Adjustable and Variable Rate Mortgages

1. Adjustable and Variable Rate Mortgages • Lecture Map • Comparison with Fixed Rate Mortgages • Loan features and risks • Typical ARM Provisions • Calculating ARM Payments • Interest and Payment Caps and Floors

2. Sharing Interest Rate Risk • Fixed Rate Loans • Risk born disproportionately by borrowers • ARMS • Risk more evenly distributed between borrowers and lenders • ARMS give borrowers more dollars today in exchange for lower initial interest rates and potential future interest rate risk

3. Price Level Adjusted Mortgages • PLM’s adjust mortgage balances at fixed intervals based on recent inflation • If inflation is 4%, loan balance at year end increases by 4% to reflect lenders’ opportunity loss • Borrower has lower payments up front, but risk of increasing principal balances • When would borrowers like this? • Low inflationary environments • Rapidly appreciating property values

4. Price Level Adjusted Mortgages (cont.) • PLM shortcomings from the lender’s perspective: • Retroactive CPI adjustments • Doesn’t cover lost interest on previous balance during the measurement period • Increase in default risk over time if balances increase significantly

5. ARMS • Adjustable rate mortgages • Rates are “indexed” • Based on underlying, specified base rate • Rate changes occur on regularly scheduled dates • Initial rate still reflects lender risk premiums at the initial loan date • Portion of spread attributable to the interest rate risk is minimized

6. ARMS and Loan Balances • ARM loan balances > fixed rate loan balances • If rates are lower: • Residential – same personal income can support higher payment • Commerical – same NOI can support higher payment • Higher loan balances against the same physical asset = higher default risk

7. ARMS and Loan Balances (cont.) • Do lenders think the interest rate risk is greater than the default risk? • What protects them against default risk? • Do they have similar protection against interest rate risk? • what are the risks to them of changes in interest rates?

8. ARM Provisions • Interest Rate • Index • Adjustment Interval • Margin • Composite Rate • Caps/Floors

9. ARM Provisions (cont.) • Interest Rate is still sum of an underlying base rate plus an initial spread • Rate will usually be lower than an equivalent maturity fixed rate loan • The Index is the base rate • Adjustment interval is the period between rate changes • 1 yr, 2 yrs, etc. • Spread, or “margin”, is specified up front • Composite Rate = Rate + Margin

10. ARM Provisions (cont.) • Caps and Floors • Designed to set limitations on the change in the composite rate • Limit the amount of rate risk the lender can pass to the borrower • ARMs with caps and/or floors have higher initial rates than fully floating ARMs • Still priced lower than fixed rate loans, however

11. Arm Provisions (cont.) • Caps • Limit the amount of upward rate movement passed to borrower • An Interest cap is an absolute limit • A Payment cap defers and accrues the difference between the actual rate and the paid rate • Floors • Set maximum reductions in payments/rates • Limit the downside benefit that borrowers can enjoy

12. How do ARM Provisions Interact? • The combination of terms sets the interest rate level and the distribution of risk between lender and borrower • Examples: • ARM with more frequent adjustment period and no caps/floors will have lowest up front rate, highest proceeds • Longer adjustment periods = higher initial rates • See exhibit 5-5, page 132 in text

13. Lender Risk with ARMs • ARMS may diminish lender rate risk, but don’t eliminate it • Too much time between adjustment periods • Index may be inappropriate • What about prepayment and default risk? • If loans are pre-payable, borrowers may repay to lock in rates in a rising rate environment • If rates rise and payments increase, borrowers may have difficulty making payments

14. Calculating ARM Payments • Initial Payments • Calculated just like FRM payments • Payments after each adjustment • Determine the outstanding mortgage balance • Balance = FV of the remaining payments • Determine the new composite rate • New index level plus the margin • Calculate the payment based on the new rate and the remaining years of the mortgage

15. An ARM Example • $10 million mortgage, 8% initial rate based on 10 year Treasury index, 2% margin, annual adjustments, 25 year amortization • Calculate year 1 payments: • PV = - $10,000,000 • I = 8 ÷ 12 • N = 25 x 12 • FV = 0 • PMT = ?

16. An ARM Example (cont.) • At the end of year 1 (adjustment period), index is 6.5% • What is the year 2 monthly payment? • Steps: • Determine the outstanding balance • Determine the new composite rate • Calculate new payments based on 29 year remaining life

17. An ARM Example (cont.) • Step 1: Calculate the balance • FV = 0 • PMT = $77,181.62 • I = 8 ÷ 12 • N = 24 x 12 • PV = $9,869,089 • Step 2: Determine the new interest rate • Index + Margin = 6.5% + 2% = 8.5%

18. An ARM Example (cont.) • Step 3: Calculate new payment • PV = $9,869,089 • I = 8.5% ÷ 12 • N = 24 x 12 • FV = 0 • PMT = $80,441.20

19. Interest Rate Caps • If caps limit borrower’s rate risk, they can cause a financial loss for lenders • Loss = lost compound interest • Example: Rate is capped at 8%, but uncapped rate would be 10% • Calculate the loss by discounting the payments actually being made at 10% • The actual loan balance less this new, lower PV amount = lender’s economic loss

20. Payment Caps and Negative Amortization • Payment Cap • Limits the current pay amount of a rate increase • May create “negative amortization” • Occurs when the actual payment at the adjusted interest rate exceeds the allowable percentage increase in the payment amount • Limits the increase in the payment, NOT the interest rate • The cap accrues the excess interest expense into the loan balance

21. Calculating Negative Amortization • Step 1: Calculate the unrestricted PMT at the new composite rate • Step 2: Calculate the allowed PMT based on the maximum percentage increase in PMT • Step 3: Determine how much of the unrestricted payment is interest vs. principal • Step 4: Deduct the interest component from the maximum allowable payment • Step 5: Calculate compound interest on the difference • Step 5: Add the difference to the loan balance

22. An Example • $60,000 loan, 9% year 1, 30 years • Year 1 payment = $482.77 • Payment cap = 7.5% • Year 2 composite rate = 12% • Therefore, max year 2 payment = $482.77 x 1.075% = • $518.98

23. An Example (cont.) • Year 2 unrestricted payment = • PV = loan balance at end of year 1= $59,590* • PMT = $482.77 • I = 12% ÷ 12 • N = 29 x 12 • PMT = 615.18 • However, the restricted payment = $518.98 • Need to deduct the restricted payment from the interest component of the $615.18 unrestricted payment

24. An Example (cont.) • Break down the unrestricted payment into principal and interest • How? • Monthly accruing interest = Loan balance x (I ÷ 12) • PMT x 12 = total paid during the year • Total PMT – interest = amortization

25. Finishing the Example • End of year 1 balance = $59,590 • Interest component of unrestricted payment = (59,590 x [.12/12]) = $595.90 • Accrual = actual payment - $595.90 = • $518.98 - $595.90 = (76.92) • Compound interest on the deferral: • PV =0; PMT = 76.92; I = .12 ÷ 12, N = 1 X 12 • Total compound interest = $975.54 • New loan balance = • $59,590 + $975.54 = $60,566