# Should home buyers choose a short- or long-term mortgage? The preferred option depends upon a variety of factors.

Choosing the term of a home mortgage is one of the most difficult decisions borrowers have to make, especially for those who can afford either a short-term mortgage payment or a long-term mortgage payment. Because there are many factors that influence the choice of mortgage term, given additional investment opportunities, making a clear-cut decision is difficult. Using a Monte Carlo simulation, the authors conclude that an individual's marginal tax rate is the key factor for borrowers who plan short-term homeownership, whereas the mortgage interest rate is the key factor for borrowers who plan long-term homeownership. Mortgage term decisions can be quite different due to the different effects of major factors. If, however, the home mortgage market correctly reflects information about those factors, it is expected that mortgage borrowers will have an individual preference for either a short- or long-term loan.[ILLUSTRATION OMITTED]

The Alternatives

What kind of mortgage should home buyers choose: a short-term or a long-term mortgage? This may be a common question, but it is not easy to answer. In fact, the choice of mortgage term can be one of the most important investment decisions an individual makes, because it can substantially influence one's investment portfolio. To get a relevant answer, one must consider many factors, such as mortgage interest rates, investment returns, and tax effects. The mortgage term decision should take into account those factors and investment options.

Upinder S. Dhillon, James D. Shilling, and Clemon F. Sirmans ("The Mortgage Maturity Decision: The Choice Between 15-Year and 30-Year FRMs," Southern Economic Journal, vol. 56, no. 4, April 1990, pp. 1103-1116) found that while a short-term mortgage is preferable for wealthy people in a high tax bracket, a long-term mortgage is better for people with relatively high house prices and interest rates. Richard A. Phillips, Eric M. Rosenblatt, and James H. VanderHoff ("The Effect of Relative Pricing on the Fixed-Rate Mortgage Term Decision," Journal of Real Estate Research, vol. 7, no. 2, 1992, pp. 187-194) found that the probability of choosing a short-term mortgage decreases with the increase in the mortgage spread and the expected housing price. David R. Vruwink and Dann G. Gisher ("The Effects of Income Tax Rates and Interest Rates in Choosing Between 15-and 30-Year Mortgages," The CPA Journal, November 1995, pp. 72-75) analyzed mortgage rates and tax savings and proposed conditions for choosing a 30-year mortgage. William G. Kistner ("Home Mortgage Loan Term Options," Healthcare Financial Management, vol. 52, no. 10, October 1998, pp. 86-88) analyzed the mortgage term decision with investment gain taxes as well as investment yields, and supported a 30-year mortgage with an increase in pretax investment growth. Delbert C. Goff and Don R. Cox ("15-Year Versus 30-Year Mortgage: Which Is the Better Option?" Journal of Financial Planning, vol. 11, no. 2, April 1998, pp. 88-95) also supported a 30-year mortgage with a significant increase in a tax-deferred investment savings. Joseph A. Tomlinson ("Advising Investment Clients About Mortgage Debt," Journal of Financial Planning, vol. 15, no. 6, June 2002, pp. 100-108) showed that the benefit of a 30-year mortgage increases with investment returns and time horizons. Peter M. Basciano, James M. Grayson, and James Walton ("Is a 30-Year Mortgage Preferable to a 15-Year Mortgage?" Journal of Financial Counseling and Planning, vol. 17, no. 1, 2006, pp.14-21) employed the Monte Carlo simulation to calculate the net benefit of a 30-year mortgage with a tax-deferred savings against a 15-year mortgage, considering mortgage rates, tax rates, and investment returns. Their results supported a 30-year mortgage in both a high and low mortgage rate environment.

The key question is whether a long-term mortgage with the payment-difference investment option is preferable to a short-term mortgage with an after-paying-off investment option. The fundamental scenario that previous studies used is this: A long-term mortgage borrower can save the interest tax shield as well as the difference in payments, but a short-term mortgage borrower can start saving after paying off the loan. Under several different conditions, it makes sense to compare two different mortgage terms with investment options for each.

Within the same fundamental scenario, it is assumed that a mortgage borrower can afford the mortgage payment, regardless of the term chosen. While a long-term borrower saves the interest tax shield and the payment difference until maturity, a short-term borrower starts saving the mort gage payment after paying off the short term mortgage loan until the long-term maturity. In addition, it is assumed that if the borrower makes contributions to a tax-deferred savings account, the deposits will amount to the maximum of the personal tax shield.

