond risk premium, respectively. Age stands for the loan age in months, and Age2 and Age3 are Age squared and cubed, respectively. January to November are month dummies. Condo is the dummy variable for condominium. The values in parentheses are asymptotic t-statistics.
6
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
U.S. data was that mortgagor’s choice between FRM and ARM at origination was explained by the ‘‘bond risk premium,’’ which is, according to Koijent et al. (2009, p. 293), ‘‘the premium earned on investing long in a long-term bond and rolling over a short position in short-term bonds.’’ Therefore, we run a Poisson regression with the bond risk premium added as an independent variable, where the bond risk premium is measured by the difference between 10year JGB yield prevailing a month ago and the average of 3-month Treasury bill yield over the last thirty six months. Incidentally, Koijen et al. (2009, p. 295) call this difference the ‘‘household decision rule’’ as a proxy for the bond risk premium. Note, however, that the mortgagors’ decision problem this paper addresses is not directly comparable to that Koijen et al. (2009) addressed, because, in this paper, mortgagors were to compare short- or medium-term rates with rates on their existing FRM, not with the prevailing rates on FRMs. Hence, we do not predict the sign of the coefficient for the bond risk premium. Additional independent variables for Poisson regression are the age of a mortgage pool, dummy variables for months from January to November to identify in which month of the calendar year prepayments were observed, and a dummy variable for pools of condominiums to distinguish them from pools of single-family homes. Furthermore, to capture nonlinear effects of pool age on prepayments, we add the pool age in months squared and the pool age in months cubed to independent variables. 4. Estimation results The estimation results are tabulated in Tables 2 and 3, where the coefficient estimates of independent variables are shown for twelve specifications (models) of Poisson regression. These models differ in interest-rate-related variables, but have pool age, dummy variables for months, and a dummy variable for condominium in common. All of the coefficients, except the one for the February dummy variable (in all models) and the one for June dummy variable (in Models 2–6), are statistically different from zero at the 1% significance level. Furthermore, as shown in the row titled ‘‘LR chi-square,’’ all models have very large values for the likelihood ratio chi-square, which implies the rejection of the null hypothesis that all coefficients are equal to zero. First, we examine the effects of the interest rate ratio on prepayments in general terms. Tables 2 and 3 show that the coefficient estimate of this variable is positive for all the rates we employ as the market mortgage rate in all specifications of Poisson regression. In other words, no matter which rate we employ as the market mortgage rate, and no matter which specification of Poisson regression we estimate, the lower the market mortgage rate is, the more often prepayments occur. Of course, this finding is consistent with prior studies on U.S. residential mortgages, such as Schwartz and Torous (1989, 1993), Richard and Roll (1989), Pavlov (2001), and Dunsky and Ho (2007). Next, we examine how the choice of the market mortgage rate affects the fit of the Poisson regression to the prepayment data. To this end, we compare Models 2–5 in terms of Akaike information criterion (AIC) and adjusted pseudo-R square (McFadden’s R square adjusted for the number of parameters as suggested by Ben-Akiva and Lerman (1985)). In addition, we compare Models 20 –50 in terms of AIC and adjusted pseudo-R square. These comparisons reveal that the ARM rate provides the best fit to the prepayment data than any of the longer-term interest rates, despite the fact that the ARM rate was stickier than the longer-term rates, as illustrated in Fig. 1. Incidentally, the stickiness of the ARM rate might be a reflection of the fact that the ARM rate is more directly affected by the Bank of Japan’s monetary policy than the longer-term rates. In addition, we examine the effects on prepayments of the slope of yield curve, the bond risk premium, and the interest rate
