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Introduction To Mortgage Backed Securities�

Alan Beilis, Ph.D.

IEOR 4722 001

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Course Outline

  • Mortgage Market Overview
    • Basics of Mortgage Backed Securities (MBSs)
      • Mortgage Securitization
      • Quantitative Characteristics
        • Prepayments, Weighted Average Maturity (WAM), Coupon (WAC), Life (WAL), Option Adjusted Spreads (OASs)
    • Governmental Agencies/Sponsored Entities
      • Government National Mortgage Association (GNMA)
      • Federal National Mortgage Association (FNMA)
      • Federal Home Loan Mortgage Corporation (FHLMC)
    • MBS Products
      • Passthroughs
      • ARMs
      • CMOs
        • IOs, POs, PACs, TACs, Floaters, Inverse Floaters, Sequentials, Z Bonds, ………………..

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Course Outline (Continued)

  • Bond and Option Math
    • Bond Math
      • Yield Curves, Spot and Forward Rates*
      • Bond Price, Duration, Convexity, ……
    • Option Math
      • Binomial Pricing Model
    • Bond with an Embedded Option (Quantitatively, this is what a mortgage is)
  • Interest Rate Models
    • Equilibrium Models
      • Vasicek
      • Cox, Ingersoll, Ross
    • Arbitrage Free Models
      • Hull & White
      • Black, Derman, Toy (Yes …Professor Derman….)
      • Libor Market Model (BGM)
  • *Log Normal Interest Rate Monte Carlo Simulators

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Course Outline (Continued)

  • Prepayment Modeling
    • PSA Rates
    • Phenomenological Modeling
      • Housing Turnover
      • Incentive Based Refinancings
        • Spreads to “Current” Mortgage Rates
        • Media Effect
        • Burnout
          • Prepay Classes
      • Curtailment
      • Defaults
    • FNMA, FHLMC, GNMA
    • Examples

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Course Outline (Continued)

  • MBS Cash Flow Modeling
    • Level Payment Fixed Rate Mortgages (derivation)
      • Pass Through and ARM Coupons
    • Cash Flows with Prepayments
      • Scheduled and Unscheduled Cash Flows
  • Pricing & Analysis of Mortgage Backed Pass Through Securities
    • Monte Carlo Simulations (Combining Cash Flows and Interest Models)
    • Weighted Average Maturity (WAM), Coupon (WAC), Life (WAL)
    • Option Adjusted Spreads (OAS), Option Costs, Zero Volatility OAS, Durations, Convexities

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Course Outline (Continued)

  • Collateralized Mortgage Obligations (CMOs)
    • A “Plain Vanilla” 4 Tranche CMO
    • Product Innovations
      • IOs, POs
      • PACs, TACs
      • Floaters, Inverse Floaters
      • ……….
  • Presentation by Trader / Practioner (Tentative)
  • Final Exam

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Course Outline (Continued)

  • Suggested Readings
    • The Handbook of Mortgage Backed Securities
      • Frank Fabozzi, 5th Edition, Published by McGraw Hill
    • Guide to Mortgage Backed and Asset Backed Securities
      • L. Hayre, Ed., Published by J. Wiley
    • The Valuation of Mortgage Backed Securities
      • W. W. Bartlett, Published by R. D. Irwin
    • Mortgage Backed Securities: Investment Analysis & Advanced Valuation Techniques
      • A. S. Davidson, M. D. Herskovitz, Published by McGraw Hill
    • Options, Futures and Other Derivatives
      • J. C. Hull, 5th Edition, Published by Prentice-Hall

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Course Outline (Continued)

  • Grading
    • Homework Assignments : 40%
    • Final Exam : 60%

​

​

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Course Outline (Continued)

  • 5.25.05 - Bond Pricing Basics
  • 6.01.05 – Options & Bond Option Pricing
  • 6.08.05 – Interest Rate Models, Monte Carlo Simulations
  • 6.15.05 – Prepayment Modeling
  • 6.22.05 – MBS Cash Flows, Pricing and OAS Analysis
        • Practitioner Presentation
  • 6.29.05 – CMOs
        • Final Exam

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Basics of Mortgage Backed Securities - Securitization

  • MBSs represent ownership in mortgage loans made by financial institutions to finance borrower’s purchase of real estate. Financial institutions : Savings & Loans, Commercial Banks, Mortgage Companies, GNMA, FNMA, FHLMC
  • MBSs are created when these loans are pooled together by issuers or servicers, for sale to investors. The mortgages in a given pool have similar mortgage characteristics
    • 30 year maturity mortgages with coupons around 6%.
    • 15 year maturity mortgages with coupons around 5%.
  • As individual loans in pool are being repaid, security investors receive payments (comprising of interest (less a servicing fee) and principal).