This study considers more factors than previous studies and uses two mortgage terms--a 15-year (short-term) fixed-rate mortgage (FRM) and a 30-year (long-term) FRM.

The factors considered are as follows:

* Mortgage interest rate

* Mortgage interest rate spread between a 30-year FRM and a 15-year FRM

* Marginal tax rate

* Annual investment return

* Investment gain tax rate

* Annual investment trading and management fee

* Default risk of the annual investment contribution

* Type of investment portfolio

* Length of homeownership.

Although Goff and Cox (1998) mentioned the default risk of the investment contribution, they did not incorporate it in their model. Previous studies overlooked the length of home ownership. If mortgage borrowers expect to refinance or sell their home before paying off the mortgage loan, the mortgage term decision may be quite different. All of these factors are incorporated into the authors' model, which investigates their dynamic effects on the mortgage term choice. A Monte Carlo simulation is used for the purpose of providing realistic and dynamic analyses through its stochastic characteristics. It is assumed that investment return is normally distributed with a mean and standard deviation. Then, results are computed using random samples generated from the normal distribution. The simulation enables the model to be implemented under various situations. The assumption of the normal distribution may be a limitation of the Monte Carlo simulation, but, as in Basciano, Grayson, and Walton (2006), it seems to be generally acceptable. Because the focus is on investigating how factors affect the mortgage term decision rather than estimating specific values, the model is entirely generic and free from any specific data, geographical areas, asset categories, rules, or policies. Unlike previous studies, the authors' study finds that when taking into account all the factors' dynamic effects together, the individual mortgage term decision can be quite different.

EXHIBIT 1 Base Scenario Actual loan amount: $200,000 30-year mortgage rate: 5% Mortgage spread: 0.5% Marginal tax rate: 25% Mean of investment return: 5% Standard deviation of investment return: 6% Investment gain tax rate: 0% (tax-deferred savings) Investment trading and management fee: 1% Default probability of investment contribution: 0% Home Ownership (in Years) Net Gain * 5 $ 6,585 (98%) 10 17,234 (96%) 15 33,220 (94%) 20 22,161 (72%) 25 7,107 (52%) 30 -12,265 37%) * The simulated probability that the net gain is positive is in parentheses.

The simulation results show that the marginal tax rate and the mortgage interest rate are the most sensitive factors for short-term and long-term homeownership, respectively. In addition, from the effect of each factor on the mortgage term, one can expect a clientele effect, in which home buyers in a relatively high tax bracket with high risk tolerance and many investment gain tax shields are likely to choose a long-term (30-year) mortgage in a low-rate environment; home buyers in a relatively low tax bracket with low risk tolerance and few investment gain tax shields are likely to choose a short-term (15-year) mortgage in a high-rate environment.

Decision-Making Process

While a 3O-year mortgage borrower is expected to save both the interest tax shield and the payment difference during the whole mortgage period, a 15-year mortgage borrower is expected to start saving after completely paying off the mortgage loan in 15 years. The default risk is applied only to the investment contribution, because it is assumed that the borrower can afford at least the mortgage payment for the entire loan period regardless of the mortgage term. Therefore, both short-term and long-term mortgage loans have no payment default for the first 15-year period (the maturity of the short-term mortgage), and whenever the borrower faces any financial problem thereafter, she may reduce or skip investment contributions. The annual investment contribution for a 30-year mortgage borrower is calculated as follows.