volatility. The comparison of Model 1 against Model 2 and that of Model 10 against Model 20 reveal that the addition of the slope of yield curve provides an improvement in goodness of fit.8 Similarly, the comparison of Model 6 against Model 2 and that of Model 60 against Model 20 uncover that the addition of the bond risk premium provides an improvement in goodness of fit that is almost comparable to the addition of the slope of yield curve. Yet, the most striking point about Tables 2 and 3 is that the interest rate volatility boost both AIC and adjusted pseudo-R square uniformly across all models. In short, the estimation results are consistent with our predictions about the effects on prepayments of the slope of yield curve and the interest rate volatility. Namely, the steeper the slope of yield curve is, the less often mortgage prepayments occur. The greater the interest rate volatility is, the less often mortgage prepayments occur. In addition, among all the specifications of Poisson regression, Model 20 in Table 3 has the best fit to the prepayment data. Therefore, we will employ Model 20 as a basis for our discussion. Before we turn to the next topic, we evaluate the economic significance of the interest rate ratio. For this purpose, we note that the intensity parameter l of Poisson regression gives the average number of occurrences of prepayments in a month. Furthermore, 0 by dividing Eq. (2) by n we have l/n being equal to ex b . Combining these facts, we see that the average prepayment rate, as measured 0 by l/n, is given by ex b . Based on this relationship, we can make some judgment about the economic significance of the interest rate ratio effects on prepayments. Specifically, let us take an example of the pool of single-family home mortgages that started repayments in May 1996. It had a WAC of 3.277% at the beginning of May 2003 when the ARM rate in the preceding month was 0 2.375%. Hence, the multiplicative factor of ex b attributable to the interest rate ratio is given by the exponential of 1.2963 3.277/ 2.375, where 1.2963 is the coefficient estimate of the interest rate ratio with the ARM rate being used as the market mortgage rate, as shown in Model 20 in Table 3. Now, assume that the ARM rate in April 2003 was higher than the actually observed rate by 50 basis points, that is, 2.375% +0.5 % =2.875 %. Then, the multiplicative 0 factor of ex b attributable to the interest rate ratio would have been given by the exponential of 1.2963 3.277/2.875, which is 21% less than 1.2963 3.277/2.375. In other words, other things being equal, the average prepayment rate, as measured by l/n, would have been 21% less if the ARM rate was higher than the actually observed rate by 50 basis points. Next, we turn to the effects of the age of a mortgage pool on prepayments. Fig. 2 draws the prepayment intensity as a function of the pool age in month, where all the other independent variables of Poisson regression are assumed to be zero, and the coefficient estimates of age-related variables are based on those of Model 20 . This figure indicates that the prepayment intensity increases initially, peaks in the seventy second month, and decreases gradually afterward. This pattern is roughly consistent with prior studies on U.S. residential mortgages. Note, however, that the month when the prepayment intensity peaks differs across studies; it is approximately seventy fifth month in Schwartz and Torous (1989), eighty fourth month in ‘‘Model 1’’ of Schwartz and Torous (1993), and approximately sixtieth month in Dunsky and Ho (2007). Considering that the peak month estimated by the U.S. studies cluster around the peak month we estimate for the Japanese mortgages, we can safely say that the pattern of prepayment intensity in relation to mortgage age is the same between U.S. and Japanese mortgages.
8 The addition of the slope of yield curve improves the goodness of fit in other specifications of Poisson regression where the ARM rate is replaced by 3-, 5-, or 10year rate.
