CFA Level I · CFA Level I Exam

Mortgage-Backed Security (MBS) Instrument and Market Features: formula sheet

Full chapter guide

Key formulas

Loan-to-value ratio: LTV = Loan amount ÷ Property value; Lenders typically use the lower of appraised value and purchase price. Lower LTV means lower credit risk.
Down payment: Down payment = Property value − Loan amount; LTV = 1 − Down payment ÷ Property value; A 20% down payment means an 80% LTV.
Level mortgage payment: PMT = PV × r ÷ [1 − (1 + r)^−n]; r is the periodic rate (annual rate ÷ 12 for monthly) and n is the number of payments.
Interest in a period: Interest = Beginning balance × periodic rate; Principal repaid = Payment − Interest.
Ending balance: Ending balance = Beginning balance − Principal repaid; Use this to build each row of an amortization schedule.
ARM rate: Rate after reset = Reference rate + Margin; Subject to periodic and lifetime caps and floors, if the loan has them.
Pass-through rate: Pass-through rate = WAC − servicing fee − other fees (e.g., guarantee fee); Fees are stated as annual rates. Investors earn the pass-through rate, never the WAC.
Weighted average coupon (WAC): WAC = Σ [ (loan balance ÷ total pool balance) × loan rate ]; Weights are outstanding balances, not the number of loans.
Weighted average maturity (WAM): WAM = Σ [ (loan balance ÷ total pool balance) × remaining months to maturity ]; Uses remaining term, not original term.
Monthly investor interest: Interest to investors = beginning pool balance × pass-through rate ÷ 12; Use the balance at the start of the month. Payments are monthly.
Investor principal: Principal to investors = scheduled principal + prepayments; Prepayments reduce the balance and so reduce later interest.
SMM: SMM = Prepayment in the month ÷ (Beginning balance − Scheduled principal payment); Prepayment is measured against the balance left after scheduled principal, not the beginning balance.
CPR from SMM: CPR = 1 − (1 − SMM)^12; Annualizes by compounding survival, not by multiplying by 12.
SMM from CPR: SMM = 1 − (1 − CPR)^(1/12); On a calculator use the 1/12 power (y^x with 0.083333...).
100 PSA CPR path: CPR = 6% × (month ÷ 30) for months 1 to 30; CPR = 6% after month 30; Equivalent to 0.2% per month of loan age up to month 30.
Scaled PSA: CPR at x PSA = (x ÷ 100) × CPR at 100 PSA; 150 PSA is 1.5 times the benchmark CPR at each age. The 6% plateau is also scaled: 150 PSA plateaus at 9%.
Risk direction: Rates fall → prepayments rise → contraction risk; rates rise → prepayments fall → extension risk; Both are adverse for the investor relative to expectations; the MBS shows negative convexity.
Sequential-pay principal rule: Principal collected → Tranche A until its balance = 0 → then Tranche B → then Tranche C; Interest is paid on each tranche's outstanding balance every period. Only principal is sequenced.
Contraction risk: Rates fall → prepayments rise → weighted average life shortens; Reinvestment is at lower rates. Among sequential tranches, the early tranches have relatively more contraction risk and less extension risk, and the later tranches the opposite. This is a relative comparison between tranches. Within a PAC structure, support tranches bear the most prepayment risk.
Extension risk: Rates rise → prepayments slow → weighted average life lengthens; Among sequential tranches, it is highest for the later tranches. Within a PAC structure, support tranches bear the most prepayment risk.
PAC protection rule: PAC schedule is met if prepayment speed stays inside the PAC collar and support tranches remain outstanding; Support tranches absorb the variation. When they are paid off, PAC protection is lost.
Risk ranking within a PAC structure: Prepayment risk: support tranche > PAC tranche; Total prepayment risk is redistributed, not eliminated.
Loss allocation order: Losses: junior tranche first → mezzanine → senior last; Principal and interest are paid in the opposite order: senior first.
Overcollateralization: Overcollateralization = collateral balance − total bond balance; Positive difference is the cushion that absorbs losses before any bond loses principal.
Excess spread: Excess spread = interest collected from loans − bond interest − fees; Can be used to cover losses or build reserves.
Subordination (credit support) level: Credit support for a tranche = balance of all tranches junior to it ÷ total deal balance; A higher percentage means more protection for that tranche.
Shifting interest rule: Senior share of prepayments = senior pro rata share + extra share set by a schedule that declines over time; Gives the senior tranche more early principal; the shift is stopped if loss or delinquency triggers are breached.
Debt service coverage ratio (DSCR): DSCR = Net operating income ÷ Debt service; Debt service is the scheduled interest plus principal payments. Higher is safer. A DSCR below 1.0 means NOI does not cover the payments.
Loan-to-value ratio (LTV): LTV = Loan amount ÷ Appraised property value; Lower is safer. A lower LTV gives the lender a larger equity cushion if the property is sold.
Net operating income (NOI): NOI = Rental income and other property income − Operating expenses; NOI is before debt service, depreciation and income taxes.
Loan-level vs pool-level: CMBS: loan-level analysis; RMBS: pool-level analysis; Commercial pools hold few, large, dissimilar loans. Residential pools hold many small, similar loans.
Balloon payment: Balloon = Remaining balance due at loan maturity; Risk is that the borrower cannot refinance. For investors this shows up as extension risk and default risk.

