This post compares 15year FRM and 30year FRM rates,
payments on 15year FRM and 30year FRM and 7year mortgage pay down estimates
for the 15year and 30year FRM.
Data for post:
The source of data is Freddie Mac.
A link to an HTML version of the 30year FRM rates
A link to an HTML version of the 15year FRM rate
Note also this data can be downloaded in Excel files also.
Question One: What are the average, standard deviation,
skew, minimum, maximum, the range, the 25^{th} and 75^{th}
percentile, and the interquartile range for the spread between the 15year and
30year FRM between January 1999 and July 2014?
Question Two: What are the average, standard deviation,
skew, minimum, maximum, the range, the 25^{th} and 75^{th}
percentile, and the interquartile range for the difference in the monthly
mortgage payment for the 15year and 30year FRM? Assume the initial loan balance is $100,000.
Question Three: What are the average, standard deviation,
skew, minimum, maximum, the range, the 25^{th} and 75^{th}
percentile, and the interquartile range for the difference in the reduction in
the mortgage balance for a $100,000 15year and 30year FRM, which is held for
exactly seven years?
Analysis: The statistics on the rate differential in
absolute terms and as a percent of the 30year FRM rate are presented in the
table below.
Rate Information:
30year FRM15year FRM

Diff as percent of
30Year 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 30year versus 15year 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:
30year FRM15year FRM

Diff as percent of 30Year 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 15year FRM payments are higher than 30year 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.
30year FRM15year 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.
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