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
7
Table 3 Poisson regression with the volatility of interest rates. Variables
Model 10
Model 20
WAC/ARM
1.3034 (26.79)
1.2963 (26.46)
WAC/3 yr
Model 30
Model 40
Model 50
1.2191 (24.87) 1.0018 (23.60)
WAC/5 yr
1.0125 (23.16)
WAC/10 yr Slope
0.3509 (19.04)
0.3691 (20.00)
0.1661 (8.22)
1.5354 (24.24) 0.1262 (6.10)
BRP Volatility Age (101) Age2 (103) Age3 (105) January February (101) March April May June July August September October November Condo
N LR chi-square AIC Adj. pseudo-R2
Model 60
7.2219 (33.80) 0.8940 (35.90) 0.8373 (17.15) 0.1966 (6.80) 0.3028 (12.12) 0.3765 (1.42) 0.2958 (11.97) 0.2300 (9.15) 0.1573 (6.15) 0.1627 (6.38) 0.2115 (8.50) 0.1459 (5.81) 0.1221 (4.91) 0.1487 (5.59) 0.2787 (10.12) 0.0990 (6.75)
6.7782 (32.14) 0.8815 (35.26) 0.8409 (17.19) 0.2117 (7.32) 0.2796 (11.18) 0.0393 (0.15) 0.2721 (11.00) 0.1971 (7.82) 0.1195 (4.66) 0.1103 (4.30) 0.1671 (6.67) 0.1493 (5.95) 0.1526 (6.12) 0.1352 (5.08) 0.2583 (9.38) 0.0994 (6.77)
6.6523 (31.38) 0.8796 (35.23) 0.8220 (16.84) 0.2021 (7.01) 0.2724 (10.89) 0.0488 (0.18) 0.2593 (10.48) 0.1827 (7.25) 0.1081 (4.21) 0.0986 (3.84) 0.1488 (5.94) 0.1416 (5.64) 0.1507 (6.05) 0.1341 (5.04) 0.2684 (9.74) 0.0927 (6.32)
6.6388 (31.26) 0.8977 (36.05) 0.8488 (17.44) 0.2224 (7.74) 0.2739 (10.95) 0.0319 (0.12) 0.2699 (10.91) 0.1950 (7.74) 0.1251 (4.87) 0.1081 (4.21) 0.1514 (6.05) 0.1317 (5.25) 0.1235 (4.94) 0.1420 (5.34) 0.2653 (9.63) 0.0939 (6.39)
7.1383 (32.48) 0.9060 (36.33) 0.8636 (17.71) 0.2220 (7.72) 0.2756 (11.02) 0.0820 (0.31) 0.2497 (10.08) 0.1703 (6.75) 0.1009 (3.93) 0.0786 (3.05) 0.1222 (4.86) 0.0924 (3.66) 0.0969 (3.86) 0.1498 (5.63) 0.2732 (9.91) 0.0931 (6.35)
0.3001 (16.69) 6.7935 (32.05) 0.8943 (35.82) 0.8504 (17.41) 0.2150 (7.45) 0.2888 (11.56) 0.1298 (0.49) 0.2769 (11.20) 0.2009 (7.97) 0.1237 (4.82) 0.1153 (4.49) 0.1725 (6.89) 0.1496 (5.96) 0.1489 (5.98) 0.1369 (5.15) 0.2621 (9.52) 0.1015 (6.91)
13,572 23,810.5 41,335.5 0.3651
13,572 24,168.6 40,979.5 0.3706
13,572 24,010.0 41,138.1 0.3682
13,572 23,985.0 41,163.1 0.3678
13,572 24,041.5 41,106.6 0.3687
13,572 24,085.3 41,062.8 0.3693
Note: Volatility denotes the volatility of interest rates. The remaining variables are defined as in Table 2. The values in parentheses are asymptotic t-statistics.
Fig. 3 illustrates the coefficient estimates of dummy variables for months of the year based on the estimation results of Model 20 . It shows that mortgagors have the tendency to prepay more in January and March and less in February, October, November, and December than in other months. As seen in the Model 20 column of Table 3, this seasonal pattern is statistically significant except February. We can conjecture that several institutional arrangements in Japan are responsible for this pattern. First, a mortgagor is allowed to deduct a fixed percentage of her mortgage balance at the end of a calendar year from her income tax.9 Hence, mortgagors 9 The tax credit system for mortgage balances changed five times during our sample period. More specifically, the fixed percentage was changed within a range of 0.5–2% and the period during which the fixed percentage of the mortgage balance was deductible from income tax was changed within a range of the initial five to the initial fifteen years of the mortgage term. Therefore, in order to confirm the robustness of the seasonal pattern of prepayments, we run Model 20 in Table 3 for each of the six sub-periods of the sample period. We find that the seasonal pattern of prepayments is fairly stable under different tax credit systems and consistent with Fig. 3.