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Basics of Mortgage Backed Securities – Some Quantitative Characteristics

  • Weighted Average Coupon – WAC

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​

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  • Weighted Average Maturity – WAM

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​

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  • Weighted Average Loan Age – WALA

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  • Weighted Average Life - WAL

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Governmental Agencies/Sponsored Entities

  • Government National Mortgage Association (GNMA)
    • Part of HUD, a branch of the U.S. Government
      • Issued securities carry full faith and credit of the U.S. government
    • Borrowers :
        • Higher LTV
        • Mortgage Assumability -> Slower prepayment rates relative to FNMA, FHLMC
        • Lower FICO Scores
  • Federal National Mortgage Association (FNMA)
    • Government sponsored entity
    • Publicly traded corporations, regulated and monitored by U.S. government.
      • Issued securities carry better than AAA ratings
  • Federal Home Loan Mortgage Corporation (FHLMC)
    • Government sponsored entity
    • Publicly traded corporations, regulated and monitored by U.S. government.
      • Issued securities carry better than AAA ratings
    • Borrowers :
        • Higher Mobility, More Affluent, More Efficient Prepayers

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MBS Products

  • Passthroughs
  • ARMs
  • CMOs
    • IOs, POs, PACs, TACs, Floaters, Inverse Floaters, Sequentials, Z Bonds

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Basics of Bond Pricing

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Zero Rates

  • A zero rate (spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T
    • derived from par yield curve via bootstrapping method (see below)

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Treasury Yield Curve/Spot Rates�3/8/05

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5.375

4.000

3.500

3.375

3.375

Coupon (%)

4.70

110.09375

30

4.38

96.96875

10

4.04

97.59375

5.0

3.78

98.8615

3.0

3.61

99.5505

2.0

3.02

98.5125

0.5

Zero Rate (BEY,%)

Yield (BEY,%)

Bond Price (%)

Maturity (Yrs)

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Treasury Yield Curve/Spot Rates�3/8/05

  • The bond yield is the discount rate, y that makes the present value of the cash flows on the bond equal to the market price of the bond:

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​

  • Consider the two year Treasury, priced at 99.5505:

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Bootstrap Method : Zero Rates

  • Interpolate (linearly) to get 1, 1.5 and 2.5 year YTM (with assumed coupons*, for the purpose of illustration)

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Maturity (Yrs)

Coupon (%)

Bond Price (%)

Yield (BEY,%)

Zero Rate (BEY,%)

0.5

​

98.5125

3.020

​

1.0

2.250*

99.0558

3.217

​

1.5

3.000*

99.4011

3.413

​

2.0

3.375

99.5505

3.610

​

2.5

3.375*

99.2425

3.695

​

3.0

3.375

98.8615

3.780

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Bootstrap Method : Zero Rates

  • Six month zero rate = Six Month Yield To Maturity
  • Bond with maturity is priced at
  • Spot rates determined, recursively:

​

​

  • The only unknown is

​

​

  • The only unknown is

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Bootstrap Method : Zero Rates

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  • Generally

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Bootstrap Method : Zero Rates

  • Interpolate (linearly) to get 1, 1.5 and 2.5 year YTM (with assumed coupons*, for the purpose of illustration)

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Maturity (Yrs)

Coupon (%)

Bond Price (%)

Yield (BEY,%)

Zero Rate (BEY,%)

0.5

​

98.5125

3.020

3.020

1.0

2.250*

99.0553

3.217

3.218

1.5

3.000*

99.4010

3.413

3.417

2.0

3.375

99.5505

3.610

3.618

2.5

3.375*

99.2425

3.695

3.728

3.0

3.375

98.8615

3.780

3.791

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Forward Rates

  • Indifference between investing for T2 years, at spot rate S2 or investing for T1 (< T2) years, at spot rate S1 and rolling the amount at T1 to T2 at the T2 - T1 year (forward) rate:

