Docstoc

Why Are There No Fixed Rate Mortgages in Taiwan

Document Sample
Why Are There No Fixed Rate Mortgages in Taiwan Powered By Docstoc
					Why Are There No Fixed-Rate Mortgages in Taiwan




                    Yao-Min Chiang


                 Department of Finance


              National Chengchi University


                ymchiang@nccu.edu.tw




                     August, 1998




                           1
                                        Abstract

In Taiwan, almost only adjustable-rate mortgages have been issued.         It is interested


to know why borrowers in Taiwan have different choice behavior from those in the


United States. A game theory approach is used to discuss how borrowers choose a


suitable mortgage contract from fixed-rate mortgages and adjustable-rate mortgages


according to their mobility. Conditions for all borrowers to choose adjustable-rate


mortgages are mainly derived from down sloping term structure of interest rates


combined with expectation of lower future income. We find that not income level


but the tilt of income stream, also, not the interest rate level but the slope of the yield


curve, are the key factors affecting mortgage choice. One interesting finding is that


when borrowers expect the ratio of future interest rate to further income becomes


higher and higher, they become more likely to choose adjustable-rate mortgages.


Empirical evidence shows that downward sloping of the term structure of interest


rates, low interest rate volatility, and the expectation of higher future


payment-to-income ratio are reasons causing there are only adjustable-rate mortgages


in Taiwan's mortgage market.




                                            2
Introduction

     In Taiwan, mortgage borrowers have few variety of financing contracts from


which to choose. The dominant contract has been the adjustable-rate mortgages


(ARMs).     Contract rates are adjusted usually annually according to the market


change. This phenomenon is different from that in the United States.       Until the


1980s, fixed-rate mortgages (FRMs) were the standard mortgage instrument in the


United States. Adjustable-rate mortgages were introduced and became common in


the early 1980s. Since then, these two standard contracts are chosen by mortgage


borrowers according to the mortgage pricing and borrowers' personal characteristics.


It is interested to know why borrowers in Taiwan and borrowers in the United States


have different choice behavior.


     Before the banking regulation change in 1990, the lending market in Taiwan was


considered to be a monopolistic one. Since borrowers bear all interest rate risk in


choosing ARMs, a monopolist provides only ARM contracts for borrowers to choose


from.     After the regulation change, Taiwan's lending market has become a


competitive market.      However, ARMs are still the only mortgage contracts that we


can see in the market.


     Factor affecting mortgage choice include market conditions, mortgage price


variables, and borrower characteristic, see for example Sa-Aadu and Sirmans (1995).


                                           3
Borrowers may prefer an ARM when the difference between the long-term rate and


the short-term rate is large (Dhillon, Shilling, and Sirmans, 1983, and Brueckner,


1986), when their affordability is larger due to a lower teaser rate (Brueckner and


Follain, 1988), or when they expect interest rates are going down (Sa-Aadu and


Sirmans (1995).


    Theoretical and empirical works have been focused on the impact of borrower


characteristics on mortgage choice. Mobility, one of the borrower characteristics,


plays a particularly important role in mortgage choice.         Theoretical models


developed by Chari and Jagannathan (1989), and Brueckner (1992), and empirical


works by Brueckner and Follain (1988), and Sa-Aadu and Sirmans (1995) all show


mobility has a significant influence on mortgage choice.      Borrowers with higher


likelihood of moving choose shorter-term contracts such as ARMs.


    Previous works by Alm and Follain (1987), Brueckner (1986), and Brueckner


and Follain (1988) show income effect is weak on borrower choice.         However,


Sa-Aadu and Sirmans (1995) and Chiang (1996) are able to show that borrowers who


expect their income to rise are more likely to choose ARMs.


    This study investigates what market conditions and borrower characteristics have


attributed to that ARMs are the dominant contracts in Taiwan. We use a game theory


approach to discuss how lenders can best design FRMs and ARMs to reveal


                                         4
borrower's private information about their mobility.      By changing parameter values


of market variables and borrower characteristics, we show how borrower mortgage


choice is affected by these factors.


     Our results can be summarized as follows.       First, the downward sloping interest


rates in Taiwan play a key role in pushing borrowers to choose ARMs. Second,


mobility has no significant influence on borrower choice behavior. Third, the tilt of


income stream raises the choice probability of FRMs over ARMs. Finally, interest


rates and income are not considered independently by borrowers when they make the


choice decision.     There is an interaction between interest rates and income on


mortgage choice.