wishing to prepay would avoid prepaying in the last few months of the year and prepay in the first few months of the year. Second, academic years of practically all academic institutions as well as fiscal years of many corporations start at the beginning of April and end at the end of March. Hence, moving related to relocation, and as a result, prepayments due to moving, tend to occur in March. Third, it is a common practice in Japan that employers, both private and public, pay their full-time employees bonuses toward the ends of June and December, typically with December bonuses bigger than June bonuses. Hence, if the balance of a mortgage loan is small, probably because it was small at origination or because the mortgagor has prepaid a large proportion of the initial mortgage balance by prior partial prepayments, a full prepayment of the loan is more likely to occur after the mortgagor receives a bonus, i.e., in January and July than in other months. Finally, we make observations about the dummy variable for condos. As shown in Tables 2 and 3, the coefficient estimate for the condo dummy variable is statistically significant and fairly stable across all models. Generally speaking, mortgagors of condos are
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N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
Fig. 2. Baseline prepayment function.
Fig. 3. Coefficient estimates for month dummies.
younger and have smaller families than those of single-family homes. In addition, mortgagors of condos tend to live in big cities, while mortgagors of single-family homes are dispersed across Japan. Therefore, the former tends to be more mobile than the latter, which is consistent with our finding of a positive coefficient for the condo dummy. 5. Conclusions In this paper, we investigate full prepayments of Japanese residential mortgages granted by Government Housing Loan Corporation (GHLC) over a ten-year period from 1996 to 2005. This investigation is important because the amount of mortgages outstanding in Japan is huge, yet the study on their prepayments is scarce. In this study, we pay close attention to two features of interest rate relationships which were observed during the sample
period and which might be relevant to full prepayments of fixed rate mortgages. First, interest rates fluctuated within a narrow range of a little over 1%. Surprisingly, full prepayments of Japanese mortgages were sensitive to small changes in interest rates. Second, long-term refinance rates did not fall well below the contract rates of most mortgages in our sample throughout this ten-year period, while short- and medium-term refinance rates did. With this interest rate relationship, if mortgagors ever refinanced GHLC mortgages, they would refinance them by mortgages where initial interest rates were pegged to shorterterm rates. Hence, we examine the sensitivity of full prepayments to short- vs. long-term mortgage rates, slope of yield curve, bond risk premium, and interest rate volatility. We find that the shortterm mortgage rate provides a slightly better fit of Poisson model to the prepayment data than longer-term mortgage rates. Also, the addition of the slope of yield curve or the bond risk premium
N. Kishimoto, Y.-J. Kim / Japan and the World Economy 30 (2014) 1–9
improves the goodness of fit. Furthermore, the addition of the volatility of short-term interest rate improves the goodness of fit considerably across all models. In addition, the age of mortgage pool has a considerable power of explaining the occurrences of full prepayments. Specifically, the prepayment intensity increases initially as the pool ages, peaks in seventy two months after the origination of the pool, and decreases gradually afterward. Our estimation results provide convincing evidence that mortgagors in Japan have the tendency to prepay more in January and March and less in February, October, November, and December than in other months. We conjecture that several institutional arrangements in Japan may be responsible for this seasonal pattern. They include the prevalence of regularly paid bonuses, tax credit on mortgage balances, and the beginning and ending of typical fiscal and academic years of Japanese institutions. Acknowledgements We thank Housing Loan Progress Association, an affiliate of Government Housing Loan Corporation (GHLC), for providing us Housing and Finance Forum scholarship and GHLC prepayment data. In addition, we thank Stephen Brown, William Greene, Hideaki Hirata, Thomas Ho, and Mari Matsumoto for helpful discussion.
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