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Forward Rates

  • Increment T1 by 0.5 and let T2 – T1 = 0.5 :

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Maturity (Yrs)

Yield (BEY,%)

Zero Rate (BEY,%)

Forwards (BEY,%)

0.5

3.020

3.020

​

1.0

3.217

3.218

3.340

1.5

3.413

3.417

3.821

2.0

3.610

3.618

4.235

2.5

3.695

3.728

4.167

3.0

3.780

3.791

4.110

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Pricing a Bond

  • Price with Spot Rates:

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​

​

​

  • Price with Forward Rates:

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Pricing a Bond

  • Can be priced in one of several ways:

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Bond Duration

  • Bond interest rate sensitivity (can be negative)

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​

​

  • Example: Zero Coupon Bond (can’t be negative)

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Bond Convexity

  • Interest sensitivity of interest rate sensitivity (can be negative)

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  • Example: Zero Coupon Bond (can’t be negative)

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Constant Coupon Bond

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Bond Sensitivity Example

  • A five year bond, with a (continuously compounded) yield of 11%, paying an annualized coupon of 8%, in annual payments

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​

​

  • Determine the new bond price when the yield drops by 0.2%.

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​

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  • Notice : Convexity ignored – Why? Try with shift of 0.85%

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Basics of Option Pricing

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Agenda

  • Binomial Option Model (Discreet Time)
    • European / American
  • Continuous Time Option Models
    • Black Scholes Merton – European
    • Barone-Adesi Whaley - American
  • Risk Neutral Valuation
  • Some Greeks (Option Price Sensitivities)
    • Delta, Gamma, Vega

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Very Brief Review

  • Call (Put) option provides the right, not the obligation, to buy (sell) the underlying security, at a specified price, at a specified time.
  • European (American) option can be exercised at (any time prior to and including) the option’s expiration date.

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Binomial Option Model – �Multiplicative Price Propagation

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S0 u

ƒu

S0d

ƒd

S0

ƒ

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Binomial Option Model – �Portfolio Replication

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Consider the portfolio that is long Δ shares and short 1 derivative

ΔS0u – ƒu

ΔS0d – ƒd

S0– f

The portfolio is riskless when ΔS0u – ƒu = ΔS0d– ƒd

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Binomial Option Model

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Under risk neutral valuation (non-rigorous application):

(ΔS0d – ƒd) = (S0u Δ – ƒu ) = (S0Δ –ƒ)erT

ƒ = [ p ƒu + (1 – p )ƒd ]e–rT

Using defined above:

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Binomial Option Model- �3 Month European Call

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S0u = 22

ƒu = 1 = Max[S0u – K,0]

S0d = 18

ƒd = 0 = Max[S0d – K,0]

S0

ƒ

p

(1 – p )

Call Option Struck at K = 21

Risk free rate = 12% (old example)

Expiration = 3 months

u = 1.1; d = 0.9

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Binomial Option Model – �European

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Risk Neutral Probability:

The value of the option is

e–0.12x0.25 [0.6523 x 1 + 0.3477 x 0] = 0.633

Exercise: Check that the terminal portfolio values (page 32) are the same regardless of the path of the underlying.

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Binomial Option Model- �1 Year European Put Option

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50

4.1923

60

40

72

0

48

4

32

20

1.4147

9.4636

A

B

C

D

E

F

u=1.2, d=0.8, r=0.05, t=1.00

p=0.6282, 1-p=0.3718

Put struck at 52

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Binomial Option Model- � 1 Year American Put Option

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50

5.0894

60

40

72

0

48

4

32

20

1.4147

12.0

A

B

C

D

E

F

u=1.2, d=0.8, r=0.05, t=1.00

p=0.6282, 1-p=0.3718

Put struck at 52

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Binomial Option Model- Step Size

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Binomial Option Model- Step Size

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European Option – �Black Scholes Merton

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In the limit that the number of time steps (between “today” and the option’s expiration date) goes to infinity, the multiplicative European binomial option model can be shown to be equivalent to the Black Scholes Merton option pricing formula :

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The Black-Scholes Formula�Numerical Example

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Compare to result using binomial lattice

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Bond With An Embedded Option

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Bond With An Embedded Option

  • Prospective home buyer takes out a loan (equivalent to issuing a bond), with the provision that the home buyer can prepay the loan at any time (equivalent to owning an option to call back the bond at any time)
  • The lender makes the loan (equivalent to buying the bond issued by the prospective home buyer) giving the home buyer the right to prepay the mortgage (equivalent to “selling” a call option to the home buyer).
  • Guess What – a mortgage is a bond with an embedded call option!!
  • What is the value of this (embedded) option?