     To establish these results, a game model is developed in Section 1. By using


numerical analysis, in Section 2 we discuss how market condition and borrower


characteristics affect mortgage choice. Empirical evidence is provided in Section 3.


Section 4 contains the summary and conclusions.




Model

     Lenders and borrowers face a two-period, three-date world.       Dates are indexed


by t=0, 1, 2.      The short-term interest rate for period 1 is r0 and the expected


short-term interest rate for period 2 is E(r1).   Interest rates have variance of 2. On


                                             5
date 0, borrowers choose an FRM or an ARM.                  Loan amount is normalized to 1.


On date 1, a borrower may move and prepay the loan. The probability of moving, ,

is private information of borrowers. Assume two types of borrowers: type one, more


mobile, has a probability of moving 1; type two, less mobile, has a probability of


moving of 2, 1 always being greater than 2. The proportion of type 1 borrowers is


 and the proportion of type 2 borrowers is (1-).             If borrowers prepay the loan at

date 1, the mortgage contract is terminated; otherwise the loan continues until date 2,


the end of the contract period.


     Lenders’ response to borrowers’ choice is to set mortgage interest rates.


Lenders are risk neutral and face perfectly competitive markets, and therefore earn


zero expected profit on each contract.


     The value of the mortgage to the lender is the sum of the present value of cash


flows received in each period. Thus the value of the mortgage is affected by the


borrowers’ prepayment decision through a change in cash flows. Since lenders have


a discount factor  and face a perfectly competitive market, the expected profit on an

FRM is:

((i f  r )  (   )(i f  E(r )))  (  )((i f  r )  (    )(i f  E(r )))   (1)


     Given that lenders earn zero expected profit, the interest rate on FRMs, if, can be


represented as:


                                                 6
                                r0   (1  E ( )) E (r1 )
                         if                                                                  (2)
                                   1   (1  E ( ))

     As Brueckner (1993) shows, markup in uncapped ARMs is zero given that


lenders earn zero expected profit from ARMs in each period:

        ((r    r )  (   )( E(r )    E(r )))
                                                                                              (3)
        (  )((r    r )  (    )( E(r )    E(r )))  

           Borrowers have Von-Neumann-Morgenstern utility functions,V(.), and


discount factors . The income level for borrowers for each of the two periods are

denoted z0 and z1, which for simplicity are assumed to be known with certainty.


Thus the only source of uncertainty is the randomness of short-term interest rates. A

borrower's utility function for each period can now be defined as: V ( z  i ) and
                                                                        0 0

V ( z  (1   )i1 ) .   The borrower's objective is to maximize his/her utility by
     1

choosing a suitable loan.       If borrowers issue FRMs, their expected utility will be:

                            V ( z 0  i f )  V ( z1  (1   )i f )                         (4)


Similarly, expected utility of borrowers who choose ARMs is

                           V ( z 0  r0 )    V ( z1  (1   )r1 )dG(r1 )                  (5)


     It is assumed that borrowers will use only a pure strategy, i.e., borrowers will


choose an FRM or an ARM with probability one.                  Possible strategy combinations are


represented in Figure 1:




                                                    7
Figure 1. Combinations of outcome of borrowers mortgage choice strategy

          Strategies                       Type 2
                             FRM                                ARM
             FRM              G1                                 G2

 Type 1
             ARM              G3                                G4


G1: type 1 chooses FRMs and type 2 chooses FRMs.
G2: type 1 chooses FRMs and type 2 chooses ARMs.
G3: type 1 chooses ARMs and type 2 chooses FRMs.
G4: type 1 chooses ARMs and type 2 chooses ARMs.




In G1, two types of borrowers all issue FRMs.                        Interest rates on FRMs will be:

                           r  (    (  )  ) E(r )
                    i f                                                                             (6)
                               (    (  )  )

Since lenders can not distinguish borrowers, interest rate on FRMs in G2 and G3 will


be the same based on the probability of moving of type 2 borrowers1.

