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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

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