EXHIBIT 2 imulation Results Other factors being held constant, the net gain is calculated, given an increase in each factor. The simulated probability that the net gain is positive is shown in parentheses. Panel A Panel A Length of Base 30-Year Mortgage Homeownership Case Mortgage Spread Interest Rate (years) 6% 7% 8% .6% .7% 5 $6,585 $5,426 $4,352 $3,411 $5,750 $4,887 (98%) (98%) (96%) (92%) (98%) (97%) 10 17,234 12,550 8,917 5,317 14,899 13,510 (96%) (92%) (84%) (71%) (94%) (91%) 15 33,220 20,731 13,331 4,004 29,010 26,875 (94%) (84%) (72%) (55%) (92%) (91%) 20 22,161 -1,505 -15,519 -36,989 17,026 14,395 (72%) (43%) (27%) (11%) (67%) (63%) 25 7,107 -27,434 -50,808 -83,130 1,369 -2,174 (52%) (23%) (11%) (3%) (48%) (43%) 30 -12,265 -57,736 -90,430 -133,897 -19,402 -23,278 (37%) (12%) (4%) (1%) (32%) (26%) Panel B Length of Base Mean of Marginal Homeownership Case Investment Tax Rate Return (years) 5.5% 6% 6.5% 28% 33% 5 $6,585 $7,034 $7,345 $7,648 $8,791 $12,827 (98%) (99%) (99%) (99%) (100%) (100%) 10 17,234 19,085 20,807 23,265 22,320 32,292 (96%) (97%) (98%) (99%) (99%) (100%) 15 33,220 38,302 43,594 50,392 42,213 58,887 (94%) (97%) (97%) (99%) (98%) (99%) 20 22,161 32,138 44,727 57,758 31,441 47,437 (72%) (80%) (89%) (93%) (80%) (90%) 25 7,107 22,093 41,368 61,684 15,805 29,946 (52%) (63%) (77%) (87%) (58%) (69%) 30 -12,265 6,887 33,820 62,470 -5,137 5,863 (37%) (48%) (66%) (78%) (39%) (48%) Panel A Length of Homeownership (years) .8% 5 $4,046 (94%) 10 11,615 (88%) 15 23,564 (88%) 20 10,068 (57%) 25 -7,015 (38%) 30 -29,532 (25%) Panel B Length of Homeownership (years) 35% 5 $14,483 (100%) 10 36,214 (100%) 15 67,392 (99%) 20 56,367 (92%) 25 39,170 (74%) 30 14,568 (53%)

Year 1 Through Year 15

A[C.sub.30] = (12[[P.sub.15] - [P.sub.30]] + [T.sub.m][[I.sub.30]-[I.sub.15])/(1 - [T.sub.m])

if [T.sub.1]= 0 (tax-deferred investment)

A[C.sub.30] = 12([P.sub.15] - [P.sub.30])+[T.sub.m]([I.sub.30]-[I.sub.15])

if [T.sub.1] > 0 (non-tax-deferred investment) A[C.sub.15] = 0

In these equations, A[C.sub.t] is the annual contribution of the t-year mortgage, [P.sub.t] is the monthly payment of the t-year mortgage, [I.sub.t] is the annual interest of the t-year mortgage, [T.sub.m] is the borrower's marginal tax rate, and [T.sub.I] is the investment gain tax rate. The annual contribution consists of the interest tax shield and the payment difference. It is assumed that the mortgage borrower makes the annual contribution that amounts to the maximum value of the marginal tax shield for a tax-deferred account.

Year 16 Through Year 30

A[C.sub.30] = [[[[P.sub.15] - [P.sub.30]] + [T.sub.m][[I.sub.30] - [I.sub.15]] - 12[P.sub.15]DP/[1 - [T.sub.m]])]/[(1 - [T.sub.m])]] if [T.sub.I] [Equal] 0

A[C.sub.30] = [[12([P.sub.15] - [P.sub.30]) + [T.sub.m]([I.sub.30] - [I.sub.15]) - 12[P.sub.15]DP]/[(1 - [T.sub.m])]] if [T.sub.I] [Greater than] 0

A[C.sub.15] = 12[P.sub.15](1 - DP)/(1 - [T.sub.m]) if [T.sub.I] [Equal] 0

A[C.sub.15] = 12[P.sub.15](1 - DP) if [T.sub.I] [Greater than] 0

In these equations, DP is the default probability of the investment contribution. Starting with year 16, a 15-year borrower starts saving, and the annual contribution is reduced by the default risk of the investment contribution.

The net gain is defined as follows:

N[G.sub.j]=I[B.sub.30j]-(L[B.sub.30j]-L[B.sub.15j])

if 1 [less than or equal to] j [less than or equal to] 15

N[G.sub.j] = (I[B.sub.30j] - I[B.sub.15j]) - L[B.sub.30j]

if 16 [less than or equal to] j [less than or equal to] 30

In these equations, N[G.sub.j] is the net gain of the 30-year mortgage in year j, and and I[B.sub.j] are the investment balance and the loan balance in year j, respectively. Because a 15-year borrower makes no investment contributions prior to year 16 and has no loan balance after year 16, the net gain for years one through 15 is defined as the investment balance of the 30-year mortgage loan in excess of the difference between loan balances, whereas the net gain for years 16 through 30 is defined as the difference between investment balances in excess of the 30-year mortgage loan balance. Therefore, if the net gain is positive, the 30-year mortgage would be preferable to the 15-year mortgage, and vice versa.