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Bond With An Embedded Option

  • The embedded option allows the home owner to prepay the mortgage when rates fall
    • Positive impact for home owner
      • Refinancing loan resulting in lower monthly payments
    • Negative impact for lending institution
      • Takes prepaid balance and has to invest it in a lower interest rate environment
  • As rates rise
    • Home owner satisfied that payments are lower than market rates
    • Lending institution not making as much as it could if the homeowner were to prepay, allowing lender to invest at higher rates

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Bond With An Embedded Option

  • We could try to value the option on the bond using a binomial approach on bond prices – BUT at maturity of the bond, the bond value is par. Period. Regardless of bond price volatility.
  • But option prices depend upon volatility (as well as other parameters)

Instead

  • Evolve interest rates, in a binomial lattice
  • Value bonds at nodes according to evolved rates
  • Value options at nodes according to nodal bond prices

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Binomial Rate Lattice

  • Generate a binomial interest rate lattice

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​

  • To consistently price bonds / options along this lattice, it is necessary to calibrate the lattice so that it can reproduce “today’s” bond prices

​

  • Price a European option on a 1.5 year constant coupon bond, struck at 99

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Interest Rate Environment

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4.110

3.791

3.780

3.0

4.167

3.728

3.695

2.5

4.235

3.618

3.610

2.0

3.821

3.417

3.413

1.5

3.340

3.218

3.217

1.0

3.020

3.020

0.5

Forwards (BEY,%)

Zero Rate (BEY,%)

Yield (BEY,%)

Maturity (Yrs)

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Calibrate Lattice

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Calibrate Lattice

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Calibrate Lattice

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Calibrate Lattice

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Calibrate Lattice

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Calibrate Lattice

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European option, struck at 99, callable in one year

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European option, struck at 99, callable in six months

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Exercise

  • Referring to the last two slides, calculate the put prices (Mmm … this sounds like a good exam problem… )

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Option Adjusted Spread

  • Calculated price of 1.5 year callable bond, struck at 99 to be 97.361.
  • What if the market price were actually 98.139?
  • “Add” a constant spread to each rate on our lattice of -125 bps, and recalculate bond and option prices :

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Option Adjusted Spread

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Option Adjusted Spread

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Option Adjusted Spread

  • Sources of spreads to the nominal curve:
    • Credit Risk
    • Liquidity (or lack thereof)
    • Embedded Optionality
  • The Option Adjusted Spread, OAS is that spread added to the interest rates so that the calculated price equals the actual market price of the callable bond.
  • Higher OAS=>Cheaper Bond
  • Lower OAS=>Richer Bond

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Call vs. Non Call Bond Prices

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“MBS Pool”

  • Pool together N such callable bonds (mortgages)
    • All around 30 years to maturity
    • All around the same coupon
    • All with the same right (option) to prepay

​

  • NOT quite the same as a pool backing a mortgaged backed security – WHY NOT?

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Interest Rate Models

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Interest Rate Models

  • Equilibrium Models
    • Assumptions about economic variables
    • Derive risk neutral stochastic (instantaneous short) rate process
    • Value / Assess risk of interest dependent products
      • Bonds
      • Options
      • Mortgage Backed Securities
  • Disadvantage – Term Structure is an output of the model - does not automatically fit today’s observed term structure

​

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Equilibrium Interest Rate Models

  • Vasicek Model

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Equilibrium Interest Rate Models

  • Vasicek Model – varying volatility

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Equilibrium Interest Rate Models

  • Vasicek Model – varying reversion speed

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Equilibrium Interest Rate Models

Vasicek yield curves –R(t,T) vs. T

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Equilibrium Interest Rate Models

  • Cox Ingersoll Ross (CIR)

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Equilibrium Interest Rate Models

CIR yield curves –R(t,T) vs. T

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Interest Rate Models

  • Arbitrage Free Models
    • Assumptions about economic variables
    • Derive risk neutral stochastic (instantaneous short) rate process
      • Current interest rate curve is input to the model
    • Value / Assess risk of interest dependent products
      • Bonds
      • Options
      • Mortgage Backed Securities

​

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Arbitrage Free Interest Rate Models

  • Hull White Model (Extended Vasicek Model)

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Arbitrage Free Interest Rate Models

  • Black Derman Toy
    • Incorporates the initial interest rate term structure and the volatility term structure.

