Valuation of Mortgage Securities

1
Valuation of Mortgage Securities

• Interest-rate Contingent Securities
• The Importance of Prepayment
• Modelling Expected Prepayments
• Average Prepaid Life
• Constant Prepayment Rate
• FHA Experience
• Public Securities Association (PSA) Model
• Others

2
Types of Mortgage Backed Securities

• Commonly Observed Securities
• Pass-Throughs
• Mortgage-Backed Bonds
• Collateralized Mortgage Obligations
• Interest Only (I/O) Strips
• Principal Only (P/O) Strips
• Servicing Rights

3
Valuing Mortgage Securities

• Given the following information about a pool of
  fixed-rate mortgages
  
• Amount 110 million
• Coupon Rate 11
• PSA 100
• Year 1- 1.3 Year 2 3.7 Year 3,
  5.75 Year 4 6.0
  
• For the first 4 years, show
• The end-of-year pool balance
• Scheduled principal and interest payments
• Total cash flows

4
Estimating Pool Wide Cashflows
5
Effective Duration of Pass-Throughs

• Problems with standard duration
• Timing of future CFs?
• Amount of future CFs?
• Impossible to calculate!
• Effective (Implied) Duration

6
Calculating Effective (Implied) Duration

• Consider the following price and yield data
• Initial yield 10.00
• Price 105.125
• Revised yield 10.25
• Revised price 104.25
• Calculate Effective Duration
• Would the duration calculated be greater or less
  if the price change did not reflect a change in
  the assumed PSA prepayment rate? Why?

7
Mortgage-Backed Bonds

• Mortgage Pool Data
• Amount 120 million
• Coupon rate 11
• Maturity 30 years
• PSA 0
• Default rate 0.5 for first 5 years
• Bond Data
• Amount 110 million
• Coupon rate 10
• Maturity 20 years
• Yield on fund 7

8
Cash Flows of Mortgage-Backed Bonds