Chapter 5
Adjustable Rate Mortgages
1

Overview
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Adjustable Rate Mortgages and Lender
Considerations
Interest Rate Risk of Constant Payment
Mortgages
Price Level Adjusted Mortgage (PLAM)
Adjustable Rate Mortgages (ARM)
ARM Effective Yield
2

Adjustable Rate Mortgages and Lender Considerations
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The need for adjustable rate mortgage instruments
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The interest rate risk of constant payment mortgages is tested in
1970s when inflation accelerated
Thrifts (Savings and Loan Associations) borrow funds short-term at low rates then invest in long-term fixed rate mortgages (Maturity mismatch)
As long as short-term rates are low, this works fine
What happens if short-term rates rise (inflationary expectations)
(1) Maturity mismatch will cause severe problems
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First, market value of constant payment mortgage portfolio will be less
Second, prepayment rate will slow reducing revenues from prepayments and penalties
(2) Tilt effect: Inflation fuels future inflationary expectations leading to high rates and payments on constant payment mortgages –
Affordability problem
3

Interest Rate Risk of Constant
Payment Mortgages
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An constant payment mortgage is just like a corporate bond: it’s value will change depending on the current market interest rates
Suppose that we own a mortgage loan with the following original term: $100,000, 30-year, 10%, monthly payments
The monthly payment on this loan is 877.57
After 5 years, the market interest rate is 12%
The remaining (outstanding) balance of the loan is 96,574
What is the market value of the mortgage?
N
300
I/Y
12
P/Y
12
PV PMT
-83,322.24
877.57
FV
0
4

Price Level Adjusted Mortgage
(PLAM)
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With the PLAM the lender receives the real rate of return as the contract rate on the loan
The lender then receives the premium for inflation through an upward adjustment on the remaining balance of the loan
The upward adjustment is equal to the rate of inflation over the previous year
Loan payment pattern depends on the inflation
5

Price Level Adjusted Mortgage
(PLAM) – Continued
Loan Amount
Interest Rate
Loan Term
Payment per Year
Number of Payments
$60,000.00
4.00%
30
12
360
Month
Beginning
Loan
Balance
Monthly
Payment
35
36
37
23
24
25
0
1
11
12
13
$60,000.00
$59,122.42
$59,033.05
$62,479.98
$64,993.19
$67,529.70
$286.45
$286.45
$286.45
$303.64
$321.85
$341.17
Interest
$200.00
$197.07
$196.78
$208.27
$61,511.85
$303.64
$205.04
$61,413.26
$303.64
$204.71
$216.64
$63,925.16
$321.85
$213.08
$63,816.39
$321.85
$212.72
$225.10
Amortization
Ending
Loan
Balance
$86.45 $59,913.55
$89.37 $59,033.05
$89.67 $62,479.98
$95.37 $62,384.61
$98.60 $61,413.26
$98.93 $64,993.19
$105.21 $64,887.98
$108.77 $63,816.39
$109.13 $67,529.70
$116.07 $67,413.63
Inflation
6.00%
6.00%
6.00%
6

PLAM Payments
Monthly Payment
1800
1600
1400
1200
1000
800
600
400
200
0
0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360
Month
7

Price Level Adjusted Mortgage
(PLAM) – Continued
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Major shortcomings of the PLAM include:
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A relatively complicated loan instrument for the average borrower
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Negative amortization that may occur if an individual property price fails to rise with the level of general inflation upon which the annual adjustments to the balance are made
PLAMs may not completely solve the maturity mismatch problem unless financial intermediaries are able to issue price-level-adjusted deposits
8

Adjustable Rate Mortgages
(ARM)
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ARM allows the interest rate on the loan to move with the market interest rate
Ability of adjusting the interest rate shifts the interest rate risk to the borrower
The lender’s interest rate risk is not completely eliminated because interest rate adjustments occur in periodic intervals
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The longer the interval the greater the interest rate risk
Borrowers would not assume all of the interest rate risk.
For that reason there will be caps on the interest rate
9

Adjustable Rate Mortgages –
Continued
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A new loan payment is computed at each reset date
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Composite Rate = index + margin
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Index
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Interest rate that the lender does not control
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Treasury securities
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Cost Of Funds Index (COFI)
London Interbank Offered Rate (LIBOR)
Margin
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Premium added to the index
10

