Mortgages
An 11/7/2010
Adjustable-Rate adjustable-rate mortgage (ARM) is a loan on which the periodic contractual interest rate can change over the life of the mortgage the mortgage. The rate is reset periodically to a fixed spread (called the margin) over a benchmark or reference rate.
Most common reference rate is short term Treasury rate as determined by current market conditions Other reference rates include a calculated cost of funds or average mortgage rates
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Why ARMs?
Supply side motive: Interest Rate Risk
In the early 1980s, lenders were burned by holding long term fixed-rate mortgages while interest rates rose.
Heads
I Win; Tails You Lose game This amounted to an unanticipated transfer of wealth from lenders (savers) to borrowers.
Lenders wanted to modify the mortgage contract to share the risk between lender and borrower.
ARMs were born! By allowing the contract rate to vary with changes in market interest rates, the price of existing mortgage contracts is less sensitive to interest rate risk.
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Why ARMs?
Demand side motive: Tilt Problem
When inflation is high, lenders need to build in expected inflation into the loan rate.
Nominal
rate = real rate + risk adjustment + expected inflation rate With an FRM, this means the borrower must make high real payments at the start of the loan and low real payments at the end of the loan. This makes it hard for borrowers to qualify/afford for loans
This is the Tilt problem we saw earlier ARMs typically offer lower initial contract rates (why?), and this helps to reduce problems with affordability and Tilt.
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As of: 9/30/04
1-year ARM rates were much lower than 30-year FRM rates as of rates as of 9-30-04 (170 basis (170 basis points)
As of: 2/14/06
1-year ARM rates were only moderately lower than 30year FRM rates as of 2-14-06 FRM rates as of (70 bp)
Why are 1-year ARM rates lower than 15 and 30-year FRM rates?
Why are 1-year ARM rates more similar to 15 and 30year FRM rates in 2006?
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Pricing ARMs
Two things to consider when pricing ARMs versus FRMS Yield Curve
Most of the time, it costs more to borrow money at a fixed rate for a long time period than for a short time period. Why? Liquidity premium Expected inflation
Borrowers usually prepay their loans before maturity.
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Pricing ARMs
ARMs should be priced more like short term loans
1-year ARM rates reset every 12 months 30-year horizon for 30-year mortgages? 20-year horizon for 20-year mortgages? No! The median homeowner moves after 6 to 7 years Average stay among homeowners is 10 years If there was no refinance risk, price FRMs more like 7-year term loans
FRMs should be priced more like ____ term loans
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Yield Curve (US Treasuries), May 2004
6 5 4
Rate (%)
3 2 1 0 1 year 10 year 20 year 30 year
Maturity (years)
How big a spread would you expect to see between 1-year ARM rates and 20-year FRM rates given this yield curve?
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Treasury rates As of March, 2004
Date
03/01/04 03/02/04 03/03/04 03/04/04 03/05/04 03/08/04 03/09/04 03/10/04 03/11/04 03/12/04
1 mo
0.97 0.98 0.97 0.97 0.95 0.95 0.98 0.97 0.96 0.96
3 mo
0.97 0.97 0.97 0.96 0.94 0.96 0.96 0.96 0.97 0.96
6 mo
1.02 1.03 1.02 1.02 0.99 1.01 1.00 1.00 1.00 1.01
1 yr
1.23 1.26 1.26 1.25 1.16 1.15 1.15 1.17 1.15 1.18
2 yr
1.67 1.74 1.74 1.73 1.57 1.52 1.51 1.54 1.52 1.54
3 yr
2.15 2.21 2.23 2.21 2.02 1.95 1.92 1.94 1.95 1.95
