Define and calculate, for relevant securitized structures, the weighted average life (WAL), weighted average maturity (WAM), weighted average coupon (WAC), debt service coverage ratio (DSCR), monthly payment rate (MPR), default ratio and delinquency ratio.
The idea
Each measure is a ratio you can compute directly. Weighted average coupon, WAC, is the pool's loan coupons weighted by loan balance. Weighted average maturity, WAM, is the remaining terms weighted by balance. Neither is a simple average. Weighted average life, written WAL, measures the average time until principal is returned. It is calculated as follows: WAL = Σ(principal × time) ÷ total principal. The debt service coverage ratio is net operating income divided by debt service. A value below 1.0 means income does not cover payments. The monthly payment rate is total cardholder payments in the month divided by the opening receivables balance. The delinquency ratio is the balance of loans past due, commonly 30 days or more, divided by the current pool balance. The default ratio is the defaulted balance divided by the pool balance, with the denominator set by the stated convention.
Formulas
Weighted average life
WAL = Σ(principal × time) ÷ total principal
- principal
- each principal payment
- time
- when it is received, in years
- total principal
- the sum of all principal payments
Use the actual time in years, not the payment number. Faster prepayments shorten WAL.
Weighted average coupon of a pool
WAC = Σ(Bᵢ × cᵢ) ÷ ΣBᵢ
- Bᵢ
- the current balance of loan or group i
- cᵢ
- its coupon
Weight by current balance, never a simple average. WAM is the same calculation with each remaining term, in months, in place of the coupon.
Debt service coverage ratio of a commercial mortgage
DSCR = NOI ÷ debt service
- NOI
- the property's net operating income
- debt service
- the loan's interest and principal payments for the period
Below 1.0, income does not cover payments. Inverting the ratio is the usual slip.
Monthly payment rate of a card trust
MPR = monthly payments ÷ opening receivables
- monthly payments
- total cardholder payments in the month, principal and finance charges
- opening receivables
- the receivables balance at the start of the month
Divide by the opening balance, not the month-end or average balance, and count finance charges as well as principal.
Delinquency ratio
delinquency ratio = delinquent balance ÷ current balance
- delinquent balance
- loans past due, commonly 30 days or more
- current balance
- the current pool balance
Divide by the current balance unless the question states another convention; using the original balance is the usual slip.
Default ratio
default ratio = defaulted balance ÷ pool balance
- defaulted balance
- the balance of defaulted loans, often cumulative
- pool balance
- the pool balance set by the stated convention, often the original balance
The denominator is a convention, so read the question: cumulative defaults are usually set against the original balance.
A practice question
A pool contains three loans: USD 100 million at 6%, USD 300 million at 7% and USD 600 million at 8%. The weighted average coupon of the pool is closest to:
- 7.0%Why not: Takes the simple average of the three coupons rather than weighting by balance.
- 7.5% - correct
- 8.0%Why not: Uses the coupon of the largest loan alone instead of weighting all three by balance.
- 6.4%Why not: Weights each coupon by the inverse of its balance, overweighting the smallest loan.
WAC = (100 x 6% + 300 x 7% + 600 x 8%) / 1,000 = 7.5%. Weights are loan balances.
A harder one
A pool has three loans: USD 120 million with 310 months remaining, USD 300 million with 340 months remaining and USD 580 million with 350 months remaining. The weighted average maturity of the pool, in months, is closest to:
- 333Why not: Takes the simple average of the three remaining terms instead of weighting by balance.
- 350Why not: Uses the remaining term of the largest loan alone.
- 340Why not: Takes the remaining term of the middle loan instead of weighting all three by balance.
- 342 - correct
WAM = (120 x 310 + 300 x 340 + 580 x 350) / 1,000 = 342.2 months, weighting by balance.
The hardest tier
A pool of USD 200 million pays principal of USD 40 million at month 6, USD 60 million at month 18 and USD 100 million at month 30. The weighted average life, in years, is closest to:
- 1.5Why not: Takes the simple average of the payment dates of 0.5, 1.5 and 2.5 years without weighting by principal.
- 1.8 - correct
- 2.5Why not: Uses the final payment date as the average life.
- 2.3Why not: Treats the payment number (1, 2, 3) as the time instead of the actual date in years.
WAL = (0.5 x 40 + 1.5 x 60 + 2.5 x 100) / 200 = 360 / 200 = 1.8 years.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in An Introduction to Securitisation
- State what securitization is, outline its process and account for what each participant does.
- Explain cash waterfall, equity piece, first-loss piece and over-collateralization as they apply within securitization.
- Analyse how issuing securitized products through a trust works differently from using a special purpose vehicle (SPV), and tell apart the three chief SPV structures: amortizing, revolving and master trust.
- Account for why securitization is undertaken and what it offers.
- Outline the different kinds of credit enhancement and weigh them up.
- Account for the tools used to analyse the performance of securitized structures and name the asset classes each suits best.
- Cover the techniques for forecasting prepayments, and compute the PSA (Public Securities Association) rate along with the CPR (constant prepayment rate).