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Arbitrage Free Interest Rate Models� BDT

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Arbitrage Free Interest Rate Models� BDT

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Arbitrage Free Interest Rate Models BDT

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Arbitrage Free Interest Rate Models� Libor Market (BGM) Model

  • Previous rate models – continuous non-observable forward rate models
    • There is no continuous series of tradable bonds
  • BGM : observable Libor rates (out to long maturities)

​

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Arbitrage Free Interest Rate Models� Libor Market (BGM) Model

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Arbitrage Free Interest Rate Models� Libor Market (BGM) Model

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Arbitrage Free Interest Rate Models� Libor Market (BGM) Model

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Monte Carlo Simulators� Log Normal Interest Rate

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Monte Carlo Simulators� Log Normal Interest Rate

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Monte Carlo Simulators� Log Normal Interest Rate

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Monte Carlo Simulators� Log Normal Interest Rate

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Prepayment Modeling

  • Pool together N such callable bonds (mortgages)
    • All around 30 years to maturity
    • All around the same coupon
    • All with the same right (option) to prepay

​

  • NOT quite the same as a pool backing a mortgaged backed security – WHY NOT?

​

Because ……..

​

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Prepayment Modeling

  • Standardized Prepayment Rates
    • Public Securities Association (PSA) model
  • Proprietary Prepayment Models

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Prepayment Modeling

  • Single Month Mortality (smm)

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​

  • Scheduled Balance = Remaining balance expected, for a given amortization schedule, with no prepayments
  • Actual Balance = Remaining balance, with scheduled balance adjusted for prepayments

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Prepayment Modeling

  • Annualized Prepayment rate

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Prepayment Modeling

  • Public Securities Association (PSA)

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Prepayment Modeling

  • Proprietary Models
    • Four Main Factors
      • Housing Turnover
      • Interest Rate Refinancing Incentive
      • Curtailment
      • Default

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Prepayment Modeling

  • Housing Turnover
    • Augmented Consumption Needs
      • Death in Family
      • Birth In Family
      • Change of Job
    • Pool Age - Seasoning
    • Cumulative Equity Growth
    • Lock-In effect
    • Seasonality

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Prepayment Modeling

  • Housing Turnover
    • Lock-In : with loan rate below current market mortgage rates, this factor captures the dampening effect to prepaying
      • Prepaying would increase costs
    • Seasoning quantifies the propensity to prepay as a function of equity growth and mortgage age
      • Newly issued pools prepayments gradually increase until some equilibrium level
    • Seasonality reflects the fact that more moving/ home purchasing occurs during warmer months of the year

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Prepayment Modeling

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Housing Turnover

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Prepayment Modeling

  • Interest Rate Refinancing Incentive
    • Dominant contributor to prepayments
      • Lower mortgage rate (monthly payments)
      • Lengthen term to maturity (lowering payments)
      • Take out accumulated equity

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Prepayment Modeling

  • Rate Refinancing Model Factors
    • CashOut
    • Seasonality
    • Rate Dependent Factors
      • Interest Rate Incentive
      • Prepay Constituency Classes (propensity to prepay as rates change)
      • Media Effect (Surge Index)

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Prepayment Modeling

  • CashOut
    • The larger the equity growth, the higher the probability of refinancing.
      • Typically refinancing to lower coupon, but some will refinance to higher coupon to capture / cashout out equity
    • The larger the incentive (measured by the difference between the Wac and lagged mortgage rate), the larger the impact of cashing out.