                                     r  (    ) E(r )
                            i f                                                                    (7)
                                         (    )

Borrowers’ expected utility in different strategy combinations will be as follows:

G1:

Type 1:   V ( z 0  i f 1 )  V ( z1  (1  1 )i f 1 )


Type 2:   V ( z 0  i f 1 )  V ( z1  (1   2 )i f 1 )

G2:

Type 1:   V ( z 0  i f 23 )  V ( z1  (1  1 )i f 23 )




                                                            8
Type 2:        V ( z 0  r0 )    V ( z1  (1  2 )r1 )dG(r1 )

G3:

Type 1:        V ( z 0  r0 )    V ( z1  (1  1 )r1 )dG(r1 )

Type 2:        V ( z 0  i f 23 )  V ( z1  (1   2 )i f 23 )

G4:

Type 1:        V ( z 0  r0 )    V ( z1  (1  1 )r1 )dG(r1 )

Type 2:        V ( z 0  r0 )    V ( z1  (1  2 )r1 )dG(r1 )




Then, if:

V ( z 0  r0 )    V ( z1  (1  1 )r1 )dG(r1 )             >     V ( z 0  i f 23 )  V ( z1  (1  1 )i f 23 )         and


V ( z 0  r0 )    V ( z1  (1  2 )r1 )dG(r1 ) > V ( z 0  i f 23 )  V ( z1  (1   2 )i f 23 )


, the Nash equilibrium is G4.


       Assuming that borrower preferences are captured by quadratic utility function


V(x) = ax - b/2x2, V 0, V 0.2                         The goal is to evaluate how changes in key

parameters affect market equilibrium. We then can get the condition for G4 to be the


equilibrium outcome is:

               b                                                    b                                           b
U  [a  bz0  (r0  i f 2 )](r0  i f 23 )   (1   )[a  bz1  ( E (r1 )  i f 2 )](E (r1 )  i f 23 )   (1   ) 2  2  0
               2                                                    2                                           2



1
    Borrowers with lower likelihood of moving choose long-term contracts such as FRMs. (Chari
and Jagannathan, 1989, and Brueckner, 1992)
2
    This function is able to show how changes in parameters' expected values and volatility
affect borrowers' expected utility and therefore mortgage choice.                            Brueckner (1993) uses the
quadratic function to discuss the loan-rate functions of FRMs and ARMs.

                                                                9
Given r0<E(r1), we have

U
     0
z 0
U
    0
z1
U
     0
 2

Given r0<E(r1) and for U to be greater than 0, we should have a smaller z0 and a larger


z1. Which means that given the term structure of interest rates shows a upward


sloping, when borrowers have lower z0 and higher z1 , they will become more likely


to choose ARMs.


Given r0>E(r1), we have

U
     0
z 0
U
    0
z1
U
     0
 2

On the contrast, given r0>E(r1), when z0 is larger, expecting a smaller z1, and smaller


interest rate volatility, borrowers are more likely to choose ARMs.




Numerical analysis

     We use numerical analysis to demonstrate the impact of important variables on


mortgage choice. Several stylized facts are considered in selecting the basic set of


parameter values. The annual average percentage of people moving is about 20%.


                                          10
Interest rate volatility is assumed to be 0.6087% (Chang, 1992). Parameter values


also have to satisfy the utility function specification, especially, V'>0 and V"<0.


     Table 1 shows a numerical example in which all borrowers choose ARMs.              In


this case, borrowers have the highest utility when choosing ARMs. Table 1 shows in


this (ARM, ARM) equilibrium, the expected utility for type 1 borrowers is 5.703742,


higher than 5.608858 in the (FRM. ARM) choice. When type 1 borrowers choose


ARMs, it is also better for type 2 borrowers to choose ARMs, in which type 2


borrowers have utility of 6.149878, higher than 6.056674 in the (ARM, FRM) choice.


      is borrowers' discount factor. Table 2 shows when  increases, implying

borrowers put more weight on future consumption, incremental wealth for choosing


ARMs over FRMs decreases. When borrowers have higher time preference, they are


more likely to choose long-term stable contracts such as FRMs (Chiang, 1996).         It is


interested to note that given the basic parameter setting and no matter how  changes,

the market equilibrium stays in G4, the (ARM, ARM) equilibrium. This implies that


parameters other than borrowers' discount factor play a more important role in


borrower choice decision.


     Table 3 shows that borrowers' choosing ARMs is not affected by the proportion


of more mobile borrowers. Given the basic market condition, even though lenders


adjust FRM prices by considering the proportion of more mobile borrowers,


                                           11
borrowers still choose ARMs.        This implies mobility actually plays no role in


mortgage choice.    Again, there should be other factors that have significant influence


on mortgage choice.