Simulation Results

The Monte Carlo simulation was implemented to calculate the net gain. Throughout, all net gains reported below are simulated averages, and the parenthetical figures are the simulated probability that the net gain is positive. Exhibit 1 shows the base scenario, under the assumption that the borrower makes contributions to a tax-deferred savings account and has no risk of defaulting on the investment contribution. It shows that a 30-year mortgage appears to be better for borrowers who plan to live in the house for less than 25 years, at which point the net gain will become negative. Because the probability of the positive net gain exceeds 90% only for an ownership duration of 15 years or less, eventually, the 30-year mortgage is a much safer choice for borrowers who plan to live in the house for less than 15 years and then sell it. Considering the length of homeownership is, therefore, a very important factor in the result.

EXHIBIT 3 Simulation Results Panel A Length of Base Investment Trading and Homeownership Case Gain Tax Management (years) Rate Fee 5% 10% 15% 2% 5 $6,585 -$4,379 (0%) -$4,595 -$4,664 $5,630 (98%) (98%) (0%) (0%) 10 17,234 -8,418 (11%) -9,529 -10,420 12,117 (92%) (96%) (7%) (5%) 15 33,220 -12,704 -15,326 -17,947 19,991 (44%) (72%) (24%) (18%) (12%) 20 22,161 -14,830 -19,266 -24,368 -2,270 (84%) (94%) (19%) (15%) (10%) 25 7,107 -16,972 -23,167 -30,567 -26,440 (20%) (52%) (27%) (19%) (11%) 30 -12,265 -19,341 -27,047 -35,911 -53,557 (11%) (37%) (27%) (19%) (11%) Panel A Length of Base Default Investment Homeownership Case Probability Portfolio Length of of Investment Homeownership Contribution (years) 10% 20% 30% Conservative 5 $6,585 - - - $8,233 (99%) (98%) 10 17,234 - - - 25,888 (98%) (96%) 15 33,220 - - - 57,175 (98%) (94%) 20 22,161 $16,396 $11,669 $9,171 $69,569 (94%) (72%) (65%) (58%) (57%) 25 7,107 -3,430 (42%) -14,295 -21,318 82,639 (88%) (52%) (33%) (29%) 30 -12,265 -29,660 -47,552 -60,424 93,329 (83%) (37%) (26%) (19%) (12%) Panel A Length of Homeownership (years) 3% 4% 5 $4,870 $3,934 (98%) (93%) 10 7,734 3,754 (66%) (81%) 15 7,798 -770 (17%) 20 -22,733 -37,836 (64%) (44%) 25 -53,093 -71,502 (4%) (0%) 30 -82,445 -100,295 . (1%) (0%) Panel A Length of Homeownership Length of Homeownership (years) Balanced Aggressive 5 $8,940 $10,178 (97%) (95%) 10 29,891 38,570 (96%) (93%) 15 70,967 91,785 (96%) (91%) 20 $98,695 $151,692 (91%) (88%) 25 130,793 ' 224,857 (88%) (87%) 30 166,840 318,085 (84%) (83%) Conservative portfolio: return = 7%, standard deviation = 7% Balanced portfolio: return = 8%, standard deviation = 10% Aggressive portfolio: return = 9.5%, standard deviation = 14% The simulated probability that the net gain is positive is shown in parentheses.

Exhibit 2 and Exhibit 3 show how the net gain changes with respect to an increase in each factor, while the others are held constant. In Panel A of Exhibit 2, as mortgage interest rates increase, net gains decrease. This means that an increase in the mortgage interest rate favors the 15-year mortgage. If, however, the borrower plans to live in the house for less than 10 years, the chances that the net gain is positive are high (92%, 84%, and 71%, respectively), and, therefore, the 30-year mortgage would be a better option. On the other hand, net gains become negative for ownership of 20 years or more, and the chances that the net gain is positive significantly decrease. An increase in the mortgage spread has a similar effect on the net gain. Given each 0.1% increment, the chances that the net gain is positive are higher than about 90% for an ownership duration of 15 years or less.

Panel B of Exhibit 2 shows how the net gain changes with an increase in the investment return and the marginal tax rate. As both factors and the length of ownership increase, net gains significantly increase. The chances that the net gain is positive exceed almost 80% or 90% for an ownership of 20 years or less. This means that, other factors being held constant, a 30-year mortgage can be a better fit for borrowers who earn a high investment return and fall within a high marginal tax bracket.

