Topic 3: Adjustable Rate Mortgage Mechanics

1. Topic 3: Adjustable Rate Mortgage Mechanics

2. Adjustable Rate MortgagesWhat Problem Do They Solve? • As we noted in our discussion of fixed rate mortgages, lenders bear a tremendous amount of interest rate risk when they hold mortgages. • Of course, for bearing this risk lenders demand that the market compensate them, which it does by “pricing” this risk into the market contract rate. That is, a risk-premium is added for the interest rate risk.

3. Adjustable Rate MortgagesWhat Problem Do They Solve? • The idea behind an adjustable rate mortgage (ARM) is to let the borrower bear at least a portion of that interest rate risk. • When market rates rise, the ARM contract rate will rise (at least for some types of ARM), resulting in a smaller decrease in the mortgage value. • When rates fall, the ARM contract rate will fall, reducing (but not eliminating) the prepayment incentive of the borrower, reducing the effects of negative convexity.

4. Adjustable Rate MortgagesWhat Problem Do They Solve? • Since this loan is now less risky for the lender, the market will not allow them to earn the same risk premium as in an FRM. • The net effect is that the contract rate (and effective yield) on the loan will be, on average, lower for the ARM than for the FRM.

5. Adjustable Rate MortgagesWhat Problem Do They Solve? • ARMs first began to achieve widespread use during the 1970s and early 1980s. This occurred largely because: • 1. Sustained interest rate volatility had reduced lenders appetite for bearing interest rate risk. • 2. High levels of interest rates were preventing some people from being able to meet income requirements for loans. By bearing the interest rate risk, these potential borrowers were able to reduce their contract rates enough to qualify for financing.

6. Adjustable Rate MortgagesWhat Problem Do They Solve? • ARMs are still widely used, despite today’s relatively low interest rate levels. • Many borrowers are willing to bear the interest rate risk for the discount in contract rate (and expected yield) which the market will grant. • Because of annual caps, if a borrower’s horizon for staying in the mortgage is rather short, ARMs frequently cannot exceed FRM rates, regardless of interest rate increases.

7. Adjustable Rate MortgagesWhat Structures Exist? • There are actually several variants of adjustable rate mortgages. These include: • Price Level Adjusted Mortgages (PLAMs) • Variable Rate Mortgages (VRMs) • Adjustable Rate Mortgages (ARMs) • Option Pay ARMs

8. Adjustable Rate MortgagesPLAMs • Price Level Adjusted Mortgages were developed during the 1970s. • Their design reflects the primary concern of the time: interest rate increases caused by unexpected increases in inflation. • Note in the design of the PLAM that the main risk it targets is interest rate increases; it largely ignores interest rate decreases, which are also problematic for lenders.

9. Adjustable Rate MortgagesPLAMs • Both lenders and borrowers are hurt during inflationary times. • For a discussion of “mortgage tilt” and its effect on borrowers see Ch. 4 of Bruggeman and Fisher. • If lenders misestimate future inflation, they will charge too low a contract rate on the mortgage, leading to a loss of value. • The PLAM was designed to reduce the effect of inflation on mortgage borrowers and lenders.

10. Adjustable Rate MortgagesPLAMs • Authors frequently assume market interest rates consist of three components: • i = r + p + f • Where: • i = real interest rate • p= risk premium • f= expected inflation

11. Adjustable Rate MortgagesPLAMs • Since determining future inflation is difficult, one approach is to create a mortgage which is relatively immune to the effects of inflation. • By doing this, you eliminate the need for the inflation premium. • One way to immunize the loan against inflation is by agreeing to adjust the balance based on future inflation.

12. Adjustable Rate MortgagesPLAMs • The mortgage would work as follows: • At time 0 the loan’s balance and interest rate would be determined as usual for a FRM. • The payment in the first year would be based upon this amount. • At the end of the first year, the balance would be adjusted by the growth (positive or negative) in the CPI, or some other index.

13. Adjustable Rate MortgagesPLAMs • Thus, if after the first year the balance were $100,000, but for that year the CPI had grown by 5%, the balance would be re-set to $105,000. • The next year’s payments would then be set such that they would amortize the new balance in the remaining term of the loan.

14. Adjustable Rate MortgagesPLAMs • Note that, especially in the early years of the loan, the nominal loan balance at the end of the year could be higher than at the beginning of the year (negative amortization), although in real dollars the balance would be lower. • The following table shows the balances, payments, and effective yield for a 10 year PLAM with a 6% contract rate and a 5% inflation rate.

