Residential mortgage loans: the features that matter
A mortgage is a loan secured by a first lien on a home. Its risk depends on the loan-to-value ratio (equity cushion), the borrower's debt-to-income ratio (ability to pay), credit quality (prime or subprime), the prepayment option, and whether the loan is recourse or non-recourse.
Before this: Fixed-Income Cash Flows and Types, Time Value of Money in Finance
On the exam
- Describe fundamental features of residential mortgage loans that are securitized
Describe the fundamental features of securitized residential mortgages. Expect: compute LTV or DTI; prime vs subprime; agency vs non-agency; recourse vs non-recourse and strategic default.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
What is a residential mortgage loan?
A mortgage loan is a loan secured by a specified property. The lender holds a first lien : a legal claim on the property that ranks ahead of other claims. If the borrower stops paying, the lender can start foreclosure , take possession of the property and sell it to recover the debt.
Buyers usually borrow less than the purchase price. The difference is the down payment , and it is the borrower’s equity on day one. Everything else in this lesson is about how much of a cushion the lender has, and what rights each side holds.
How do lenders measure the cushion? LTV and DTI
Two ratios carry most of the weight. The loan-to-value ratio measures the equity cushion in the property. The debt-to-income ratio measures the borrower’s ability to make the payments from income. Lower is safer for both.
DTI uses pre-tax (gross) income and all monthly debt payments, not just the mortgage. LTV matters for commercial mortgages too (lesson 4).
Questions ask for either ratio, or for the input that is missing.
A buyer borrows 360,000.00 to buy a property worth 450,000.00. The loan-to-value ratio is closest to:
360,000.00 ÷ 450,000.00 = 80.00%
Loan-to-value ratio, LTV80.00%
- 360000÷450000=LTV as a decimal
- 360000ENTER450000÷LTV as a decimal
ENTER enter (on the HP, puts the number on the stack)
A borrower's monthly debt payments, including the mortgage, total 2,340.19. Gross income is 120,000.00 a year. The debt-to-income ratio is closest to:
2,340.19 ÷ (120,000.00 ÷ 12) = 23.40%
Debt-to-income ratio, DTI23.40%
- 2340.19÷(120000÷12)=DTI as a decimal
- 2340.19ENTER120000ENTER12÷÷DTI as a decimal
ENTER enter (on the HP, puts the number on the stack)
Try this 0 of 3
- With no payments made yet, find the price fall that wipes out the down payment
- Put the borrower underwater on a non-recourse loan
- With the worked example, switch on the common mistakes
Above 100% (red) the borrower is underwater: negative equity.
Zones are illustrative; lenders set their own limits.
The borrower has EUR 90,000 of equity (20.0% of the home's value) and spends 23.4% of gross income on debt. Repayments push LTV down over time; a falling home price pushes it up.
Show working
Monthly rate and term: r = 4.2% ÷ 12 = 0.35%; N = 25 × 12 = 300 payments.
Payment = r × loan ÷ [1 − (1 + r)−N] = 0.0035 × 360,000 ÷ [1 − 1.0035−300] = EUR 1,940.19.
Home value = 450,000 × (1 + 0%) = EUR 450,000.
LTV = loan balance ÷ property value = 360,000.00 ÷ 450,000 = 80.0% (a 20.0% down payment).
DTI = monthly debt payments ÷ monthly gross income = (1,940.19 + 400) ÷ (120,000 ÷ 12) = 2,340.19 ÷ 10,000.00 = 23.4%.
- 2NDCLR TVMwith P/Y set to 1
- 300N4.2÷12=I/Ymonthly rate 0.35%
- 360000+|-PV0FV
- CPTPMT1,940.19, the monthly payment
2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · +|- change sign · PV present value · FV future value · CPT compute · PMT payment
- fCLEAR FIN
- 300n4.2g12÷monthly rate 0.35%
- 360000CHSPV0FV
- PMT1,940.19, the monthly payment
f gold shift key · CLEAR FIN clear the financial registers · n number of periods · g blue shift key · CHS change sign · PV present value · FV future value · PMT payment
LTV does not stay put. Repayments reduce the balance, which pushes it down. A fall in the home’s price pushes it up. A loan with LTV above 100% is in negative equity , also called “underwater”: the home is worth less than the debt.
What kinds of borrower and guarantee exist?
In the US, lenders separate prime loans from subprime loans . Prime borrowers have strong employment and credit histories, a low DTI, substantial equity and a first lien. Subprime loans have weaker credit, a high DTI or LTV, or are secured by a second lien (ranking behind another lender).
Residential mortgage-backed securities (RMBS), which are securities backed by residential mortgages, are also split by who guarantees them. agency RMBS are backed by a federal agency or a government-sponsored enterprise (GSE). Federal agency RMBS carry the full faith and credit of the government; GSE RMBS carry the GSE’s own guarantee of timely interest and principal, for which it charges a fee. non-agency RMBS (private label) have no guarantee, so they use credit enhancements to reach acceptable quality.
