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1
Chapter 5
Adjustable Rate Mortgages
2
Overview
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
3
Adjustable Rate Mortgages and Lender Considerations
The need for adjustable rate mortgage instruments 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
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
4
Interest Rate Risk of Constant Payment Mortgages
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 I/Y P/Y PV PMT FV
300 12 12 -83,322.2
4
877.57 0
5
Price Level Adjusted Mortgage (PLAM)
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
6
Price Level Adjusted Mortgage (PLAM) – Continued
Loan Amount $60,000.00Interest Rate 4.00%Loan Term 30Payment per Year 12Number of Payments 360
MonthBeginning
Loan Balance
Monthly Payment
Interest AmortizationEnding Loan
BalanceInflation
01 $60,000.00 $286.45 $200.00 $86.45 $59,913.55
11 $59,122.42 $286.45 $197.07 $89.37 $59,033.0512 $59,033.05 $286.45 $196.78 $89.67 $62,479.98 6.00%13 $62,479.98 $303.64 $208.27 $95.37 $62,384.6123 $61,511.85 $303.64 $205.04 $98.60 $61,413.2624 $61,413.26 $303.64 $204.71 $98.93 $64,993.19 6.00%25 $64,993.19 $321.85 $216.64 $105.21 $64,887.9835 $63,925.16 $321.85 $213.08 $108.77 $63,816.3936 $63,816.39 $321.85 $212.72 $109.13 $67,529.70 6.00%37 $67,529.70 $341.17 $225.10 $116.07 $67,413.63
7
PLAM Payments
0
200
400
600
800
1000
1200
1400
1600
1800
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
Mon
thly
Pay
men
t
Monthly Payment
8
Price Level Adjusted Mortgage (PLAM) – Continued
Major shortcomings of the PLAM include: A relatively complicated loan instrument for the
average borrower 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
9
Adjustable Rate Mortgages (ARM)
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
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
10
Adjustable Rate Mortgages – Continued
A new loan payment is computed at each reset date Composite Rate = index + margin Index
Interest rate that the lender does not control Treasury securities Cost Of Funds Index (COFI) London Interbank Offered Rate (LIBOR)
Margin Premium added to the index
11
Adjustable Rate Mortgages – Continued
Expected Start Rate 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 Market driven and likely to be lower than expected start
rate Teaser Rate – low rate to attract borrowers
Reset Date When mortgage payment is readjusted
Negative Amortization Payment does not cover the interest due and inflates the
amount owed. The negative amortization may be allowed in the loan agreement
12
Adjustable Rate Mortgages – Continued
Limits or Caps Maximum increases allowed in payments, interest
rates, maturity, and negative amortization Floors
Maximum reductions allowed in payments or rates Assumability Points Prepayment Conversion
Right of a borrower to convert ARM into FRM
13
Adjustable Rate Mortgages – Continued
3/1, 5/1, and 7/1 Hybrid ARMs 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 Payment per month for the first 3 years:
Balance of the loan after 3 years is 96,084 Payment for the following year assuming a new rate of 6.5%
N I/Y P/Y PV PMT FV
360 6 12 -100,00
0
599.55 0
N I/Y P/Y PV PMT FV
324 6.5 12 -96,084 629.88 0
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Adjustable Rate Mortgages – Continued
Interest Only Hybrid ARM I.O. for initial reset period
I.O. Option ARM Borrower choice
Pay interest only Pay interest & some principal Sometimes negative amortization occurs Fully amortizing payments required in future
15
Adjustable Rate Mortgages Teaser Rate
Initial rate below market composite rate (index + margin)
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
16
Adjustable Rate Mortgages
Yield & Rates
Yields are a function of: Initial interest rate Index & margin Any points charged Frequency of reset date Any rate or payment limits