Adjustable Rate Mortgages –
Continued
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Expected Start Rate
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Index plus margin on loan closing date. This rate is lower than
Fixed Rate Mortgage (FRM) rate since interest rate risk is lower for lender
Actual Start Rate
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Market driven and likely to be lower than expected start rate
Teaser Rate – low rate to attract borrowers
Reset Date
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When mortgage payment is readjusted
Negative Amortization
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Payment does not cover the interest due and inflates the amount owed. The negative amortization may be allowed in the loan agreement
11

Adjustable Rate Mortgages –
Continued
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Limits or Caps
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Maximum increases allowed in payments, interest rates, maturity, and negative amortization
Floors
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Maximum reductions allowed in payments or rates
Assumability
Points
Prepayment
Conversion
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Right of a borrower to convert ARM into FRM
12

Adjustable Rate Mortgages –
Continued
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3/1, 5/1, and 7/1 Hybrid ARMs
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Longer initial reset period
The extension of initial reset period will reduce the spread between
ARM and FRM rates
Example: $100,000 with 6% initial rate for the first 3 years, monthly payments, and 30 years
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Payment per month for the first 3 years:
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N
360
I/Y
6
P/Y
12
PV PMT
-100,000 599.55
FV
0
Balance of the loan after 3 years is 96,084
Payment for the following year assuming a new rate of 6.5%
N
324
I/Y
6.5
P/Y
12
PV
-96,084
PMT
629.88
FV
0
13

Adjustable Rate Mortgages –
Continued
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Interest Only Hybrid ARM
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I.O. for initial reset period
I.O. Option ARM
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Borrower choice
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Pay interest only
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Pay interest & some principal
Sometimes negative amortization occurs
Fully amortizing payments required in future
14

Adjustable Rate Mortgages
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Teaser Rate
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Initial rate below market composite rate (index + margin)
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Market Competition
Accrual Rate – The loan payments are based on teaser rate, however, balance of the loan increases by difference between market interest rate and teaser rate
Negative Amortization – The existence of accrual rate will cause negative amortization
Payment Shock – Significant increase in payment when there is a reset of interest rate
15

Adjustable Rate Mortgages
Yield & Rates
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Yields are a function of:
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Initial interest rate
Index & margin
Any points charged
Frequency of reset date
Any rate or payment limits
16

17

Adjustable Rate Mortgages
Yield & Risks
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Default Risk
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Can borrower afford new payments?
Impact of negative amortization
Pricing Risk
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Allocation of interest rate risk
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Impact on default risk of specific borrowers
18

Adjustable Rate Mortgages
Yield & Risks
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Basic Relationships:
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ARM yield is lower than FRM yield at origination otherwise no one would be willing to take interest rate risk
Short-term vs. long-term indices – short-term rate are more volatile than long-term rates. Less risk averse borrowers will prefer ARM based on a short-term index
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Shorter reset periods vs. Longer reset periods – frequent rate adjustments reduce lender’s interest rate risk
Impact of caps & floors – they will reduce the borrower’s interest rate risk by limiting the adjustments
Negative amortization
19

ARM Examples
Initial interest rate, or start rate loan maturity
Maturity of instrument making up index
Percent margin above index
Adjustment interval, or reset date
Points
Payment cap
Annual interest rate cap
Lifetime cap
Negative amortization
BOY
2
3
4
Index
10.00%
13.00%
15.00%
5 10.00%
BOY = Beginning Of Year
ARM I
8.00%
30
1 year
2.00%
1 year
2.00%
None
None
None
No
ARM III
11.00%
30
1 year
2.00%
1 year
2.00%
None
2.00%
5.00%
No
20

ARM I – Payments / Balances
Loan Amount
Initial Rate
Loan Term
Payment per Year
Number of Payments
Year 1 Payment:
N I/Y
360 8.00%
P/Y
12
Balance After 1 Year:
N
348
I/Y
8.00%
P/Y
12
Year 2 Payment:
N
348
I/Y
12.00%
= Index + Margin
P/Y
12
ARM I:
PV
-60,000
PV
59,499
PV
-59,499
$60,000.00
8.00%
30
12
360
PMT
440.26
PMT
440.26
PMT
614.24
FV
0
FV
0
FV
0
21