- Agency RMBS Memorize the first two sectors
- Federal agency Memorize full faith and credit of the government
- Government-sponsored enterprise (GSE) Memorize the GSE guarantees timely interest and principal, for a fee; not the government
-
- Non-agency RMBS Memorize private label; issued by private entities
- No guarantee Memorize relies on credit enhancement
- Credit enhancements Use it pool insurance, letters of credit, guarantees, subordination
-
Go deeper Why non-agency RMBS shrank after 2008, and what is back
Non-agency RMBS were often backed by non-conforming or subprime loans. After the global financial crisis, tighter regulation and scrutiny almost wiped the sector out. Some residential loans that rank behind a first mortgage, such as home-improvement loans for solar panels, are now securitized in growing volume. They sit behind the main lender, so their risk differs from a first-lien mortgage.
What options and rights do the parties hold?
The borrower’s most important right is the prepayment option : to repay more than the scheduled principal, in part or in full, before maturity. This creates the prepayment risk of the previous lesson, for any mortgage that allows prepayment. A prepayment penalty compensates the lender if the borrower prepays when rates have fallen. It reduces the incentive to refinance. Penalties are common in Europe and rare in the US.
When a borrower defaults, foreclosure proceeds may fall short of the balance. In a recourse loan , the lender can claim the shortfall from the borrower. In a non-recourse loan , the lender can look only to the property. In the US this is set by state, and residential loans are non-recourse in many states. Most European residential mortgages are recourse loans.
That matters most when LTV is above 100%. A strategic default is a borrower choosing to stop paying, and let the lender foreclose, even though the borrower could keep paying. It is more likely with a non-recourse loan that is deep underwater. A recourse loan makes it less likely, because the shortfall can be recovered from other assets and income.
Exam tip Non-recourse plus negative equity is the combination that points to strategic default.
Put together, these are the things that make one home loan riskier than another.
- Equity cushion Memorize loan-to-value ratio; higher means riskier
- Income cushion Memorize debt-to-income ratio; higher means riskier
- Borrower quality Use it
- Prime strong credit, low DTI, substantial equity, first lien
- Subprime weaker credit, high DTI or LTV, or second lien
-
- Contract rights Memorize
- Prepayment option creates timing risk for investors
- Prepayment penalty reduces it; common in Europe, rare in the US
- Recourse or non-recourse decides whether the lender can pursue the borrower for a shortfall
-
Go deeper What a housing slump does to defaults
When house prices fall after a period of loose lending, many loans slip underwater at once. The pattern is consistent: borrowers who still have equity rarely default, because selling the home beats losing it. The deeper the negative equity, the more defaults rise, and the more of them are strategic, especially where loans are non-recourse. That is why LTV, recourse and the direction of house prices are read together, not one at a time.
Go deeper Fixed and adjustable rates, in one line
Most of this module assumes a level-payment, fixed-rate, fully amortizing mortgage. Adjustable-rate mortgages reset their rate to a reference rate on a schedule, which shifts rate risk toward the borrower. The prepayment option exists either way.
Memorize this
MemorizeThe two ratios
| Ratio | Formula | Lower is |
|---|---|---|
| LTV | Loan ÷ property value | Safer (more equity) |
| DTI | Monthly debt payments ÷ monthly gross income | Safer (more room to pay) |
Memory hook Both put the debt on top and the cushion underneath: loan over value, debts over income.
Know it cold DTI matches months with months. LTV above 100% means negative equity.
MemorizeAgency or not
| Agency RMBS | Non-agency RMBS | |
|---|---|---|
| Guarantor | Government agency or GSE | None |
| Credit risk handled by | The guarantee | Credit enhancement |
| Full faith and credit | Agency yes; GSE no | No |
Memory hook Agency = a guarantee. Non-agency = no guarantee, so it needs enhancement.
Know it cold Only federal agency RMBS carry the full faith and credit of the government. GSE RMBS carry the GSE guarantee.
MemorizeRecourse
| Recourse | Non-recourse | |
|---|---|---|
| Shortfall after foreclosure | Lender can pursue the borrower | Lender looks only to the property |
| Strategic default | Less likely | More likely when deeply underwater |
| Where | Most of Europe | Many US states |
Memory hook Non-recourse means the house is all the lender gets, so a borrower deep underwater can hand over the keys.
Know it cold Non-recourse plus negative equity = strategic default risk.
- Agency RMBS Memorize the first two sectors
- Federal agency Memorize full faith and credit of the government
- Government-sponsored enterprise (GSE) Memorize the GSE guarantees timely interest and principal, for a fee; not the government
-
- Non-agency RMBS Memorize private label; issued by private entities
- No guarantee Memorize relies on credit enhancement
- Credit enhancements Use it pool insurance, letters of credit, guarantees, subordination
-
- Equity cushion Memorize loan-to-value ratio; higher means riskier
- Income cushion Memorize debt-to-income ratio; higher means riskier
- Borrower quality Use it
- Prime strong credit, low DTI, substantial equity, first lien
- Subprime weaker credit, high DTI or LTV, or second lien
-
- Contract rights Memorize
- Prepayment option creates timing risk for investors
- Prepayment penalty reduces it; common in Europe, rare in the US
- Recourse or non-recourse decides whether the lender can pursue the borrower for a shortfall
-
Quick example
A loan of JPY 26,000,000 on an apartment worth JPY 40,000,000. 26,000,000 ÷ 40,000,000 = 65.0%.