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Prepayment Modeling

  • Seasonality
    • Reflects higher prepayments in warmer months

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Prepayment Modeling

    • Rate Dependent Factors
      • Interest Rate Incentive
        • Temporal => decreased time due increased efficiency of refi process
        • Capacity Constraint => increased time due to large amount fo refinancings in a falling rate environment (media effect)
        • Cost Adjustment => refi transaction costs

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Prepayment Modeling

  • Example of refinancing incentive formulation:

​

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  • General shape needs to be fit to observed data (Homework Assignment)

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Prepayment Modeling

  • Prepay Classes
    • Slow Prepayers
    • Medium Prepayers
    • Fast Prepayers

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Prepayment Modeling

  • Class Evolution

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Prepayment Modeling

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Prepayment Modeling

  • Curtailment
    • Principal prepayments unrelated to interest rate incentives
    • Relatively minor impact to prepayments
      • 0.5% - 2% during the first 20 years of pool’s existence

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Prepayment Modeling

  • Default
    • Modeled by Standard Default Assumption

(SDA)

      • Function of age pool
    • Relatively minor impact to prepayments
      • 0.6% up to 10 years, dropping to a fraction of that beyond 10 years

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Prepayment Modeling

  • Putting it all together :

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Prepayment Modeling

  • Prepayments vs. Interest Rates:
    • Rates Fall, Prepayments Rise
    • Rates Rise, Prepayments Fall
    • Rates Fall, Rise, Then Fall Again
      • Prepayments Rise, Fall, Then Rise Again
      • Observe Burnout

​

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Prepayment Modeling

  • Burnout
    • First major rate drop in pools life
      • Pool prepay rate rises (most fast prepayers “leave” leaving medium and slow prepayers)
      • Enhanced by “Media Effect”
    • Rates rise or level off – prepayments slow
    • Rates drop (to lower rates than first drop
      • Prepay rate rise, but not as pronounced as earlier – less fast prepayers!

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Prepayment Modeling

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Prepayment Modeling

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Prepayment Modeling

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MBS Cash Flow Modeling

  • Constant Monthly Payments
    • Principal plus Interest (no prepayments)
  • Present Value of payments to maturity is the initial loan balance

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MBS Cash Flow Modeling

  • After the ith payment, the remaining cash flows are an annuity with M-i payments. The remaining balance is

​

​

  • The i+1st interest payment is given by

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MBS Cash Flow Modeling

  • Since each monthly payment is constant, the i+1st principal payment is the difference between monthly payment and the interest portion of the monthly payment:

​

​

​

  • “Sanity Check”:

​

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MBS Cash Flow Modeling

  • For most of the life of the mortgage (with no prepayments), interest is the larger portion of the fixed payment. When is the principal payment equal to the interest payment? When do the principal payments dominate?

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MBS Cash Flow Modeling

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Remaining Balance: Level Payment Mortgage

M = $100,000; N = 25; R = various

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MBS Cash Flow Modeling

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Mortgage Payments: Level Payment Mortgage

M = $100,000; R = .09; N = 25

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MBS Cash Flow Modeling

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Mortgage Payments: Level Payment Mortgage

M = $100,000; R = .15; N = 25

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MBS Cash Flow Modeling

  • Cash flow passed to investor:

​

    • s is the fee paid to mortgage servicer
    • Notice that the monthly cash flows passed to the investor are not fixed!

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MBS Cash Flow Modeling

  • Cash Flows with Prepayments
    • Recall, from the definition of smm

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  • Generally, along path

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MBS Cash Flow Modeling

  • As interest and principal depend upon the remaining balance

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MBS Cash Flow Modeling

  • No Prepayments:

​

​

  • Prepayments:
    • No Prepay CFs diminished by Q
    • Mortality of Diminished Balance

​

​

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MBS Cash Flow Modeling

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MBS Cash Flow Modeling

  • Unscheduled Interest Payment

​

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  • Unscheduled Principal Payment

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MBS Cash Flow Modeling

  • One can show that the sum of scheduled and unscheduled principal payments account for the balance reduction from one period to the next

​

​

  • (Mmm … this sounds like a good exam problem… )

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MBS Cash Flow Modeling

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MBS Cash Flow Modeling

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Note: Duration and Convexity are positive --- Why?

🡸Prove this ….