     Empirical works by Alm and Follain (1987), Brueckner (1986), and Brueckner


and Follain (1988) show income effect is weak on borrower choice. Results in Table


4 are consistent with these works by showing that changes in borrowers income level


have no strictly simple influence on borrower choice.       Income level may have an


ambiguous effect on borrower choice. The tilt of income stream may be the key


factors in making the choice decision. (Sa-Aadu and Sirmans, 1995, and Chiang, 1996)


Table 5 also shows the impact of the tilt of income stream on mortgage choice. We


see that during a reasonable range, when borrowers expect that they have lower future


income, they become more likely to choose ARMs.          In fact, later we will show that


this result is actually derived from the mixed effect of interest rate and income.


     Table 6 shows that with higher interest rate volatility, borrowers become less


likely to choose ARMs.


     With doubt, we see from Table 7 that borrowers become more likely to choose


ARMs when the initial interest rate increases.     It is believed that with higher initial


interest rate, borrowers may be less likely to choose ARMs because of the


affordability problem.   In his theoretical work, Brueckner (1992) actually shows that


                                           12
interest rate level has an ambiguous effect on the mortgage choice. We find from


Table 8 that borrowers become more likely to choose ARMs when the future interest


rate is expected to be lower.          This result is consistent with previous works by


Brueckner (1986) and Sa-Aadu and Sirmans (1995). We, therefore, believe that not


the interest rate level but the slope of the interest rate curve is the key factor on


mortgage choice.


       When borrowers make a choice decision, they simultaneously consider market


conditions and their personal characteristics.           Interest rates and income are not


considered independently.         We need to understand how the interaction between


interest rates and income affects borrower choice.


       Given initial interest rate and initial income level, we adjust the values of future


interest rate and future income3 to see the mixed effect of interest rate and income on


mortgage choice. Table 9 shows that the higher the ratio of future interest rate to


future income, the more likely (ARM, ARM) is the market equilibrium.




Empirical evidence

       In this section, we provide empirical evidence to justify the numerical analysis


results. Figure 2 shows the historical interest rate trend in Taiwan.               The prime

3
    This approach is the same as a direct changing in the tilt of income stream and the slope of
the yield curve.

                                                13
lending rate shows a decreasing trend during the past 30 years.        It is normal for


borrowers in Taiwan expect future interest rates will go down. As Brueckner (1993)


indicates that with a decreasing trend in interest rates, borrowers prefer ARMs.


     Interest rate volatility for the past 30 years is shown to be around 0.6028%


(Chang, 1992), which is much lower than that in the United States. Yang (1992)


indicates that the average annual variance of three-month Treasury bill rates during


1971-1990 is 2.25%.    Low interest rate volatility pushes borrowers to be more likely


to choose ARMs.


     Table 10 and Figure 3 show the average payment-to-income ratio of Taiwanese


households. Housing price increased dramatically during the past 30 years. Even


though interest rates had a decreasing trend, Taiwanese households' income did not


increase in the same speed as that of mortgage payment.         Expectation of higher


payment-to-income ratio pushes borrowers to choose ARMs.




Conclusion

     Consistent with previous works, our model shows that with a decreasing trend in


interest rates, borrowers prefer choosing ARMs. Our model also shows that the tilt


of income stream, not the income level, plays a key role on borrower choice behavior.


Besides, the slope of the yield curve, not the interest rate level, is the key factor


                                          14
affecting mortgage choice. Another contribution of this paper is to show that income


and interest rates do not affect mortgage choice independently.       They have an


interaction on mortgage choice.


    In summary, we find that downward sloping of the term structure of interest rates,


low interest rate volatility, combined with the expectation of higher future


payment-to-income ratio are the reason causing there are only ARMs in Taiwan's


mortgage market.