5 yr
2.98 3.04 3.06 3.02 2.81 2.74 2.68 2.71 2.72 2.73
7 yr
3.49 3.55 3.57 3.53 3.32 3.26 3.20 3.21 3.23 3.24
10 yr
4.00 4.05 4.07 4.04 3.85 3.78 3.73 3.74 3.74 3.78
20 yr
4.86 4.90 4.92 4.89 4.73 4.69 4.64 4.65 4.66 4.68
Steep upward sloping yield curve: 7-year rates > 1-year rates
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Treasury rates as of February, 2006
Date
02/01/06 02/02/06 02/03/06 02/06/06 02/07/06 02/08/06 02/09/06 02/10/06 02/13/06
1 mo
4.33 4.32 4.31 4.32 4.33 4.34 4.32 4.36 4.38
3 mo 6 mo
4.47 4.48 4.48 4.48 4.49 4.50 4.52 4.53 4.55 4.60 4.62 4.63 4.68 4.67 4.67 4.67 4.70 4.71
1 yr
4.60 4.61 4.62 4.66 4.65 4.66 4.66 4.70 4.70
2 yr
4.59 4.59 4.59 4.62 4.61 4.64 4.66 4.69 4.68
3 yr
4.54 4.54 4.54 4.57 4.57 4.61 4.62 4.67 4.66
5 yr
4.51 4.51 4.50 4.51 4.52 4.55 4.55 4.59 4.58
7 yr
4.52 4.53 4.51 4.52 4.54 4.55 4.55 4.59 4.58
10 yr
4.57 4.57 4.54 4.55 4.57 4.56 4.54 4.59 4.58
20 yr
4.77 4.76 4.70 4.69 4.73 4.75 4.72 4.76 4.76
30 yr
N/A N/A N/A N/A N/A N/A 4.51 4.55 4.56
Slightly inverted yield curve: 7-year rates < 1-year rates!
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Defining an ARM: Margin
The periodic rate on an ARM is typically set as a fixed spread over an index or benchmark rate. For example, the coupon rate on a mortgage can be set at 275 basis points (BP) over the one year Treasury rate.
To find the rate on the loan, we look up the one year Treasury rate (say 1.5% in 2004) and add 275 BP to it to get the annual contract rate of 4.25%. The monthly periodic rate is set to 4.25/12 for 12 months. At the end of the 12 months, the contract rate is reset to 275 BP above the then current one year Treasury rate If the Treasury rate rises to 4.5% (as in 2006) the mortgage contract rate could rise to 7.25%!
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Defining an ARM: Margin
The spread over the index is called the loans margin. The margin on an ARM reflects an adjustment for risk relative to the index relative to the index
A perfect ARM is one for which the interest rate continually adjusts to offset changes in market interest rates
For a perfect ARM, interest rate risk to the lender is zero. Why?
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Defining an ARM: Margin
The margin is from our previous discussion of interest rates Recall that the mortgage interest rate (i) has three that the mortgage interest rate has three components
The risk free interest rate r The risk premium The expected inflation rate e i = r + + e
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Example of 1 Year ARM with 30-year amortization (No Caps)
Time Period Period 0 1 2 3 4 Index Index 6.1 4.5 6.0 9.0 12.0 Margin Margin 2.75 2.75 2.75 2.75 2.75 Loan Rate Rate 8.85 7.25 8.75 11.75 14.75
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Pricing ARMs: Margin
Suppose a perfect ARM
Are lenders exposed to risk? Why should the margin > 0?
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Figure 6-4: Margin and Loan Value, Perfect ARM
Percentage of Par 110
105
100
95
Why is a 150 BP margin required for the Perfect ARM to sell for PAR?
90 50 100 150 200 250 300
Basis Points
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Pricing ARMs: Margin
Why does the figure suggest that a margin of roughly 150 basis points is necessary if a perfect ARM is to sell for PAR?
Perfect ARMs eliminate lender exposure to interest rate risk But, a perfect ARM does not eliminate default risk!
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Defining an ARM: Rate caps
In order to provide some protection for borrowers, ARMs provide limits on how much the loan rate and/or payment can change and/or payment can change.
