### MBS Pricing and Analytics

This one-day program will cover the bond math of MBS and a number of analytic tools and techniques used to evaluate the relative value and risk of the securities. It will cover single family residential mortgage securitizations (agency and non-agency) as they account for a great majority of MBS, though there will be some commentary directed towards CMBS and agency multi-family issues.

**MBS PRICE AND YIELD CONVENTIONS**

**Bond and MBS Price/Yield Formulas**

- Bond: price = present value of coupon and principal payments to maturity
- Bond: contractual cash flow discount by yield to maturity as periodic rate
- MBS: price equated to cash flows projected at some PSA or CPR speed
- Period cash flows: amortized and prepaid principal + pass through interest

**MBS Yields**

- Cash flow yield: monthly rate that equates present value to price x 12
- Bond equivalent yield of MBS

**Interpretation of MBS Yields**

- Yield (cash flow, bond equivalent or to maturity) versus rate of return
- Yield (cash flow and others): price re-expressed as a single interest rate

**PROJECTING MBS CASH FLOWS AND QUANTIFYING PREPAYMENTS**

**Mortgage Loan Payment Calculation**

- Calculating monthly payment given size, term and loan interest rate
- Apportioning the monthly payments between interest and principal
- Impact of partial prepayments

**Projecting Cash Flows for Relating Price to Yield**

- PSA and CPR most widely used though there are others
- Single monthly mortality (SMM)
- SMM x outstanding principal = prepaid principal
- Prepayment benchmark versus prepayment models
- Cash flow usually projected using a single PSA or CPR speed
- Schedule of CPRs sometimes used (especially to new issues)

**PSA (Public Securities Association/Prepayment Speed Assumptions) Benchmark**

- 30 month long ramp of rising CPRs, constant CPR beyond
- PSA standard (100% PSA) ramp speeds increasing 2%/month to 6%
- Other PSA speeds expresses as multiple of CPR
- PSA profile implications: seasoning for first 30 months, seasoned beyond
- Market views on and implications of seasoning and seasoned MBS

**CPR (Constant or Conditional Prepayment Rate) Benchmark**

- SMM = 1 – (1-CPR)
^{1/12} - PSA speed must be converted to implied CPR to calculate SMM

**Calculating Actual Prepayment Rate**

- Actual monthly mortality ÷ outstanding principal = SMM
_{Act} - CPR
_{Act} = 1 – (1 – SMM_{Act})^{12} - PSA
_{Act} = CPR_{Act} ÷ CPR value at PSA standard for that month

**Illustration of Cash Flow Projection**

**OPTION-ADJUSTED SPREAD ANALYSIS**

**Evaluation of Spread Between Treasury and MBS Spot Rate Curves**

- Reason for using spread between curves rather than security yields
- Higher MBS rates and lower cost per dollar of future cash flows
- OAS analysis: solve for portion due to more liquidity and credit risk
- Remainder due to premium for selling option

**Calculation of Z (Zero Volatility) or Static Spread**

- Project cash flows at vector of prepayment rates
- Rates based on forward interest rates and prepayment model
- Solve for constant spread to Treasury spot rates so price = PV

**OAS of MBS Uses Monte Carlo Simulation**

- Project numerous (100-300) interest rate paths
- Assume some volatility and appropriate rules (e.g. mean reversion)
- Random generation of monthly risk-free rates
- Use to generate mortgage rates, in turn used to obtain cash flows
- OAS based on spread to projected rates the equate average PV to price

**Cost of Option = Z Spread – OAS**

**Analytic Applications of OAS Analysis**

**DURATION AND CONVEXITY OF RMBS**

**Duration**

- Development of Duration
- Types of duration: Macaulay, modified, effective and dollar
- Duration as a measure of bond/portfolio values sensitivity to interest rates

**Duration and Convexity of Non-callable Bonds**

- Positive convexity
- Modified duration determination and interpretation

**Duration of MBS**

- Effective or OAS duration
- Other methodologies for estimating sensitivity of MBS to yield changes

**Applications of Duration**

- Evaluation of the relative value and risk of different bonds
- Structuring bond position hedges
- Active portfolio management – adjusting duration versus benchmark index

**Convexity of MBS**

- Negative convexity due to prepayment risk
- Negative convexity for yield below and a bit above pass-through rate
- Positive convexity at yield well above pass-through rate

**Factors Impacting Negative Convexity**

- Tied to value of prepayment option
- Implication of greater or lesser negative convexity
- Factors impacting: loan size, cost of refinancing, underwater loans, etc.