                                         15
Table 1 Basic assumption for variables.

Basic assumptions
               0.7
               0.9
               0.2
1             0.75
2             0.25
Z0               10
Z1                5
a                 8
b                 2
r0             1.08
E(r1)          1.05
 (r1)
  2
          0.006087

if1                1.067647
if2                1.069672
 is the lender's discount factor.  is borrowers' discount factor. The proportion of type I, more mobile
borrowers is .           The probability of moving for type I borrowers is 1, and the probability for type II
borrowers is 2. Borrowers have income Z0 and Z1 for period 1 and 2. Interest rate for period 0 is
known as r0 and the expected interest rate for period 2 is E(r1).               Interest rates have volatility of 2.
         r0   (1  E (  )) E ( r1 )
i f1                                      is the interest rate on FRMs when both types of borrowers choose FRMs.
             1   (1  E (  ))

           r0   (1  E (  )) E ( r1 )
i f 23                                     is the interest rate on FRMs when only one type of borrowers choose
               1   (1  E (  ))

FRMs.


Market Equilibrium
                                                       Type 2      borrowers
                                           FRM                    ARM
                    FRM                    G1            5.618502 G2                 5.608858
Type 1                                                   6.066258                    6.149878
 borrowers ARM                             G3            5.703742 G4                 5.703742
                                                         6.056674                    6.149878
The market equilibrium is G4, in which both types of borrowers choose ARMs.
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.




                                                                16
Table 2 Change of market equilibrium due to a change in borrowers' discount factor

   delta                 Incremental wealth Incremental wealth equilibrium
                              for type I        for type II
   0.05                       0.101352           0.101259          G4
     0.1                          0.100972              0.100785           G4
   0.15                           0.100591              0.100311           G4
     0.2                          0.100211              0.099838           G4
   0.25                           0.09983               0.099364           G4
     0.3                          0.09945               0.09889            G4
   0.35                           0.099069              0.098416           G4
     0.4                          0.098689              0.097942           G4
   0.45                           0.098308              0.097468           G4
     0.5                          0.097928              0.096995           G4
   0.55                           0.097547              0.096521           G4
     0.6                          0.097167              0.096047           G4
   0.65                           0.096786              0.095573           G4
     0.7                          0.096406              0.095099           G4
   0.75                           0.096025              0.094625           G4
     0.8                          0.095645              0.094152           G4
   0.85                           0.095264              0.093678           G4
     0.9                          0.094884              0.093204           G4
   0.95                           0.094503              0.09273            G4
         1                        0.094123              0.092256           G4
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.



                      0.104
   Wealth increment




                      0.102
                        0.1
                      0.098
                      0.096
                      0.094
                      0.092
                       0.09
                              0         0.2       0.4         0.6        0.8    1   1.2

                                              Borrower's Discount Factor



                                                                    17
Table 3: Borrowers' behavior change due to a change in the proportion of more mobile
borrowers.
    pie                  Incremental wealth Incremental wealth equilibrium
                              for type I        for type II
   0.05                       0.094884           0.093204          G4
    0.1                        0.094884         0.093204             G4
   0.15                        0.094884         0.093204             G4
    0.2                        0.094884         0.093204             G4
   0.25                        0.094884         0.093204             G4
    0.3                        0.094884         0.093204             G4
   0.35                        0.094884         0.093204             G4
    0.4                        0.094884         0.093204             G4
   0.45                        0.094884         0.093204             G4
    0.5                        0.094884         0.093204             G4
   0.55                        0.094884         0.093204             G4
    0.6                        0.094884         0.093204             G4
   0.65                        0.094884         0.093204             G4
    0.7                        0.094884         0.093204             G4
   0.75                        0.094884         0.093204             G4
    0.8                        0.094884         0.093204             G4
   0.85                        0.094884         0.093204             G4
    0.9                        0.094884         0.093204             G4
   0.95                        0.094884         0.093204             G4
        1                      0.094884         0.093204             G4
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.




                       0.095
   Wealth increment




                      0.0945

                       0.094


                      0.0935

                       0.093
                               0      0.2     0.4       0.6        0.8       1   1.2

                                   The Proportion of Type I Borrowers

                                                              18
Table 4 Borrowers' choice behavior change due to a change in borrowers' initial
income
        z0                Incremental wealth Incremental wealth equilibrium
                               for type I        for type II
      0.8                      2.522265           2.670758          G4
      1.6                      1.854268            1.974536         G4
      2.4                      1.273303            1.368234         G4
      3.2                      0.77937             0.851854         G4
          4                    0.37247             0.425396         G4
      4.8                      0.052603            0.088859         G4
      5.6                      -0.18023            -0.15776         G1
      6.4                      -0.32603            -0.31445         G1
      7.2                      -0.3848             -0.38122         G1
          8                    -0.35654            -0.35807         G1
      8.8                      -0.24125             -0.245          G1
      9.6                      -0.03892            -0.04201         G1
   10.4                        0.250443            0.250901         G4
   11.2                        0.626836            0.633735         G4
       12                      1.090262            1.106492         G4
   12.8                        1.64072             1.669169         G4
   13.6                        2.278211            2.321768         G4
   14.4                        3.002735            3.064289         G4
   15.2                        3.814291            3.896731         G4
       16                      4.712879            4.819094         G4
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.