In Exhibit 3, net gains decrease when the investment gain tax rate, the trading and management fee, and the default probability increase. If the borrower makes a taxable investment rather than a tax-deferred investment, the 15-year mortgage seems preferable, regardless of the length of ownership. Panel B of Exhibit 3 shows net gains for three different types of portfolios: conservative, balanced, and aggressive. The historical average return and standard deviation from 1928 to 2009 for stocks are 11.27% and 20.33%, respectively; for Treasury bonds, they are 5.24% and 7.78%. The conservative portfolio consists of 30% stocks and 70% bonds, the balanced portfolio consists of 50% stocks and 50% bonds, and the aggressive portfolio consists of 70% stocks and 30% bonds. As the borrower's risk tolerance and length of ownership increase, net gains increase considerably, with high probabilities.

Exhibit 4 summarizes a positive or a negative effect of each factor on the net gain, with other factors being held constant. A clientele effect may result from those factors and the borrower's degree of risk tolerance. On the whole, home buyers in a relatively high tax bracket with a high risk tolerance and many investment gain tax shields are likely to choose a long-term mortgage in a low-rate environment; home buyers in a relatively low tax bracket with a low risk tolerance and few investment gain tax shields are likely to choose a short-term mortgage in a high-rate environment. If the home mortgage market is efficient, a clientele effect would be expected.

EXHIBIT 4 Relationship Between the Net Gain and Factors Did a positive or a negative relationship between the net gain and each factor result from the simulation results? Mortgage Mortgage Mean of Investment Rate Spread Return et Gain Negative Negative Positive Marginal Investment Trading and Tax Rate Gain Tax Rate Management Fee Net Gain Positive Negative Negative Default Probability Net Gain Negative EXHIBIT 5 Sensitivity Test Assume that the base scenario for the sensitivity test is the same as the base case of Exhibit 1, with a 15% investment gain tax rate and 10% default probability. The percentage changes in the net gain, as compared to the base scenario, are shown below. Length of Homeownership 5 Years 10 Years 15 Years 20 Years Mortgage Interest Rate -11.39% -11.96% -15.62% -43.47% Mortgage Spread -6.53% -6.35% -7.32% -17.03% Marginal 26.86% 24.22% 20.82% 27.31% Tax Rate Mean of Investment Return 4.94% 8.51% 14.58% 36.45% Investment Gain Tax Rate -.62% -5.36% -4.05% -6.22% Trading and Management Fee -.06% -6.50% -9.18% -21.15% Default Probability - - - -8.65% Length of Homeownership 25 Years 30 Years Mortgage Interest Rate -200.84% -154.57% Mortgage Spread -58.08% -46.19% Marginal 83.35% 32.02% Tax Rate Mean of Investment Return 192.04% 148.54% Investment Gain Tax Rate -7.29% -7.32% Trading and Management Fee -81.38% -61.17% Default Probability -82.83% -12.12%

Sensitivity Test

Implementing a sensitivity test will increase each factor by 10%; the results can be approximately interpreted. Exhibit 5 shows the percentage change in the net gain as compared to the base scenario depicted in Exhibit 1. It turns out that while the net gain is most sensitive (the largest percentage change) to a change in the marginal tax rate for an ownership period of 15 years or less, it is most sensitive to a change in the mortgage interest rate for an ownership period of 20 years or more. On the other hand, in terms of length of ownership, 25 years shows the largest percentage change for all factors, except for the investment gain tax rate.

Advice for Different Homeowners

From the results of the Monte Carlo simulation above, the authors reached the following conclusions for home buyers facing different environments and individual circumstances:

* Mortgage term decisions can be quite different, due to the differing effects of the major factors involved.

* The length of ownership and the default risk of the investment contribution have a substantial effect on a borrower's most advantageous choice of mortgage.

* If the home mortgage market is infor-mationally efficient, one should expect the clientele effect in which home buyers in a high tax bracket with a high risk tolerance and many investment gain tax shields are likely to choose a long-term (30-year) mortgage in a low-rate environment; home buyers in a relatively low tax bracket with a low risk tolerance and few investment gain tax shields are likely to choose a short-term (15-year) mortgage in a high-rate environment.

* While the individual marginal tax rate is the key factor for borrowers who plan short-term home ownership, the mortgage interest rate is the key factor for borrowers who plan long-term homeownership.

Chung Baek, PhD, is an assistant professor of finance, and Khamis Bilbeisi, PhD, is a professor of accounting, both at the Sorrell College of Business, Troy University, Dothan, Ala.

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Title Annotation: | personal financial planning |
---|---|

Author: | Baek, Chung; Bilbeisi, Khamis |

Publication: | The CPA Journal |

Geographic Code: | 1USA |

Date: | Jun 1, 2011 |

Words: | 3839 |

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