## Sunday, September 7, 2014

### Comparing 15-year FRM and 30-year FRM since 1999.

This post compares 15-year FRM and 30-year FRM rates, payments on 15-year FRM and 30-year FRM and 7-year mortgage pay down estimates for the 15-year and 30-year FRM.

Data for post:

The source of data is Freddie Mac.

A link to an HTML version of the 30-year FRM rates

A link to an HTML version of the 15-year FRM rate

Question One:  What are the average, standard deviation, skew, minimum, maximum, the range, the 25th and 75th percentile, and the interquartile range for the spread between the 15-year and 30-year FRM between January 1999 and July 2014?

Question Two:  What are the average, standard deviation, skew, minimum, maximum, the range, the 25th and 75th percentile, and the interquartile range for the difference in the monthly mortgage payment for the 15-year and 30-year FRM?  Assume the initial loan balance is \$100,000.

Question Three:  What are the average, standard deviation, skew, minimum, maximum, the range, the 25th and 75th percentile, and the interquartile range for the difference in the reduction in the mortgage balance for a \$100,000 15-year and 30-year FRM, which is held for exactly seven years?

Analysis:   The statistics on the rate differential in absolute terms and as a percent of the 30-year FRM rate are presented in the table below.

Rate Information:

 30-year FRM-15-year FRM Diff as  percent of 30-Year FRM Average 0.55 10.6% Median 0.53 8.6% STD 0.19 5.8% Skew 0.50 82.8% Min 0.25 3.3% Max 0.98 23.2% Range 0.73 19.9% Q1 0.39 5.7% Q3 0.68 13.2% Interquartile Range 0.29 7.5% Value July 2014 0.9 21.5%

The average 30-year versus 15-year FRM differential over this period was 0.55 percentage points with a range from 0.25 to 0.98 percentage points.

Right now the spread is large -- 0.9 percentage points.

Payment Differences:

 30-year FRM-15-year FRM Diff as percent of 30-Year FRM Average 217.31 37.9% Median 216.97 36.9% STD 9.54 6.5% Skew -0.01 34.7% Min 194.72 25.4% Max 239.72 53.0% Range 45.01 27.6% Q1 209.98 33.6% Q3 224.62 42.5% Interquartile Range 14.65 8.9% Value July 2014 217.2 44.8%

Naturally 15-year FRM payments are higher than 30-year FRM payments because you have a smaller period of time to pay off the mortgage.

The average monthly difference is  \$217.  The range is around \$45.

The payment differential in July 2014 is around the average.

Mortgage Pay down difference over 7 years.

The median mortgage duration is around 7 years.  At this term the average difference in mortgage balance is around \$26,300.   A person borrowing at July 2014 can expect a bit more equity build up.

 30-year FRM-15-year FRM Average \$26,294 Median \$26,309 STD \$446 Skew -0.1 Min \$25,204 Max \$27,204 Range \$2,000 Q1 \$25,949 Q3 \$26,618 Interquartile Range \$668 Value July 2014 \$27,004

Some of the math behind these calculations was previously laid out in my mortgage math problem.