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Analyzing ARM vs. Fixed Mortgages with Quantrix


So how do you make the decision between a fixed rate and ARM home loan? Many factors come into play including how long you plan to stay in the house and future projected interest rates. You would want to model many different interest rate scenarios in order to make a reasonable decision. Building a model to calculate this over the life of a 30 year loan can be a pretty daunting task in a traditional two-dimensional spreadsheet. Fortunately with Quantrix, you can build multiple scenarios into a model quickly and easily.

In a February 2004 speech to credit unions, Federal Reserve Board Chairman Alan Greenspan said that Federal Reserve research showed that “many homeowners might have saved tens of thousands of dollars had they held adjustable-rate mortgages rather than fixed-rate mortgages during the past decade”. However, the Mortgage Bankers Association reported that the more expensive fixed-rate loans accounted for 81% of mortgage originations in 2003. It shows that most borrowers are risk-averse and they are more comfortable with fixed-rate mortgages that protect them from potential higher payments if interest rates rise. Additionally, fixed rate mortgages are much easier to understand since modeling ARM loans can be quite complex in a traditional two-dimensional spreadsheet. So how do you make the decision between a fixed rate and ARM home loan? Many factors come into play including how long you plan to stay in the house and future projected interest rates. Borrowers need to model many different interest rate scenarios in order to make a reasonable decision.

Fortunately with Quantrix, you can build in multiple interest rate scenarios quickly and easily. By utilizing the Random (RAND) function to model how future interest rates might behave, you can become more confident as to which loan is right for you. This model takes into account the following scenarios:
Mortgage Case: Best-case ARM – Rates stay at the original terms of the ARM
Mid-case ARM
– Uses the RAND function to randomize rates between the Best and Worst cases Worst-case ARM – Pegs the rate to the highest possible rate in the shortest allowed time
30 year Fixed
- Rate is fixed over the life of the loan
ARM


Interest Rate Scenarios: The interest rate scenarios calculate the interest rates to use for the Mid-case calculation. Take a look at the Random Numbers matrix. The formula year=(rand) generates a random number for each year in each interest rate scenario. The Yearly Rate Schedule matrix uses these random numbers to calculate a projected interest rate for each Mid-case year. The formula uses the assumptions in the Main Inputs matrix to properly regulate the interest rate calculations. Want to add more interest rate scenarios? It is as easy as adding more items to the Scenario category in the Yearly Rate Schedule matrix. The more interest rate scenarios you add, the more stable the interest rate calculations for the Mid-case ARM become. The Differences matrix shows the cash flow results of the difference between the mid and worst case against the best case. The Cumulative Difference Matrix accumulates the differences by month (one might take this a step further to adjust for the time value of money). This cumulative difference is then charted which is shown above. You can easily change the Main Inputs matrix to enter the specifics of your current loan. Using this analysis, you can compare when an ARM might cost you more in payments than a traditional fixed mortgage. Factoring in how long you plan to stay in the house, you can make an informed decision on which mortgage is best for your personal situation. 

Downloads:

>> Mortgage Analysis Model


Note: This model is provided as an example, and only an example, of how Quantrix may be used to perform such analysis. Other variables and techniques, including the analysis of historical interest rates, may be used to model variable rate loans. Quantrix provides no advice or recommendations, either through this note or otherwise, with respect to choice of mortgage.

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