15. Adjustable Rate MortgagesPLAMs Note that you can click on the above spreadsheet to enter and modify it.

16. Adjustable Rate MortgagesPLAMs • PLAMs are not seen much today for a couple of reasons: • The relatively low rate of inflation for the past 25 years. • Consumers really dislike the potential for negative amortization. • If inflation comes back, however, you might see this type of mortgage return.

17. Adjustable Rate MortgagesVRMs and ARMs • The PLAM only helps the lender avoid interest rate risk due to changes in the inflation rate. There are, of course, other reasons for volatility in interest rates. • Lenders designed other types of contracts to address those risks. • We will examine two closely related mortgages, the VRM and the ARM.

18. Adjustable Rate MortgagesVRMs and ARMs • These mortgages share a common basic structure and terminology, so let’s examine those first. • These mortgages are based upon the idea that interest rate risk – from whatever underlying source – can be shifted to the borrower by allowing the contract rate (and hence the payments) on the mortgage to adjust when market rates change.

19. Adjustable Rate MortgagesVRMs and ARMs • The contract rate is tied to some well-known interest rate. This rate is then called the index rate. • At set intervals (typically annually or quarterly) the contract rate is reset to the current value of the index rate plus a fixed risk premium, usually known as the margin. • The payment amount is then set so that it will amortize the loan in the remaining term.

20. Adjustable Rate MortgagesVRMs and ARMs • Thus, in its most pure form, the contract rate of an adjustable rate mortgage would be equal to: • c = r + m • Where c=contract rate • r= index rate • m = margin. • The more frequently the bank is allowed to reset the rate, the lower the lenders interest rate risk.

21. Adjustable Rate MortgagesVRMs and ARMs • Since the index rate and contract rate will change over time, we will use subscripts to denote these values at specific points in time: • c1 = r1 + m

22. Adjustable Rate MortgagesVRMs and ARMs • The most common index rates are: • LIBOR • The one-year treasury rate • One of several Cost of Funds Indices (COFI) • Lenders will select the index rate which allows them to most easily hedge their position.

23. Adjustable Rate MortgagesVRMs and ARMs • Consumers actually tend to dislike the pure ARM we described because they can get hit with a “sticker shock” if there are large interest rate movements between two resetting dates. • In practice, all adjustable rate mortgages have some form of process in them to limit the degree to which the monthly payment can jump at any one point in time.

24. Adjustable Rate MortgagesVRMs and ARMs • These limits come in two variants • Some mortgages, those we will refer to as Variable Rate Mortgages, limit the amount that the payment can change, but not the contract rate. • What we will refer to as Adjustable Rate Mortgages limit the amount that the contract rate can change, but not the payment amount. • Note that the book makes no distinction and calls each of these ARMs.

25. Adjustable Rate MortgagesVRMS • Rules of the contract: • The initial interest rate is set to the index rate plus a margin (ci = ri+m). • The contract rate is reset periodically (we will assume annually) to the current index rate plus margin (ci = ri+m) • The payment amount is set to amortize the remaining balance over the remaining term:

26. Adjustable Rate Mortgages VRMS • Rules of the contract (cont.) • The most the payment can change in at any given reset date is p%. Thus, the real way to determine the payment in year i is to take the minimum of the calculated payment and (1+p) of the previous period’s payment.

27. Adjustable Rate Mortgages VRMS • Rules of the contract (cont.) • Note, however, if the payment cap is hit, so that the payment only rises by p%, the contract rate has not been capped. Its rise has been unimpeded. This means that it is possible, if rates have moved far enough, that because of the payment cap, the payments may not cover even the interest owed. In such a case, the interest will be capitalized into the balance, resulting in negative amortization.

28. Adjustable Rate Mortgages VRMS • Rules of the contract (cont.) • You can determine the balance at the end of the year, including any negative amortization, once you know both the contract rate and the capped payment. The formula to do this is:

29. Adjustable Rate Mortgages VRMS • The following page has an embedded Excel spreadsheet with a VRM example. The details on this contract are: • r = LIBOR m = 2% • n =10 years p = 7.5% • Initial balance =$100,000 • As you can see, the effective interest rate on the loan is 11.81%

30. Adjustable Rate Mortgages VRMS

31. Adjustable Rate MortgagesAnother VRM Problem • It is possible that if interest rates are volatile enough, the payment cap could prevent the loan from amortizing within its stated term. • To see this, consider the following 30 year VRM, and the rather extreme interest rate volatility associated with it.