Lifetime limits or caps on how high the interest rate can rise are common
Life
caps are often in the 5% to 6% (500 to 600 basis point) range
Periodic rate caps limit how much the rate can change at any one time
Periodic
caps are often in the 1% to 2% (100 to 200 bp)
range
Caps allow for a sharing of interest rate risk between lenders and borrowers
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Defining an ARM: Rate caps
When an ARM has rate caps, you can think of the rate adjustment process as having three steps:
Step 1: Calculate the rate as if there were no caps: Index + Margin Margin Step 2: See if the rate calculated in step 1 exceeds the lifetime cap on the loan. If it does, reduce the rate obtained in step 1 to the maximum rate allowed by the lifetime cap. Step 3: See if the change from the current rate to the rate calculated in step 2 exceeds the periodic limit. If it does, set the rate equal to the old rate plus (or minus) the periodic limit.
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Calculating the Rate on a Capped ARM
Lifetime Cap = 500 BP over original loan rate Periodic Cap = +/- 200 BP over previous period loan rate
STEP 1 Index + Margin -STEP 3 Check Periodic Rate Cap OK:8.85
Time Period 0 1 2 3 4
Index 6.1 4.5 6.0 9 12
Margin 2.75 2.75 2.75 2.75 2.75
STEP 2 Check Life Cap --
New Loan Rate 8.85
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Calculating the Rate on a Capped ARM
Lifetime Cap = 500 BP over original loan rate Periodic Cap = +/- 200 BP over previous period loan rate
STEP 1 Index + Margin -7.25 STEP 3 Check Periodic Rate Cap OK:8.85 OK:7.25
Time Period 0 1 2 3 4
Index 6.1 4.5 6.0 9 12
Margin 2.75 2.75 2.75 2.75 2.75
STEP 2 Check Life Cap -OK: 7.25
New Loan Rate 8.85 7.25
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Calculating the Rate on a Capped ARM
Lifetime Cap = 500 BP over original loan rate Periodic Cap = +/- 200 BP over previous period loan rate
STEP 1 Index + Margin -7.25 8.75 STEP 3 Check Periodic Rate Cap OK:8.85 OK:7.25 OK:8.75
Time Period 0 1 2 3 4
Index 6.1 4.5 6.0 9 12
Margin 2.75 2.75 2.75 2.75 2.75
STEP 2 Check Life Cap -OK: 7.25 OK: 8.75
New Loan Rate 8.85 7.25 8.75
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Calculating the Rate on a Capped ARM
Lifetime Cap = 500 BP over original loan rate Periodic Cap = +/- 200 BP over previous period loan rate
STEP 1 Index + Margin -7.25 8.75 11.75 14.75 STEP 3 Check Periodic Rate Cap OK:8.85 OK:7.25 OK:8.75 Cap:10.75 Cap:12.75
Time Period 0 1 2 3 4
Index 6.1 4.5 6.0 9 12
Margin 2.75 2.75 2.75 2.75 2.75
STEP 2 Check Life Cap -OK: 7.25 OK: 8.75 OK:11.75 Cap: 13.85
New Loan Rate 8.85 7.25 8.75 10.75 12.75
The periodic cap is binding in periods 3 and 4. Why doesnt the loan rate equal 13.85 in period 4 since the lifetime cap is binding?
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Pricing ARMs: Rate caps
What is the effect of rate caps on ARM prices?
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Figure 6-1: Periodic Rate Caps, Reset Frequency, and Loan Value
Percentage of Par 100
How does loan value change with the rate cap? How does loan value change with the frequency of the rate adjustments? rate adjustments?
99.5
990
98.5
98.2 1 2 Rate Caps (%) 3
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Figure 6-1: Periodic Rate Caps, Reset Frequency, and Loan Value
Percentage of Par 100
6 months
99.5
1 year
Why does loan value increase with the rate cap? Why is loan value higher with higher ith hi frequency rate adjustments?