- 26000000÷40000000= 0.65
- 26000000ENTER40000000÷ 0.65
ENTER enter (on the HP, puts the number on the stack)
Quick example
Mortgage payment 1,800 and other debt payments 350 a month; gross income 78,000 a year. 2,150 ÷ (78,000 ÷ 12) = 33.1%.
- 1800+350= 2,150
- ÷(78000÷12)= 0.3308
- 1800ENTER350+ 2,150
- 78000ENTER12÷ 6,500
- ÷ 0.3308
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Compute LTV
Loan JPY 26 million on a JPY 40 million apartment. LTV?
26 ÷ 40 = 65.0%. Traps: 35.0% (down payment share) and 153.8% (inverted).
-
Compute DTI
Payments 1,800 and 350 a month; income 78,000 a year. DTI?
2,150 ÷ 6,500 = 33.1%. Traps: 2.8% (annual income) and 27.7% (leaves out the other debt).
-
LTV after the balance and value both move
Balance 258,000; home value fell from 360,000 to 320,000. LTV?
258 ÷ 320 = 80.6%. Use the new balance and the new value.
-
Who walks away
A borrower who can afford the payments abandons a home worth far less than the loan. Which loan?
Non-recourse. Trap: recourse, where the lender can pursue other assets.
Exam traps
- Inverting LTV (value ÷ loan). The loan goes on top.
- Using annual income against monthly payments in DTI. Match months with months.
- Thinking RMBS issued by a GSE carry the government's full faith and credit. Only federal agency RMBS do.
- Leaving out other debt payments in DTI. It counts all monthly debt payments, not only the mortgage.
Checkpoint
5 exam-style questions. About 90 seconds each.
1A buyer borrows JPY 27,000,000 to buy a JPY 36,000,000 apartment. The loan-to-value ratio is closest to:
2A borrower's mortgage payment is USD 2,100 a month and other debt payments are USD 300 a month. Gross income is USD 96,000 a year. The debt-to-income ratio is closest to:
3A borrower who could afford the payments walks away from a home now worth far less than the loan. This is most likely when the mortgage is:
4A homeowner's mortgage balance has fallen from EUR 380,000 to EUR 342,000, while the home's value has dropped from EUR 475,000 to EUR 400,000. The current loan-to-value ratio is closest to:
5Which type of residential mortgage-backed security most likely relies on credit enhancement rather than a guarantee?
Key takeaways
- LTV = loan ÷ value; DTI = monthly debt payments ÷ monthly gross income. Lower is safer for both.
- Prime loans have strong borrowers and a first lien; subprime loans have weaker credit, higher DTI or LTV, or a second lien.
- Agency RMBS carry a guarantee; non-agency RMBS rely on credit enhancement.
- The prepayment option creates prepayment risk; a penalty reduces it. Non-recourse plus negative equity raises strategic default risk.
Quick example
A loan of JPY 26,000,000 on an apartment worth JPY 40,000,000. 26,000,000 ÷ 40,000,000 = 65.0%.
- 26000000÷40000000= 0.65
- 26000000ENTER40000000÷ 0.65
ENTER enter (on the HP, puts the number on the stack)
Quick example
Mortgage payment 1,800 and other debt payments 350 a month; gross income 78,000 a year. 2,150 ÷ (78,000 ÷ 12) = 33.1%.
- 1800+350= 2,150
- ÷(78000÷12)= 0.3308
- 1800ENTER350+ 2,150
- 78000ENTER12÷ 6,500
- ÷ 0.3308
ENTER enter (on the HP, puts the number on the stack)
All Fixed Income formulas, every lesson
Practice exam-style questions on Mortgage-Backed Securities: RMBS, CMOs and CMBS
Questions about this lesson?
Where this comes back
- Mortgage pass-throughs and CMOs Mortgage-Backed Securities: RMBS, CMOs and CMBS
Questions candidates ask
What is a loan-to-value ratio?
The mortgage amount divided by the property's value. A lower ratio means more borrower equity, so default is less likely and the lender recovers more if it happens. It changes over time: repayments push it down, a fall in the home's value pushes it up.
What is the difference between agency and non-agency RMBS?
Agency RMBS are guaranteed by a government agency or a government-sponsored enterprise. Non-agency (private label) RMBS have no guarantee and use credit enhancements such as insurance, letters of credit, guarantees or subordination.
What is a non-recourse mortgage?
One where the lender can recover only from the property after foreclosure, not from the borrower's other assets or income. If the home is worth less than the loan, a borrower who can still pay may choose a strategic default.
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