David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

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

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

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

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

Valuing Mortgage Securities Given the following information about a pool of fixed-rate

mortgages:

Amount: $110 millionCoupon 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

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

Estimating Pool Wide Cashflows

YearBeg. Pool Bal.

P & I Prin. Int. Pre-pays

Total CF

End. Pool Bal.

1

2

3

4

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

Effective Duration of Pass-Throughs

Problems with standard duration Timing of future CF’s? Amount of future CF’s?

Impossible to calculate!

Effective (Implied) Duration

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

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?

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

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%

David M. Harrison, Ph.D.Real Estate FinanceTexas Tech University

Cash Flows of Mortgage-Backed Bonds

YrBeg. Pool Bal.

P & I Prin Int Pre-pays Def

Total CFin

PMTs to

Bond.Res

Res. Fund Bal.

End. Pool Bal.

1

2

3

4