                         4
                       3.5
   Wealth Increment




                         3
                       2.5
                         2
                       1.5
                         1
                       0.5
                         0
                      -0.5 0     2        4    6       8      10   12     14   16
                        -1

                                     Borrower's Initial Income Level



                                                              19
Table 5 Borrowers' choice behavior change due to a change in borrowers' expectation
about future income
      z1                   Incremental wealth Incremental wealth equilibrium
                                for type I        for type II
     0.8                        4.080258           6.051215          G4
     1.6                       3.144319           4.450016           G4
     2.4                        2.29159           3.068271           G4
     3.2                        1.52207            1.90598           G4
         4                     0.835759           0.963143           G4
     4.8                       0.232658            0.23976           G4
     5.6                       -0.28723            -0.26417          G1
     6.4                       -0.72392            -0.54864          G1
     7.2                       -1.07739            -0.61366          G1
         8                     -1.34766            -0.45923          G1
     8.8                       -1.53471            -0.08534          G2
     9.6                       -1.63856             0.508            G2
   10.4                         -1.6592           1.320796           G2
   11.2                        -1.59663           2.353047           G2
      12                       -1.45085           3.604751           G2
   12.8                        -1.22186            5.07591           G2
   13.6                        -0.90966           6.766523           G2
   14.4                        -0.51425            8.67659           G2
   15.2                        -0.03563           10.80611           G2
      16                       0.526196           13.15509           G4
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.


                      25
   Wealth Increment




                      20

                      15

                      10

                      5

                      0
                           0              5              10               15   20
                      -5

                                 Borrower's Expected Income for Period 1




                                                              20
Table 6 Borrowers' choice behavior change due to a change in the interest rate
volatility
  sigma                 Incremental wealth Incremental wealth equilibrium
                             for type I        for type II
  0.002                      0.095113           0.095273          G4
  0.004                         0.095001           0.09426               G4
  0.006                         0.094888           0.093248              G4
  0.008                         0.094776           0.092235              G4
   0.02                         0.094101           0.08616               G4
   0.04                         0.092976           0.076035              G4
   0.06                         0.091851           0.06591               G4
   0.08                         0.090726           0.055785              G4
   0.2                          0.083976           -0.00496              G3
   0.4                          0.072726           -0.10621              G3
   0.6                          0.061476           -0.20746              G3
   0.8                          0.050226           -0.30871              G3
       2                        -0.01727           -0.91621              G1
       4                        -0.12977           -1.92871              G1
       6                        -0.24227           -2.94121              G1
       8                        -0.35477           -3.95371              G1
     20                         -1.02977           -10.0287              G1
     40                         -2.15477           -20.1537              G1
     60                         -3.27977           -30.2787              G1
     80                         -4.40477           -40.4037              G1
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.


                      0.15
   Wealth Increment




                       0.1
                      0.05
                         0
                      -0.05 0         0.1    0.2        0.3        0.4        0.5   0.6   0.7

                       -0.1
                      -0.15
                       -0.2
                      -0.25

                                            Interest Rate Volatility



                                                              21
Table 7 Borrowers' choice behavior change due to a change in the initial interest rate
    r0                       Incremental wealth      Incremental wealth equilibriu
                                  for type I             for type II       m
   1.01                           -0.12884                -0.13245         G1
   1.02                             -0.09655                -0.1               G1
   1.03                             -0.06437             -0.06762              G1
   1.04                             -0.0323              -0.03532              G1
   1.05                             -0.00034             -0.00308              G1
   1.06                             0.031509             0.029084              G4
   1.07                             0.063251             0.061179              G4
   1.08                             0.094884             0.093204              G4
   1.09                             0.126407             0.125158              G4
    1.1                             0.157822             0.157042              G4
   1.11                             0.189127             0.188855              G4
   1.12                             0.220323             0.220598              G4
   1.13                             0.25141               0.25227              G4
   1.14                             0.282388             0.283872              G4
   1.15                             0.313257             0.315404              G4
   1.16                             0.344016             0.346864              G4
   1.17                             0.374667             0.378255              G4
   1.18                             0.405208             0.409575              G4
   1.19                             0.43564              0.440824              G4
    1.2                             0.465963             0.472004              G4
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.