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MBS Cash Flow Modeling

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7.375%

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7.375%

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7.375%

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Pricing & Analysis of Pass Through Mortgage Backed Securities

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Pricing & Analysis of Pass Through Mortgage Backed Securities

  • “Pool” with a single pass through security

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Pricing & Analysis of Pass Through Mortgage Backed Securities

  • OAS Analysis

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Pricing & Analysis of Pass Through Mortgage Backed Securities

  • ZVOAS = OAS + OC
  • As coupon increases
    • Option cost first increases, then decreases
    • Duration decreases, Convexity decreases, then increases, around the current coupon
    • WAL decreases

​

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Pricing & Analysis of Pass Through Mortgage Backed Securities

  • OAS Analysis

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Pricing & Analysis of Pass Through Mortgage Backed Securities

  • Positive Parallel Shifts
    • Duration increases
    • Convexity goes to zero

​

  • Negative Parallel Shifts
    • Duration decreases
    • Convexity goes to zero

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Deep Discount MBS – OC monotonic -> as rates shift down, hump will become evident

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Adjustable Rate Mortgages

  • Coupon is set periodically subject to ARM features :
    • Stated security margin
    • Index
      • EDCOFI
      • One Year CMT
    • Periodic, Lifetime Cap
    • Periodic, Lifetime Floor
    • Teaser Rate

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Adjustable Rate Mortgages

  • Security Margin
    • Spread above the chosen index (weighted average of margins of underlying mortgages in the pool, less servicing)
      • GNMA : 150 bps
      • FNMA & FHLMC :
        • EDCOFI : 125 bps
        • 1 Year CMT : 150 – 200 bps

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Adjustable Rate Mortgages

  • Index
    • One Year CMT
      • Behave very much like the 1 Year Treasury Bill
    • EDCOFI – 11th District Cost of Funds
      • Average monthly liability interest expenses of member institutions
  • Volatility of EDCOFI is lower than volatility of One Year CMT

​

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Adjustable Rate Mortgages

  • Periodic Cap
    • Restriction on the amount the coupon can increase upon periodic reset
      • GNMA : 1%
      • FNMA, FHLMC :
          • EDCOFI : None
          • 1 Year CMT : 2%
  • Lifetime Cap
    • Maximum value coupon can attain over the life of the security
      • GNMA : 5%
      • FNMA, FHLMC :
          • EDCOFI : 5%
          • 1 Year CMT : 5% - 6%

​

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Adjustable Rate Mortgages

  • Periodic Floor
    • Restriction on the amount the coupon can decrease upon periodic reset
      • GNMA : 1%
      • FNMA, FHLMC :
          • EDCOFI : None
          • 1 Year CMT : 2%
  • Lifetime Floor
    • Minimum value coupon can attain over the life of the security
      • GNMA : -5%
      • FNMA, FHLMC :
          • EDCOFI : -5%
          • 1 Year CMT : None

​

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Adjustable Rate Mortgages

  • Teaser Rate
    • Low introductory rate designed to make the ARM attractive relative to a fixed rate mortgage
      • Risk aversion would imply a preference for fixed rate mortgages
    • GNMA: lowest pool ARM teaser
    • FNMA, FHLMC: Function of WAC of ARM
      • Independent of Index

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Adjustable Rate Mortgages

  • ARM Coupon

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Adjustable Rate Mortgages

  • Realized Margin

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Adjustable Rate Mortgages

  • Effective Margin
    • Average of realized margins over an array of index paths over the life of the security
      • Impacted by volatility and ARM features
      • Allows investor to compare ARMs with the same index, but differing features

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Adjustable Rate Mortgages

  • Effective Margin FHLMC, One Year CMT, Stated Margin of 195 bps, 6% CPR
    • As volatility increases, EM decreases
      • Greater likelihood that caps/floors will be hit
    • Price dependency

Discount – Features compensate investor

At Par – Features cost investor

Premium – Features cost investor

​

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Adjustable Rate Mortgages

  • Effective Margin FHLMC, One Year CMT, Stated Margin of 195 bps, priced at par
    • Higher prepayments reduce balance, thereby reducing the gain

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Collateralized Mortgage Obligations

  • Mortgage pass through security cash flows may be “re-packaged” or redirected to create collateral structures designed with different maturities and risk characteristics.
    • Motivation (in part) for creation of CMOs is arbitrage:
      • Investors will pay more for bonds that meet their specific needs
        • Consequently, value of CMOs derived from collateral may be higher than the collateral itself.

