Mortgage-Backed Securities. Leah DiMartino Matt Houser Brendan LaCerda Kaity McCoy Brian Seremet Justin Sibears

Transcription

1 Mortgage-Backed Securities Leah DiMartino Matt Houser Brendan LaCerda Kaity McCoy Brian Seremet Justin Sibears 1

2 Introduction Mortgage-backed securities (MBS) are debt obligations that represent claims to cash flows from pools of mortgage loans Mortgages are purchased and assembled into pools by governmental, quasi-governmental, or private entities These entities then issue securities that represent claims to the principal and interest payments on the mortgages 2

3 Types Most simple MBS are pass-through securities in which the holder of the security is entitled to a pro-rata share of all interest and principal payments CMOs Divide pool into tranches so that securities with different maturities and different risks can be issued 3

4 Benefits and Risks Benefits High yields for the amount of risk taken Credit risk minimal due to diversification Risks Prepayment risk risk that some homeowners will make principal payments ahead of schedule, especially prevalent during low interest rate periods in which many homeowners refinance Detrimental to investors because money must then be reinvested at lower interest rates Extension risk sometimes prepayments can occur slower than expected, which leads to longer maturity and more exposure to interest rate risk 4

5 Market for MBS Fast Growth $110.9 billion outstanding in 1980 $3,968 billion outstanding in

6 General pricing strategy 6

7 Previous attempts Econometric models Use historical prepayment data Disadvantage is that changes in economic factors can make historical data obsolete as predictor of future prepayments For example, Internet and widespread dissemination of information has dramatically decreased the drop in interest rates needed before homeowners refinance Option-theoretic models Attempt to value option of homeowners to refinance, this reduces the value of MBS to investors from value of bond with similar cash flows and no prepayment risk Assume unrealistic homeowner behavior and have had trouble fitting market data 7

8 Our Model Proposed by Kalotay,, Yang, Fabozzi Shares similarities with option-theoretic Based on idea of homeowners exercising option to refinance Model allows for varying behavior of homeowners using imputed coupon Distinguishes between mortgage interest rates and MBS interest rates unlike previous models Allows for multiple types of prepayments 8

9 Interest Rate Model Based on Black-Derman Derman-Toy d(ln r) = [θ(t)[ + ln r (σ (t)/( (t)/ σ(t))]dt + σ(t)dw t Binomial model Fits current yield curve Assumes constant volatility (σ( = 10%) For fixed w, interest rates in the binomial tree related by: r wt = r wh e 2σ t 9

10 Treasury Securities 10

11 Yield Curve Yield Curve Yield 6.00% 5.50% 5.00% 4.50% 4.00% 3.50% 3.00% Years to Maturity 11

12 Creating Binomial Tree Set r 0 = 4.97%, the current yield on a treasury security with one year to maturity. Consider treasury security with 2 years to maturity, coupon of 3.125, and price of 97:00 12

13 Creating Binomial Tree Three cells at each node Top cell PV of future cash flows Middle cell Coupon payment Bottom cell Interest rate Input is interest rate in lowest node for time 1. Compare PV at time 0 to current price of two year security < 97 r T too high 13

14 Creating Binomial Tree 14

15 Creating Binomial Tree Now consider treasury security with 3 years to maturity, coupon of 4, and price of 98:07 Input is interest rate in lowest node of time > interest rate too low 15

16 Creating Binomial Tree This process is continued until we find a binomial tree for interest rates with ten time periods 16

17 Simulation There are 2 10 different paths for interest rates under this model. Randomly select 21 of these that are representative of all the possible paths. Risk-free interest rate 10.0% 8.0% 6.0% 4.0% 2.0% 0.0% Interest rate paths Year 17

18 Prepayments Housing Turnover Mortgage usually repaid when home sold Significant cause of prepayments Important to forecast housing turnover rate which depends on such factors as economic growth and federal taxation of home sales Refinancing Homeowners repay old loan and take out new loan to benefit from decrease in interest rates 18

19 Prepayments Default When foreclosure or liquidation of mortgage occur Minor cause of prepayments, less than 0.5% CPR Curtailments Homeowners pay more than scheduled payment to build up equity in home, less than 0.5% CPR 19

20 Modeling Refinancing Model based on behavior of individual homeowners Most homeowners do not refinance optimally and in particular they refinance too late Assigned each homeowner a value for a variable l Assume mortgage rate of m Homeowner refinances as if they have mortgage with rate of m - l. 20

21 Assumptions MBS consists of eight groups of investors with equal principal Values of l range from 0.0% to 3.5% in increments of 0.5% 21

22 Binomial Mortgage Tree Each node contains two cells Top cell R w PV of mortgage assuming that refinancing occurs if optimal R w = min(v w, P w * (1 + c) where P w is the principal remaining on the (m-l( m-l)% mortgage after w has been followed and c is the cost of refinancing Bottom cell V w PV of mortgage payments assuming no refinancing V w = K + 0.5R wh + 0.5R wt 1 + r mortgage w where K is the mortgage payment on (m-l)% mortgage and r mortgage w = r w

23 Binomial Mortgage Tree And the corresponding binomial mortgage tree: 23

24 Binomial Mortgage Tree Consider the following interest rate path: 6.0% 5.0% Interest Rate 4.0% 3.0% 2.0% 1.0% 0.0% Time 24

25 Cash Flows Refinancing occurs at time 6. Use this to get cash flows from MBS for this group of homeowners and then repeat for other seven groups. 25

26 MBS Prices 26

27 Assumptions Used 10-year mortgages with yearly payments, obviously unrealistic but easily can be extended to 30-year mortgages with monthly payments Mortgage interest rates 80 basis points above risk-free rate at any period and MBS interest rate 30 basis points above risk-free rate at any period Assume refinancing decision based on movement of short term interest rates, in actuality long term rates also considered 27

28 Assumptions Assumed simply model for prepayments due to housing turnover Initially 0.0% and then increases by 0.2% per month until reaching 6.0%, at which time the rate stabilizes Ignored prepayments due to defaults or curtailments 28