## Thursday, October 9, 2014

### Comparing two ARMS

Comparing the 5-1 and 7-! ARM

Question: Right now the 5-1 ARM is around 2.8 percentage points and the 7-1 ARM is around 3.2 percentage points.  A person takes out a \$500,000 loan and amortizes the loan over 30 years.

How much debt remains on these mortgages at the time of the first payment adjustment if the mortgage is amortized over 30 years?

Assume that after the mortgage interest rate resets at 6.0%.   The first reset occurs at 5 years for the 5-1 ARM and at 7 years for the 7-1 ARM.

What is the required payment at the time the interest rate first resets?

Why might looking exclusively at the first interest rate reset understate the risk differential between the 5-1 ARM and the 7-1 ARM?

Analysis:

 ARM Comparisons 30-year Term 5-1 ARM 7-1 ARM Diff. % Diff rate 0.028 0.032 period 360 360 PV \$500,000 \$500,000 Payment when loan taken out (\$2,054) (\$2,162) \$108 -5.3% FV of loan (\$442,894) (\$422,064) (\$20,830) 4.7% Payment at first reset (\$2,854) (\$2,823) (\$31) 1.1%

Observations:

The initial 5-1 ARM payment is around \$108 less than the initial 7-1 payment.

The additional two years prior to interest rate reset reduces the loan balance by around \$21,000.

The 7-1 ARM payment is \$31 less than the 5-1 ARM payment at reset because of the additional reduction in the loan balance.

Conclusions and Caveats:

The 7-1 ARM has two additional years to prepare for the reset.  This extra time and extra equity means that the borrower has a much better shot at refinancing once interest resets start.

The scenario presented here understates interest rate risk associated with both of these loans because interest rates are reset annually.   The 5-1 ARM will reset three times by the time the 7-1 ARM resets once.   Hence interest shocks could be much larger for 5-1 ARMs than 7-1 ARMs.