​

​

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Sequential CMO�(slide borrowed from another source)

  • Passthroughs or other pools provide cashflows (“collateral”)
  • Multi-class deal is created with sequential classes (“tranches”)
  • Interest is paid to all classes
  • All principal is directed to first class, until it is completed paid off
  • Principal is then directed to next class, until it is paid off
  • Classes receive principal cash flows from collateral until all tranches are paid off

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Sequential CMO�(slide borrowed from another source)

Collateral

(Passthroughs) Generate

principal and interest cash

flows

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Tranche 1

Short

receives P&I

Tranche 2

Intermediate

paid interest only (until Tranche 1 matures)

Tranche 3

Long

paid interest only (until Tranches 1 & 2 mature)

Interest

Principal

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Sequential CMO

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Note: The Z bond gets absolutely no cash flows until earlier tranches are paid off

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Sequential CMO

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10% CPR

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Sequential CMO

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20% CPR

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Sequential CMO

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Note: At this prepay speed and given tranche characteristics, the weighted average price of the tranches is less than the collateral price, at a given discount rate – Sell collateral, buy tranches (under a different set of tranche characteristics, it is possible that the collateral is priced lower than the weighted average sum of the tranches)

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Sequential CMO

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Planned Amortization Class (PAC)

  • PAC tranches, yield and average life are more likely to be stable over the life of the security
  • PAC payment schedules are protected by priorities which assure that PAC payments are met first out of principal payments from the underlying mortgages
    • Principal payments in excess of the scheduled payments are diverted into non-PAC (companion or support) tranches
    • When prepayments are minimal, the PAC payments are met and the companion may have to wait
    • When prepayments are heavy, the PAC gets only the scheduled amount, and the companion absorbs the rest
    • Because they offer more certainty, they have lower yields

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Planned Amortization Class (PAC)� (slide borrowed from another source)

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Collateral (Passthroughs)

Generate principal and interest cash flows

PAC Classes

Receive interest and principal paid to the balance schedule

Support Classes

Receive interest and remaining principal after the PAC schedule is met

Interest

Principal

Note -

​

  1. At prepayment speeds faster than the pricing speed, Support bonds pay down more quickly and have shorter average lives than at pricing.

​

  • Conversely, if prepayment speeds are slower than at the pricing speed, Support bonds pay down more slowly and have longer average lives than at pricing.

​

  • As actual cash flows are allocated by the structure, the amount of Support bonds available to allow the PACs to meet their balance schedule changes.

​

  • Both PAC and Support classes can be sequentially tranched in order to meet average life targets within

their sector, creating short, intermediate, and long PACs and Support bonds.

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Planned Amortization Class (PAC)� (slide borrowed from another source)

  • PACs and supports can be divided (“tranched”, “carved”) sequentially
  • PAC structures are created by defining a PAC “band” or “collar”—essentially a range of prepayment speeds in which the PAC’s cash flows remain stable
  • PAC bands and structures change as collateral pays down—initial structure is a snapshot at the time the deal is closed (like a balance sheet)
  • PACs can break down if speeds are significantly different from the speed when the deal is structured—creates “broken” PACs

​

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Planned Amortization Class (PAC)

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Targeted Amortization Class (TAC)

  • Provides cash flow certainty at one prepayment rate, rather than a range. In effect, It can be viewed as a PAC with the lower band equal to the collateral pricing speed.
  • If prepays are lower than upper band, TAC holders may receive less than the scheduled amount.
  • Accordingly, yields on TACs are higher (compensation for no protection against rising rates) than PAC yields.
  • Tranche performance depends upon priority in CMO structure and whether there are PAC Tranches over it

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Targeted Amortization Class (TAC)

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Interest Only / Principal Only IOs / POs

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Interest Only / Principal Only IOs / POs

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Interest Only / Principal Only IOs / POs

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Interest Only / Principal Only IOs / POs

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Floaters / Inverse Floaters

  • Fixed Rate, , Tranche cash flows directed to:
    • Floating Rate Tranche

​

    • Inverse Floating Rate Tranche

​

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Floaters / Inverse Floaters

  • Non-Amortizing 7.5% Fixed Rate Tranche, $100 million Face Value directed to
    • $67 million floating rate tranche with a 75 bps spread to Libor
    • $33 million inverse floating rate tranche

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Floaters / Inverse Floaters

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Floaters / Inverse Floaters

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8% Cap, 5% Floor

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Summary

  • MBS Pricing
    • Cash Flows
      • Prepayment
    • Interest Rate Models
    • Monte Carlo Simulations, OAS
  • Pass Through & CMO Structuring
    • Sequential Structure with a Z Bond, Residual
    • PAC, TAC
    • IOs, POs
    • Floater/Inverse Floater

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