Fixed loans are for the conservative, polite, quiet, keep to themselves chumps with those steady jobs whose fixed payments sound as soothing as calm ocean waves rushing upon shore on a cool summer day. Variable rate loans are for the bold, aggressive, “brass balls” types that are comfortable with the fact that their future payment amounts are unknown, willing to look uncertainty straight in the eye.  Well, actually, this is essentially the non-helpful  conclusion that I came to after searching “variable versus fixed loans” on google. Although it is valid advice that the better of the two loans depends on the type of individual, there is a more quantitative way to contemplate things. And, as always, I have created an excel spreadsheet to help calculate things out.

Methodology

For a fair comparison I want to keep payments on both loans the same and see which one is paid off quicker, essentially finding the one that you end up paying less interest on. Usually the payments are dictated by the type of loan and interest rates, but here I am taking the approach that the consumer of the loan is dedicated to making a fixed payment amount monthly regardless of the type of loan. For the fixed rate, it is simple, just do the calculations and sum up the total interest paid each month…done. But for the ARM, how do we know what the future path of interest rates is going to be? Well, in short, we don’t, but we can use Eurodollar futures that are very actively traded in the market for the consensus on the anticipated path of interest rates 10 years out. It’s far from being a crystal ball that glimpses into the future, but many large banks and institutions have put up large sums of money betting that is where the rates will be to the best of their knowledge. What I’m trying to say is, these aren’t just petty $5 bets between you and you’re coworker, these are some serious calls here. In any case, these eurodollar futures provide an estimate of future libor, which is a common index used for variable loans. Even if your loan’s index isn’t libor, it is most likely highly correlated to it. So now, having a set of predictions for interest rates the process of calculating total interest paid on a variable loan is just a matter of plugging in this predicted rate path into the spreadsheet.

Download the Spreadsheet
ARM versus Fixed

Inputs

• Eurodollar Data – A tab where the latest eurodollar information goes. For the latest data simply copy and paste the table from here http://www.cmegroup.com/trading/interest-rates/stir/eurodollar.html
• Loan Amount – The total amount of your loan
• Fixed Rate – The fixed rate that you have been quoted
• Fixed Rate Length in Years -
• Fixed Rate Monthly Payment – The amount you plan on paying each month. The minimum required payment is conveniently calculated a few rows below and is called “Minimum fixed rate payment”, which is the amount the bank is going to charge you each month. I would keep this payment and the variable payment the same for comparisons sake.
• Variable Spread or Margin – The amount above the libor rate that you will be charged for a variable rate loan. If the variable loan index isn’t libor then you will need to do a few simple calculations and figure out your spread against libor
• Variable Rate in Months – The number of months between the reset of your rate
• Variable Rate Monthly Payment – The amount you plan on paying each month. For comparison purposes I would highly recommend keeping it the same as the fixed rate monthly payment as the goal here is to see which loan comes out to be cheaper

Sample Results

The sample results here are from using data from March 13, 2010. The graphs below are simply the amount of principal remaining on the loan after an amount of time.

Example #1

Let’s compare today’s 30 year fixed versus a variable rate that resets yearly. We will set the fixed interest rate at 5.00% and the variable rate spread to a very reasonable 2.50%. The minimum 30 year fixed payment is $536.82, but let’s round that up to $600. The chart below graphs what your remaining balance would look like for the next 30 years if you made $600 payments in the fixed and variable loan.

What in the world is going on here? Well, interest rates are predicted to rise at a fast enough rate to where making constant $600 payment each month isn’t enough for the variable rate. The fixed rate clearly wins here, unless you plan to get out of the loan before 72 months .

Example #2

What if we increased the payment in example #1 to $800 a month? Then variable leads up until 75 months and starts losing after that.

Example #3

What if the variable spread was only 1.50% instead of 2.50% and we were making $800 payments? Then variable wins, but just barely. Between 30 and 90 months is where the savings for the variable loan are the greatest.

Example #4

What if the variable reset was only 1 month instead of 12 and we use the same assumptions as in example 3 above? Then fixed wins again, but variable leads up until 120 months in.

Example #5

OK, so for the most part, it looks like the fixed rate loan is the superior choice if your goal is to pay it off in it’s entirety. You can’t justify picking the variable rate loan, gambling on the hope that interest rates play out like expected for such a minor advantages like in example #3. If interest rates actually rose faster than anticipated by the market then the choice of selecting the fixed rate is a no-brainer. But, what if the consumer thought that interest rates would remain low longer than what the market thought? Below we use an extended period of low interest rates and see how the loans end out. Everything else is the same with a 5% fixed rate and $800 monthly payment for both the variable and fixed.

Wait, what? That’s it dude? I guess, even when you hope for the absolute best scenario for a variable loan, you don’t end up saving that much. And note that the scenario considered is quite an unrealistic one.

Example #6

And here are the results using a future rate path of quickly rising interest rates (yellow line from example above). As expected, the variable ends up costing the consumer a lot more in the long run and the savings are drastically reduced in the short run.

Conclusion

If you are planning to fully pay off the loan, then in this low interest rate environment, it looks like the fix rate is definitely the way to go. If you are planning to exit within 7 years or less, then the variable starts making more sense. But, all this depends on the terms of the loan that you can get and current market conditions. Everything calculated here is based off of a snapshot on March 13, 2010. Utilize your own judgement and numbers when selecting the best type of loan for you. Evaluate the trade-offs between how much you can save and what happens if interest rates don’t play out the way you or the market expects them to. And just remember, if there was anything to be sure of, it is that you and the market are both going to be wrong as no one can accurately predict these things. So be safe and leave room for error. That’s all folks. Peace out.