                              0.7
                              0.6
          Wealth Increment




                              0.5
                              0.4
                              0.3
                              0.2
                              0.1
                               0
                             -0.1 0.8          0.9         1             1.1        1.2   1.3
                             -0.2

                                                      Initial Interest Rate




                                                                    22
Table 8 Borrowers' choice behavior change due to a change in the expectation about
future interest rate
   E(r1)                 Incremental wealth Incremental wealth equilibrium
                              for type I        for type II
   1.01                       0.222045           0.220667          G4
   1.02                            0.190234         0.188899          G4
   1.03                            0.158437         0.157066          G4
   1.04                            0.126653         0.125168          G4
   1.05                            0.094884         0.093204          G4
   1.06                            0.063128         0.061174          G4
   1.07                            0.031386         0.029079          G4
   1.08                            -0.00034         -0.00308          G1
   1.09                            -0.03206         -0.03531          G1
    1.1                            -0.06376         -0.0676           G1
   1.11                            -0.09544         -0.09996          G1
   1.12                            -0.12712         -0.13238          G1
   1.13                            -0.15878         -0.16487          G1
   1.14                            -0.19042         -0.19742          G1
   1.15                            -0.22205         -0.23004          G1
   1.16                            -0.25367         -0.26273          G1
   1.17                            -0.28528         -0.29548          G1
   1.18                            -0.31687         -0.32829          G1
   1.19                            -0.34844         -0.36117          G1
    1.2                            -0.38001         -0.39412          G1
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.




                        0.3
                        0.2
     Wealth Increment




                        0.1
                          0
                        -0.1 0.8              0.9    1          1.1        1.2   1.3
                        -0.2
                        -0.3
                        -0.4
                        -0.5
                        -0.6
                        -0.7

                                          Expected Interest Rate for Period 1

                                                               23
 Table 9 Borrowers' choice behavior change due to change in the ratio of expected
future interest rate over expected future income
  ratio  Incremental   Incremental equilibrium
          wealth for    wealth for
            type I        type II
    0.02      -3.10669      -2.99471 G1
    0.04       -2.30482        -2.24499 G1
    0.06       -1.54663        -1.52346 G1
    0.08         -0.8321       -0.83012 G1
     0.1       -0.16124        -0.16497 G1
    0.12       0.465963        0.472004 G4
    0.14       1.049495        1.080787 G4
    0.16       1.589362        1.661385 G4
    0.18       2.085564        2.213797 G4
     0.2       2.538099        2.738023 G4
    0.22       2.946969        3.234063 G4
    0.24       3.312173        3.701918 G4
    0.26       3.633712        4.141586 G4
    0.28       3.911585        4.553068 G4
     0.3       4.145792        4.936364 G4
    0.32       4.336334        5.291474 G4
    0.34       4.483209        5.618398 G4
    0.36        4.58642        5.917137 G4
    0.38       4.645964        6.187689 G4
     0.4       4.661843        6.430055 G4
    0.42       4.634056        6.644235 G4
    0.44       4.562603         6.83023 G4
    0.46       4.447485        6.988038 G4
    0.48       4.288701        7.117661 G4
     0.5       4.086252        7.219097 G4
    0.52       3.840136        7.292348 G4
    0.54       3.550355        7.337412 G4
    0.56       3.216909        7.354291 G4
    0.58       2.839796        7.342983 G4
     0.6       2.419018         7.30349 G4
    0.62       1.954575         7.23581 G4
    0.64       1.446465        7.139945 G4
    0.66        0.89469        7.015894 G4
    0.68       0.299249        6.863656 G4
G1:Type I borrowers choose FRMs and type II borrowers choose FRMs.
G2:Type I borrowers choose FRMs and type II borrowers choose ARMs.
G3:Type I borrowers choose ARMs and type II borrowers choose FRMs.
G4:Type I borrowers choose ARMs and type II borrowers choose ARMs.
Incremental wealth indicates the difference between the expected utility in the (ARM, ARM)
equilibrium and that in the out-of-the equilibrium.


