ARMs or FRMs？ ─以蒙地卡羅模擬術探討固定利率房貸(FRMs)與指數型房貸(ARMs)之成本現值差異

Abstract

自台灣開放利率自由化與金融自由化以來，以往一直被大型行庫所把持的個人房貸市場也就此進入百家爭鳴的戰國時代，尤其近兩年利率水準不斷下降，各家銀行前仆後繼爭相推出『指數型房貸』，都標榜超低利率對消費者有利。 但是，指數型房貸真的利息支出較省嗎？以直覺的財務觀點來看，除非利率水準持平或不斷下降，否則在長達二、三十年的房貸期間內，很難保證民眾可以透過『對利率走勢的預期』，來達成節省利息支出的目的；而此時也有銀行預期利率已至谷底，而趁機推出超低利率的固定利率房貸，足見對未來的利率走勢大家看法不一，更沒有人能準確的預測。 為此，本文採用成本現值模型(Present Value Cost Model)，以台灣目前金融機構與金融市場的實際狀況，並參考國外相關之文獻及模型，來設立模型參數，透過蒙地卡羅模擬術，以數萬次模擬後得出之平均結果，探討不同情況下，指數型房貸(ARMs)與固定利率房貸(FRMs)究竟何者比較有利？以探求在台灣的制度及現狀下，借款人是否應相信指數型房貸(ARMs)包裝的美麗糖衣。 本研究結論整理如下：(1)不使用成本現值模型，僅比較指數型房貸與固定利率房貸之名目利率時，將忽略房貸之實際現金流量 (2)貸款人所適用之個人所得稅稅率，對FRMs與ARMs之成本現值比較並無影響(3)在固定之折現率下，指數型房貸之成本現值優勢將被誇大，應採用浮動之折現率較符合實際狀況(4)一般狀況下，指數型房貸之成本現值優勢約可持續12年(5)在低利率環境下，指數型房貸之成本現值優勢只能持續5年以內，貸款人應採用固定利率房貸(FRMs)(6)在高利率環境下，指數型房貸之成本現值可持續約整個貸款期間，故貸款人於利率高時應採指數型房貸(7)指數型房貸之指標利率(Index)機動性越高，較能反映市場狀況，對貸款人也較有利(8)設計模擬目前尚未出現之『反浮動利率房貸』，得出其成本現值優勢期間約12年(9)在貸款前三年可享有4.25%固定利率優惠之『混合型房貸』下，成本現值優勢較純粹之指數型延長。

Individual mortgage market that was once held by some large banks in Taiwan currently comes into a serious competition due to the boundless of interest rate and the deregulation of banking industry. Especially in the recent two years, a good deal of banks put great efforts to propose ARMs (Adjustable Rate Mortgages) even though the interest rates continue to decline. The major reasoning behind this is that they believe that a low interest rate environment is good for loan borrowers. However, the crucial argument being concerned is that whether mortgagors are able to cut interest expenses via a new financial instrument (ARMs). In the points of view of Finance, there is no guarantee as to if ARMs is always good on behalf of loan borrowers within loan term unless interest rate keeps unchanged or continue to going down. Meanwhile, some banks expect that interest rate will not drop further in the ongoing future, so they propose FRMs (Fixed Rate Mortgages), with the historical lowest level, against ARMs to attract borrowers to make business. What this means is that nobody can really predict the direction of interest rate precisely. Questions we are about to examine is that whether ARMs is better than FRMs or vice versa. Also, the most interest of this research is to see which one is a better deal under a variety of personal tax brackets. In order to find out these, this study follows the “present value cost model” with import parameters based upon financial market conditions of Taiwan. Then we can further investigate if ARMs is beneficial to mortgage borrowers or if it is just a beautiful veil. Results are summarized as follows ：(1)Without Present Value Cost Model employed, borrowers will neglect total cash flows for mortgages if they just consider nominal interest rates.(2)Different personal tax brcket has no effect on comparing present value for ARMs and FRMs.(3)Floating discount rate is better than fixed discount rate because it’s much more reasonable to be fitted in the real situation.(4) The present value of ARMs will be larger than that of FRMs on the 11th year under normal interest rate situation.(5)Also, the present value of ARMs will be larger than that of FRMs on the 5th year when interest rate is historical low. (6)The present value of ARMs will be larger than that of FRMs on the 19th year when interest rate is high. (7)When index rate of ARMs is much more active, then it’s better for borrowers.(8)The present value for inverse floating rate mortgages is large than that of FRMs on the 12th year.(9)The present value of mixed rate mortgages (Fixed rate 4.25% for first 3 years) is larger than that FRMs on the 14th year.