17Adju
stable
Rate
Mort
gage
Ris
ks
18
Adjustable Rate Mortgages
Yield & Risks
Default Risk Can borrower afford new payments? Impact of negative amortization
Pricing Risk Allocation of interest rate risk Impact on default risk of specific
borrowers
19
Adjustable Rate Mortgages
Yield & Risks Basic Relationships:
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
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
20
ARM ExamplesARM I ARM III
Initial interest rate, or start rate 8.00% 11.00%loan maturity 30 30Maturity of instrument making up index 1 year 1 yearPercent margin above index 2.00% 2.00%Adjustment interval, or reset date 1 year 1 yearPoints 2.00% 2.00%Payment cap None NoneAnnual interest rate cap None 2.00%Lifetime cap None 5.00%Negative amortization No No
BOY Index2 10.00%3 13.00%4 15.00%5 10.00%
BOY = Beginning Of Year
21
ARM I – Payments / Balances
Loan Amount $60,000.00Initial Rate 8.00%Loan Term 30Payment per Year 12Number of Payments 360
Year 1 Payment:N I/Y P/Y PV PMT FV
360 8.00% 12 -60,000 440.26 0
Balance After 1 Year:N I/Y P/Y PV PMT FV
348 8.00% 12 59,499 440.26 0
Year 2 Payment:N I/Y P/Y PV PMT FV
348 12.00% 12 -59,499 614.24 0= Index + Margin
ARM I:
22
ARM I – Payments / Balances – Continued Balance After 2 Years:
N I/Y P/Y PV PMT FV336 12.00% 12 59,255 614.24 0
Year 3 Payment:N I/Y P/Y PV PMT FV
336 15.00% 12 -59,255 752.26 0= Index + Margin
Balance After 3 Years:N I/Y P/Y PV PMT FV
324 15.00% 12 59,106 752.26 0
Year 4 Payment:N I/Y P/Y PV PMT FV
324 17.00% 12 -59,106 846.20 0= Index + Margin
23
ARM I – Payments / Balances – Continued
Year Month Month Interest Payment Balance Index1 1 12 8.00% $440.26 $59,4992 13 24 12.00% $614.24 $59,255 10.00%3 25 36 15.00% $752.26 $59,106 13.00%4 37 48 17.00% $846.20 $58,991 15.00%5 49 60 12.00% $617.60 $58,639 10.00%
ARM I
Balance After 4 Years:N I/Y P/Y PV PMT FV
312 17.00% 12 58,991 846.20 0
Year 5 Payment:N I/Y P/Y PV PMT FV
312 12.00% 12 -58,991 617.60 0= Index + Margin
Balance After 5 Years:N I/Y P/Y PV PMT FV
300 12.00% 12 58,639 617.60 0
24
ARM III – Payments / Balances
Loan Amount $60,000.00Initial Rate 11.00%Loan Term 30Payment per Year 12Number of Payments 360
Year 1 Payment:N I/Y P/Y PV PMT FV
360 11.00% 12 -60,000 571.39 0
Balance After 1 Year:N I/Y P/Y PV PMT FV
348 11.00% 12 59,730 571.39 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)
ARM III:
25
ARM III – Payments / Balances – Continued
Balance After 2 Years:N I/Y P/Y PV PMT FV
336 12.00% 12 59,485 616.63 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 I/Y P/Y PV PMT FV324 14.00% 12 59,301 708.37 0
Year 4 Payment:N I/Y P/Y PV PMT FV
324 16.00% 12 -59,301 801.65 0= MIN (Index + Margin, Previous Rate + Annual Cap, Initial Rate + Lifetime Cap)
26
ARM III – Payments / Balances – Continued
Index Year Month Month Interest Payment Balance1 1 12 11.00% $571.39 $59,730
10.00% 2 13 24 12.00% $616.63 $59,48513.00% 3 25 36 14.00% $708.37 $59,30115.00% 4 37 48 16.00% $801.65 $59,15910.00% 5 49 60 12.00% $619.37 $58,807
ARM III
Balance After 4 Years:N I/Y P/Y PV PMT FV
312 16.00% 12 59,159 801.65 0
Year 5 Payment:N I/Y P/Y PV PMT FV
312 12.00% 12 -59,159 619.37 0= MIN (Index + Margin, Previous Rate + Annual Cap, Initial Rate + Lifetime Cap)Balance After 5 Years:
N I/Y P/Y PV PMT FV300 12.00% 12 58,807 619.37 0
27
ARM I Effective Yield
CF0 = -58,800.00C01 = 440.26 F01 = 12C02 = 614.24 F02 = 12C03 = 752.26 F03 = 12C04 = 846.20 F04 = 12C05 = 617.60 F05 = 11C06 = 59,256.86 F06 = 1
CPT IRR 1.0851 %Annual 13.02 %
ARM I
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ARM III Effective Yield
CF0 = -58,800.00C01 = 571.39 F01 = 12C02 = 616.63 F02 = 12C03 = 708.37 F03 = 12C04 = 801.65 F04 = 12C05 = 619.37 F05 = 11C06 = 59,426.10 F06 = 1
CPT IRR 1.1231 %Annual 13.48 %
ARM III