                                                      24
Figure 2 Prime lending rate in Taiwan (1960-1997)



                                             INTEREST RATES
                     20
     INTEREST RATE



                     15

                     10

                     5

                     0
                          -       -
                      O ct 54 M ar 60 Sep-       -
                                          65 M ar 71 A ug-76 Feb-82 A ug-87   Jan-93      -
                                                                                       Jul 98   Jan-04
                                                        TIME


Source: TEJ




                                                             25
Table 10 Disposable income, housing price, and mortgage payment

Year        Average annual        Housing price             Prime        Mortgage
            disposable income     (per PIN)                 lending      payment
            Per household                                   rate
            (NT$)
       1964      28,591        8%
       1966      32,008        9%
       1968      38,514       11%
       1970      44,486       12%
       1971      50,280       14%
       1972      57,510       16%
       1973      71,054       19%
       1974      92,813       25%
       1975     101,821       28%
       1976     116,297       32%
       1977     130,830       36%
       1978     155,737       42%
       1979     188,407       51%
       1980     233,112       64%
       1981     266,433       73%
       1982     275,250       75%
       1983     295,887       81%
       1984     314,245       86%
       1985     320,495       87%
       1986     341,728       93%
       1987     366,487      100%       12.11        100%         6.25         $9.08      100%
       1988     410,483      112%       26.98        223%         6.75        $21.85      241%
       1989     464,994      127%       32.57        269%           10        $39.08      430%
       1990     520,147      142%       32.64        270%          8.5        $33.29      367%
       1991     587,242      160%       30.97        256%            8        $29.73      327%
       1992     639,696      175%       36.81        304%         7.75        $34.23      377%
       1993     727,879      199%        35.2        291%         7.63        $32.23      355%
       1994     769,755      210%       32.57        269%         7.25        $28.34      312%
       1995     811,338      221%       38.58        319%         7.03        $32.55      358%
       1996     826,378      225%       34.57        285%         7.03        $29.16      321%


Figure 3: Indices of disposable income, housing price and mortgage payment

              5

              4                                                       Average annual
                                                                      disposable income
              3
                                                                      (NT$)
              2                                                       Housing price(per
                                                                      PIN)
              1
                                                                      Mortgage payment
              0
               1960       1970     1980       1990      2000

                                  Year

Mortgage payment is calculated based on housing price and the interest rate assuming that a 20-year,
monthly payment mortgage hase been issued.
Source: Minister of Interior

                                                26
References

Alm, J. and Follain, J. Consumer demand for adjustable rate mortgages”
Housing Finance Review 6, 1987, 6-16.


Brueckner, J. The pricing of interest rate caps and consumer choice in the
market of adjustable rate mortgages” Housing Finance Review 5, 1986,
119-136.


Brueckner, J. Borrower mobility, self-selection, and the relative prices of
fixed-rate and adjustable-rate mortgages” Journal of Financial Intermediation,
2, 1992, 401-421


Brueckner, J. Why do we have ARMs?” Journal of the American Real estate
and Urban Economics Association, 21, 1993, 333-345.


Brueckner, J. and Follain, J. "The rise and fall of the ARM: an econometric
study of mortgage choice” Review of Economics and Statistics, 1988, 92-103.


Chiang, Yao-Min, "Balloon mortgage as an alternate choice", Unpublished
doctoral dissertation, The University of Iowa, 1996.


Chari, V. and Jagannathan, R. Adverse selection in a model of real estate
lending” The Journal of Finance, 1989, 499-508.


Dhillon, Upinder S., Shilling James D. and Sirmans C.F. Choosing between
fixed and adjustable rate mortgages” Journal of Money, Credit, and Banking
19, 1987, 260-167.


Sa-Aadu, J. and Sirmans, C.F. Differentiated contracts, heterogeneous
borrowers and the mortgage choice decision” Journal of Money, Credit, and
Banking, 1995, 498-510.


Yang, Tyler T. L. Self-selection in the fixed rate mortgage” Journal of the
American Real Estate and Urban Economics Association 20, Fall 1992,
359-391.



                                         27

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:7
posted:8/14/2012
language:English
pages:27