ARM I – Payments / Balances
– Continued
Balance After 2 Years:
N I/Y
336 12.00%
P/Y
12
PV
59,255
PMT
614.24
FV
0
Year 3 Payment:
N
336
I/Y
15.00%
= Index + Margin
P/Y
12
Balance After 3 Years:
N
324
I/Y
15.00%
P/Y
12
Year 4 Payment:
N
324
I/Y
17.00%
= Index + Margin
P/Y
12
PV
-59,255
PV
59,106
PV
-59,106
PMT
752.26
PMT
752.26
PMT
846.20
FV
0
FV
0
FV
0
22

ARM I – Payments / Balances – Continued
Balance After 4 Years:
N I/Y
312 17.00%
P/Y
12
PV
58,991
PMT
846.20
FV
0
Year
1
2
3
4
5
Year 5 Payment:
N
312
I/Y P/Y
12.00%
= Index + Margin
12
Balance After 5 Years:
N I/Y
300 12.00%
P/Y
12
Month
1
13
25
37
49
PV
-58,991
PMT
617.60
FV
0
PV
58,639
PMT
617.60
FV
0
Month
12
ARM I
Interest Payment Balance Index
8.00% $440.26
$59,499
24
36
48
60
12.00%
15.00%
17.00%
12.00%
$614.24
$752.26
$846.20
$617.60
$59,255
$59,106
$58,991
$58,639
10.00%
13.00%
15.00%
10.00%
23

ARM III – Payments /
Balances
ARM III:
Loan Amount
Initial Rate
Loan Term
Payment per Year
Number of Payments
Year 1 Payment:
N I/Y
360 11.00%
$60,000.00
11.00%
30
12
360
P/Y
12
PV
-60,000
PMT
571.39
FV
0
Balance After 1 Year:
N
348
I/Y
11.00%
P/Y
12
PV
59,730
PMT
571.39
FV
0
Year 2 Payment:
N I/Y P/Y PV PMT FV
348 12.00% 12 -59,730 616.63 0
= MIN (Index + Margin, Previous Rate + Annual Cap, Initial Rate + Lifetime Cap)
24

ARM III – Payments /
Balances – Continued
Balance After 2 Years:
N I/Y
336 12.00%
P/Y
12
PV
59,485
PMT
616.63
FV
0
Year 3 Payment:
N I/Y P/Y PV PMT FV
336 14.00% 12 -59,485 708.37 0
= MIN (Index + Margin, Previous Rate + Annual Cap, Initial Rate + Lifetime Cap)
Balance After 3 Years:
N
324
I/Y
14.00%
P/Y
12
PV
59,301
PMT
708.37
FV
0
Year 4 Payment:
N
324
I/Y
16.00%
P/Y
12
PV
-59,301
PMT
801.65
FV
0
= MIN (Index + Margin, Previous Rate + Annual Cap, Initial Rate + Lifetime Cap)
25

ARM III – Payments / Balances – Continued
Balance After 4 Years:
N
312
I/Y
16.00%
P/Y
12
PV
59,159
PMT
801.65
FV
0
Year 5 Payment:
N
312
I/Y
12.00%
P/Y
12
PV
-59,159
PMT
619.37
FV
0
= MIN (Index + Margin, Previous Rate + Annual Cap, Initial Rate + Lifetime Cap)
Balance After 5 Years:
N
300
I/Y
12.00%
P/Y
12
PV
58,807
PMT
619.37
FV
0
Index
10.00%
13.00%
15.00%
10.00%
Year
1
2
3
4
5
Month
1
13
25
37
49
ARM III
Month Interest Payment Balance
12 11.00% $571.39
$59,730
24
36
48
60
12.00%
14.00%
16.00%
12.00%
$616.63
$708.37
$801.65
$619.37
$59,485
$59,301
$59,159
$58,807
26

ARM I Effective Yield
CF
0
=
C01 =
C02 =
C03 =
C04 =
C05 =
C06 =
CPT IRR
Annual
ARM I
-58,800.00
440.26
F01 =
614.24
F02 =
752.26
F03 =
846.20
F04 =
617.60
F05 =
59,256.86
F06 =
1.0851 %
13.02 %
12
12
12
12
11
1
27

ARM III Effective Yield
ARM III
CF
0
= -58,800.00
C01 = 571.39
F01 =
C02 =
C03 =
616.63
708.37
F02 =
F03 =
C04 =
C05 =
801.65
619.37
F04 =
F05 =
C06 = 59,426.10
F06 =
CPT IRR
Annual
1.1231 %
13.48 %
12
11
1
12
12
12
28