3
25
990
3 years
98.5
5 years
98.2 1 2 Rate Caps (%)
Figure 6-3: Life of Loan Caps and Loan Value
Percentage of Par 100
2% rate cap
99.5
990
1% rate cap
98.5
98.2 1 5 Life-of-Loan Cap (%)
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Defining an ARM: Teaser rates
ARM rates adjust over the life of the loan based on a formula of index + margin, subject to caps But, the initial loan rate is not constrained by any specific formula
In this example, we have set the initial rate to the current index rate plus the margin. In fact, it is often the case that lenders offer initial rates below the index + margin These lower initial rates are typically called Teaser Rates
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Defining an ARM: Teaser rates
Teaser rates
Lower the borrowers initial monthly payment Lower the lifetime cap if it is specified as the initial rate plus a maximum % increase in the loan rate Cause future payments to increase at the first reset of the loan even if index values do not change.
The
loan rate reverts to the formula index + margin after the teaser period expires
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Effect of Teaser Rate on ARM Adjustment
Lifetime Cap = 500 BP over original loan rate Periodic Cap = +/- 200 BP over previous period loan rate
Time Period 0 1 2 3 4 STEP 1 Index + Margin -7.25 8.75 11.75 14.75 STEP 2 Check Life Cap -OK: 7.25 OK: 8.75 Cap: 11% 11% Cap: 11% STEP 3 Check Periodic Cap 6.0 OK:7.25 OK:8.75 Cap: 10.75 10.75 OK:11.0
Index 6.1 4.5 6.0 9.0 12
Margin 2.75 2.75 2.75 2.75 2.75 2.75
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Pricing ARMs: Teaser rates
How do teaser rates affect ARM prices?
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Figure 6-2: Teaser Rates and Loan Values
Percentage of Par
Perfect ARM
100
95
2% capped ARM
1% capped ARM
90
Fully Indexed Rate
85 6% 7% 8% 9%
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Initial Period Rate
Pricing loans and refinancing: ARMs versus FRMs
Consider mortgages a with 7% coupon How does a decline in market rates affect the price of existing ARMs and FRMs?
Present value of cash flows increase, raising loan prices But, with a sufficiently large decline in market rates relative to the loan coupon, borrowers will exercise their refinance option
Recall that the refinance option is a Call Option. The borrower has the right but not the obligation to call the bond to buy back the principal by paying off the loan
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Pricing loans and refinancing: ARMs versus FRMs
Borrowers refinance for two different reasons
Extract equity from home (e.g. the Federal Reserve Bulletin 2002 paper by Canner, Dynan, and Passmore)
This is sometimes called cash-out refinancing
Take advantage of lower market mortgage rates
It is expensive to refinance (fixed costs and related fees) Market rates usually must be 100 or more BP below the coupon rate before refinancing saves the borrower money Financial benefits of refinancing also depend on the anticipated remaining time in the home anticipated remaining time in the home
The longer the remaining stay in the home, the longer the period over which refinancing fees are implicitly spread out Moving soon, dont refinance!
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Pricing loans and refinancing: ARMs versus FRMs
Federal Reserve Chairman Alan Greenspan, testimony to the Joint Economic Committee, Congress, November 13, 2002.
the extraction of equity from homes has been a significant support to consumption during a period when other asset prices were declining sharply. Were it not for this phenomenon, economic activity would have been notably weaker in the wake of the decline in the value of household financial assets.
Consumer spending financed through cash-out refinancing boosted the economy and softened the 2001 recession Cash-out refinancing was prompted by the dramatic run-up in house prices that began in 1996/7
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Pricing loans and refinancing: ARMs versus FRMs
If cash-out refinancing is prompted mostly by increases in house prices, then such refinancing is not necessarily bad for lenders
Higher house prices reduce default risk Interest rates dont necessarily change so no direct implications for interest rate risk
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As of 2002, 49.1% of homeowners with mortgages had refinanced their loans accounting for 52 refinanced their loans, accounting for 52.8% of all of all mortgage debt.
Refinancing is a common event!
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Cash-out refinancers (when equity is liquefied) are more likely to increase maturity and monthly payment
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True, cash-out refinancers are less likely to lower their loan rate But the dominant pattern is that regardless of whether equity is liquefied, refinancers lower their loan rates by 170 to 200 BP!