Quick revision

An MBS pays investors from a pool of mortgage loans: interest, scheduled principal and prepayments.
Recourse loans let the lender claim beyond the property; non-recourse loans limit the lender to the collateral.
Falling rates raise prepayments and cause contraction risk; rising rates slow them and cause extension risk.
MBS have negative convexity because borrowers hold a prepayment option.
CPR = 1 − (1 − SMM)^12, and SMM = 1 − (1 − CPR)^(1/12).
A higher PSA speed means faster prepayments.
CMOs redistribute prepayment risk across tranches; they do not remove it from the pool.
Sequential tranches: earlier tranches get principal first, so they have shorter average lives.
Non-agency RMBS rely on credit enhancement such as subordination and overcollateralization.
Senior tranches are paid before subordinated tranches, and losses hit the subordinated tranches first.
CMBS depend on property cash flow and usually have call protection, so prepayment risk is lower.
CMBS loans often have balloon payments, so refinancing risk is important.

Common mistakes

Using the annual rate in a monthly interest calculation. Fix: Divide by 12 and set n to months before computing interest or payment.
Thinking the principal portion is level on a fixed-rate loan. Fix: The payment is level. Interest falls and principal rises each period as the balance drops.
Using the WAC as the rate investors earn. Fix: Always subtract servicing and guarantee fees first. Investors earn the pass-through rate.
Weighting WAC or WAM by the number of loans or the original balance. Fix: Weight by current outstanding balance. Check if the balances differ.
Calculating CPR as SMM × 12. Fix: Use CPR = 1 − (1 − SMM)^12. The multiply-by-12 result overstates CPR.
Dividing prepayment by the beginning balance to get SMM. Fix: Subtract scheduled principal from beginning balance, then divide.
Saying a CMO eliminates prepayment risk. Fix: Remember the pool's total prepayment risk is unchanged. A CMO only redistributes it, so some tranches become safer and others riskier.
Thinking only the first sequential tranche gets interest or principal. Fix: Every outstanding tranche gets interest on its balance. Only principal is paid in sequence.
Treating non-agency RMBS as guaranteed like agency pass-throughs. Fix: Non-agency means no agency or government guarantee. Credit risk is the key risk.
Allocating losses to the senior tranche first. Fix: Payments flow top-down, losses flow bottom-up. Junior takes the first loss.

Exam tips

Questions often test who bears which risk. Link each feature to borrower or lender before reading the options.
Read carefully for which value the LTV uses: appraised value or purchase price.
For payment calculations on the TI BA II Plus, set P/Y = 12 (C/Y should also be 12; it follows P/Y by default). Then enter N = months, I/Y = annual rate, PV = loan, FV = 0, and press CPT PMT. When PV is positive, the PMT result is negative because it is a cash outflow; ignore the sign.
With three options and no penalty for wrong answers, always answer. Eliminate any option with the wrong direction, such as interest rising over time on a level-payment loan.
Remember that prepayment risk rises when mortgage rates fall below the loan rate.
Expect three-option items asking which rate investors earn. The answer is the pass-through rate, below the WAC.
Numerical options are ordered smallest to largest. Compute the fee-adjusted rate first to remove two options quickly.
For agency versus non-agency, link guarantee to credit risk and credit enhancement to non-agency, and keep prepayment risk in both.