32. Adjustable Rate MortgagesAnother VRM Problem • The parameters of this loan are: • m=1% p=7.5%, • balance=$150,000 n=30 years • 0 Points

33. Adjustable Rate MortgagesVRMs Double click on spreadsheet to enter.

34. Adjustable Rate MortgagesAnother VRM Problem • To prevent this from happening, the contract will specify some method for dealing with such a situation. • A common method is to state that if the balance ever rises above some fixed amount (say 150% of original balance), the payment can be reset to the amount needed to amortize the loan, regardless of the caps. • The caps are then reinstated from this new, higher level.

35. Adjustable Rate MortgagesAnother VRM Problem • Thus the payment formula becomes: • Applying this to the example yields:

36. Adjustable Rate MortgagesVRMs

37. Adjustable Rate MortgagesARMs • As was the case with PLAMs, borrowers often find the possibility of negative amortization unappealing, yet they still want protection from large contract (and payment) increases in a given year. • To achieve this lenders really had only one choice: limit the contract rate changes (and hence the payments) in any given year.

38. Adjustable Rate MortgagesARMs • Note that doing this means that the lender retains more interest rate risk than in the VRM. This result in the borrower being charged a higher margin than in a VRM. • In return for this higher margin, however, the borrower does not have to contend with the possibility of negative amortization.

39. Adjustable Rate MortgagesARMs • The Contract Rules: • Contract rate is again tied to some index rate. • There is again a risk margin (m). • At any given adjustment period, however, the interest rate can not rise or fall by more than Y percentage points from the previous year’s rate. This is called the annual cap. • Thus, if the annual cap were 2 percentage points and last years rate were 7, this years rate can be no less than 5% and no more than 9%.

40. Adjustable Rate MortgagesARMs • The Contract Rules: • Further, the contract rate can never rise more than L percentage points above the initial rate. This is the Lifetime cap. • Finally, most of these loans also include a Teaser rate (), which is a one-year reduction in the margin (m).

41. Adjustable Rate MortgagesARMs • You can determine the contract rate in any year by the following formula: • c1=r1+m- • ci>1=max[min(ri+m,ci-1+y,c1+L),ci-1-y] • The next slide calculates the contract rate for a 10 year ARM with the following parameters: • r=LIBOR, m=3, y=2, L=5, =2

42. Adjustable Rate MortgagesARMs Once again, you can click into the above excel sheet and experiment with the formula yourself.

43. Adjustable Rate MortgagesARMs • After determining the contract rate, determining the payment and balance is straightforward • At the beginning of each year, the payment is set such that it would fully amortize the balance in the remaining term if the contract rate never reset. Thus, payment is determined by:note n is original term of loan in years.

44. Adjustable Rate MortgagesARMs • The balance can be determined at any point in time by discounting the remaining payments at the current contract rate. So, at the end of a year, the balance is equal to the remaining payments at that year’s contract rate (don’t switch to the next year’s contract rate until after determining the balance.)

45. Adjustable Rate MortgagesARMs • Note that under this scheme, negative amortization can never occur. This is a major reason that this type of loan is more popular with borrowers than the VRM. • Of course, the lender has less protection from interest rate risk – so they add a larger premium into the contract rate.

46. Adjustable Rate MortgagesARMs • The next slide shows the index rate, contract rate, monthly payment, and balances for a hypothetical ARM with the following parameters: • Loan term: 30 years Principal: 150,000 • Index: LIBOR • Parameters: m=2, L=6, y=2, =1 • The index rate is the same series from the last VRM example.

47. Adjustable Rate MortgagesARMs Click on spreadsheet to enter and modify it.

48. Adjustable Rate MortgagesARMs • Of course after determining the cash flows, we can determine the effective yield on the loan by finding the rate, r, which makes the following equation true:

49. Adjustable Rate MortgagesARMs • In the example we worked, that worked out to be 10.66%. • Note that ARMs (and VRMs) can have points associated with them. Points serve to raise the effective interest rate and as a prepayment penalty. • In the previous example, if the ARM had contained 2 points and the loan never prepaid, its effective interest rate would have been 10.90%.

50. Adjustable Rate MortgagesARMs vs. VRMs • A natural issue to examine is the behavior of an ARM relative to a similar VRM. • Let’s use the ARM and VRM examples we have already done. Note that the ARM has a 2% margin while the VRM is 1%. • This is okay, because the ARM has more interest rate risk for the lender.