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On average, cashout refinancers took out about 10 percent of their home equity when they refinanced.
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Cash-out refinancers used most of the liquefied home equity for consumer spending (including paying off other debts). Investment in other assets accounted for only about 21 percent of liquefied funds.
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Pricing loans and refinancing: ARMs versus FRMs
Borrowers also refinance to take advantage of lower market mortgage rates Refinance options are valuable to borrowers but costly to lenders
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Pricing loans and refinancing: ARMs versus FRMs
Consider an FRM for the moment. We know what the bond price function looks like when refinancing is not allowed like when refinancing is not allowed
Lower market rates cause bond price to rise. Why?
But, when rates fall sufficiently far below the coupon rate, borrowers refinance.
How does this affect the bond price? does this affect the bond price? Why?
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Figure 3-2: Value of Mortgages
Mortgage Value
Noncallable mortgage
Value
Par Callable mortgage with no prepayment penalty but some refinancing cost
rc Market Interest Rate
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Pricing loans and refinancing: ARMs versus FRMs
Now Consider three types of ARMs, each with a 7% coupon rate
Perfect ARM ARM 2% capped ARM Bound ARM Equivalent to an FRM
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Pricing loans and refinancing: ARMs versus FRMs
Perfect ARM
Loan rate declines with market rate so no incentive to refinance ARM sells for PAR When market rates are 7%, loan sells for PAR As market rates begin to fall below the coupon (7%), loan sells for a premium above PAR With further decline in market rates, borrowers refinance
2% capped ARM with 7% coupon rate capped ARM with 7% coupon rate
When borrowers refinance, they payoff the outstanding balance on the loan The loan is then valued at PAR
Bound ARM Equivalent to an FRM
Because loan rate doesnt decline, with initial decline in market loan rate doesn decline with initial decline in market rate loan price rises more sharply than with a 2% capped ARM With further decline in market rates, refinance earlier than with a 2% capped ARM Bound ARM price returns to PAR at a higher rate than with a 2% capped ARM
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Figure 6-6: Value of Various ARMS
Mortgage Value 110
Bound ARM (FRM)
105
Perfect ARM
100
95
2% Capped ARM
90
7 Average Level of One-year T-bill Rate
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Pricing loans and refinancing: ARMs versus FRMs
How does interest rate volatility affect the value of refinance options? Consider two cases:
First, when refinancing is not allowed Second, when refinancing is allowed
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Convex Bond-rate function and interest rate volatility without refinance options
Mortgage Price
If refinancing is not allowed, interest rate volatility would cause bond (mortgage) prices to be higher, all else equal. The gain from lower interest rates would more than offset losses from higher rates E[PV(i) > PV[E(i*)]
E[PV(i)] PV[E(i*)]
i* - d
i*
i* + d
Interest Rate
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Pricing loans and refinancing: ARMs versus FRMs
So when refinancing is not allowed, interest rate volatility causes bond prices (e.g. mortgage prices) to rise. How about when refinancing is allowed? about when refinancing is allowed?
With volatile interest rates, the likelihood that a borrower would want to refinance in the future increases. Why?
Greater likelihood that rates will fall enough to justify
refinancing
This increases the value of the refinance option for borrowers all else equal and is bad for lenders
Instead of mortgage price rising with a further decline in
interest rates, mortgage price goes to PAR, as in Figure 6-6
Loan values fall!
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Figure 6-5: Interest Rate Volatility and Loan Value
Percentage of Par 102
Bound ARM (FRM) Perfect ARM
100
98
2% Capped ARM
96
94
5
10
15
20
25
50
Standard Deviation in Interest Rates
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ARMs versus FRMs
ARMs without periodic caps that also adjust frequently Perfect ARMs are best for reducing the lenders interest rate risk.
Borrowers bear all of the interest rate risk Monthly payments can jump up If combined with negative net equity, it seems likely that a big increase in monthly payment could further encourage default
FRMs can be viewed as the limiting loan type as rate caps get tighter
A bound ARM is an ARM for which rate caps are set to zero this is the same as an FRM
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Types of ARMs
ARMs can be classified by how frequently they adjust the rate and the index they adjust to
Periodicity
Monthly, 6 months, annually, every three years, every five months annually every three years every five years Many ARMs have an initial period where the loan rate is fixed and then begin to adjust 3/1 5/1 7/1 Most ARMS have interest rate caps but some cap the payment instead
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Fixed/Adjustable
Rate vs. Payment Capped
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Payment caps Negative amortization
Some ARMs limit how much the payment can increase (e.g. no more than 15%)
The Fed has a website that summarizes some recent types of ARMS that include payment caps types of ARMS that include payment caps
http://www.federalreserve.gov/pubs/mortgage_interestonly/
If payment caps restrict the size of the monthly payment, two possibilities can arise
Payment > interest due
Payment - interest due > 0 and the loan balance is reduced the loan amortizes loan amortizes Payment < interest due Payment interest due < 0 and the loan balance increases this is referred to as negative amortization
With negative amortization, the outstanding balance 53 on the loan increases over time
Benefits of Payment vs. Rate Cap
Lenders earn market interest rate in all periods
Interest is accrued at the market rate even when the loan is negatively amortizing
Borrower can plan for the worst case in the next years payment increase Rules of Thumb
7.5% payment cap --- 1% interest rate cap 15% payment cap --- 2% interest rate cap
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Payment Capped ARMs and Default Risk
ARMs with payment caps and no periodic interest rate caps
reduce the default risk from payment shock increase the risk of negative amortization negative amortization increases default risk
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Limits on Negative Amortization
Lenders generally impose limits on the amount of negative amortization.
Maximum % increase over original loan or linked to original house value house value Payment caps are generally removed after a set number of years into the loan Borrowers do not like negative amortization
Experience has shown
They often voluntarily make extra payments to avoid negative amortization amortization
Default rates on neg. amortizing ARMs is much higher
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Indexes
Some common indexes used for ARMs
Treasury securities
6 month, 1 year, 3 year, 5 year COFI (11th district)
Cost of Funds at Thrift Institutions
National average rate on new mortgage loans Fannie Mae or Freddie Mac purchase yields for new loans
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When/Why are ARMs Popular?
ARMs are popular
When the yield curve is very steep
Loans priced off the short end of the yield curve appear to be less costly than fixed rate loans less costly than fixed rate loans
When FRM rates are high
ARMs are more affordable Borrowers may hope to roll down to a lower fixed-rate after paying the low teaser rate for a couple of years.
When house prices rise more rapidly than income creating affordability problems ARMs help to address Tilt affordability problems, ARMs help to address Tilt
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Alphabet Soup: Other types of AMI
Many other mortgage types exist:
GPM PLAM RAM SAM
Each of these loan types addresses challenges that lenders and borrowers face (i.e. interest rate risk, tilt and other affordability problems, )
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GPM
The direct answer to Tilt A graduated payment mortgage is a fixed rate loan with payment that starts out below the regular with a payment that starts out below the regular amortizing payment and is scheduled to increase each year
e.g. nominal payments could increase 5% per year for a specified number of years (for example, 5 years, 10 years, or more) Loan negatively amortizes in the first few years and then payment increases to the point that the loan is fully amortized by maturity
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For how many years does the monthly payment increase?
By how much does the monthly payment increase per month during the adjustment period?
5 years & 7.5%/year
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PLAM
A price level adjusted mortgage is effectively a variable rate loan
Borrower agrees to make payments based on a constant real rate of interest rate of interest At the end of each year, the balance of the loan is adjusted to reflect the inflation that occurred in a given year The borrowers payment is adjusted to amortize the new balance over the remaining term
PLAMs reduce interest rate risk for both lenders and borrowers PLAMs also eliminate the tilt problem th tilt But PLAMs can suffer from negative amortization and increased default risk
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