The Financial Risks Associated with Mortgage-Backed Securities

Transcription

1 The Financial Risks Associated with Mortgage-Backed Securities Global Association for Risk Professionals (GARP) Raleigh, NC Chapter Meeting October 25, 2012 Tao Pang, PhD, FRM Department of Mathematics North Carolina State University

2 1. Introduction MBS(Mortgage-Backed Securities) is a very important class of financial instruments. It is directly related to the recent financial crisis. Ownership of a unit of an MBS entitles the owner to a cash flow from the principal and/or interest of the mortgage payment. 1

3 Mortgage Money Mortgage Borrowers Mortgage Lender MBS Investors Monthly Payments MBS Payments The Cash-Flow for MBS Bonds 2

4 An example of Pass-though MBS Mortgage 1 $200k, i=6.5% Maturity: 30 years Mortgage 2 $300k, i=7% Maturity: 30 years Mortgage 3 $500k, i=6% Maturity: 30 years A pool of mortgages Principal=$1 million WAC=6.4% Maturity: 30 years 1000 MBS bonds face value: $1000 coupon rate: 6.4% (payable monthly) Maturity: 30 years Remark: The MBS investors will receive both principal payments and interest payments WAC=Weights average coupon rate (all coupon rates weighted by principal weights 3

5 MBS Agencies There are three major housing finance agencies, Ginnie Mae, Fannie Mae and Freddie Mac. MBS products issued by those three agencies are considered to have no credit risk (default risk) or to have negligible credit risk. However, there are also private-label MBS which are issued by other agencies and they do bear credit risk. 4

6 More MBS Products The cash flows backed by a pool of mortgage payment can be reallocated to create various MBS products Collateralized Mortgage Obligations (CMO) Different tranches with different average life A tranche can not receive principal payment until the tranche before it has been paid off 5

7 Cash Flow for a CMO: An example with floating rates Mortgage 1 Mortgage 2 Mortgage 3 Mortgage n Principal: $100 million Special Purpose Vehicle Senior Tranche Principal: $75 million Return = LIBOR + 70bp Mezzanine Tranche Principal:$20 million Return = LIBOR+ 200bp Equity Tranche Principal: $5 million Return =LIBOR+1,000bp 6

8 Cash Flow Allocation Order Mortgage Principal Cash Flows Senior Tranche Principal Mezzanine Tranche Principal Equity Tranche Principal 7

9 Effects of Prepayment Prepayment is allowed for Mortgage loans Form of prepayment: Sell the house Refinance Pay more than scheduled payment Prepayment is a call option sold to mortgage borrower Mortgage rate is higher with this option embedded. Investors needs to consider the prepayment risk 8

10 Payment An Example with fixed rates: Total Principal: $200k; Interest rate: 4.875% Maturity: 30 years Tranche A: $80k; Tranche B: $30k; Tranche C: $90k No Prepayment CMO Payment Scheme (No Prepayment) Tranche A Tranche B Tranche C Tranche A Interest Tranche B Interest Tranche C Interest Month 9

11 Payment Total Principal: $200k; Interest rate: 4.875% Maturity: 30 years Tranche A: $80k; Tranche B: $30k; Tranche C: $90k Prepayment Rate: 100%PSA CMO Payment Scheme (100%PSA Prepayment) Tranche A Tranche B Tranche C Tranche A Interest Tranche B Interest Tranche C Interest Month 10

12 Payment Total Principal: $200k; Interest rate: 4.875% Maturity: 30 years Tranche A: $80k; Tranche B: $30k; Tranche C: $90k Prepayment Rate: 300% PSA CMO Payment Scheme (300%PSA Prepayment) Tranche A Tranche B Tranche C Tranche A Interest Tranche B Interest Tranche C Interest Month 11

13 More MBS Products (continued) Planed Amortization Class (PAC) and Companions Prepayment risk is absorbed by companions with a certain limit Interest only (IO) and principal only (PO) Floaters and inverse floaters Products with floating interest rates can be created 12

14 Payment Total Principal: $200k; Interest rate: 4.875% Maturity: 30 years PAC with Planed Prepayment Rates between 300% and 100% PSA PAC Payment PAC Payment Scheme (300%/100% PSA) Slow Principal Payment Fast Principal Payment PAC Principal Month 13

15 2. Risks involved in MBS Products 2.1 Prepayment risks Typically, mortgage borrowers have the right to prepay a mortgage at any time during the life of the loan. Note: Refinancing is also a type of prepayment. Mortgage borrowers tend to prepay when interest rate is low, which is not good for the investors. 14

16 Four factors to effect the prepayment rates: Refinancing Incentive Age of the mortgage (Seasoning) The month of the year (Seasonality) Premium Burnout (Principal balance). 15

17 Terminology of the prepayment model WAC: weighted average coupon rate (for a combination of loans) CPR: conditional prepayment rate PSA prepayment rate: industry convention adopted by the Public Securities Association (PSA) in which CPR s are assumed to follow a standard path over time. 16

18 Prepayment rate Standard PSA Prepayment Rate 9.00% 7.50% 150% PSA 6.00% 4.50% 3.00% 100% PSA 75% PSA 1.50% 0.00% Months 17

19 Refinancing Incentive (RI(t)) Most Crucial Component of CPR model. It is a function of the (refinancing) interest rate R and the current mortgage coupon rate C. 18

20 Seasoning Multiplier Seasoning Multiplier (SM(t)) Seasoning or aging reflects the observation that newer loans tend to prepay slower than older loans Months 19

21 Seasonality Multiplier (MM(t)) Seasonality takes into consideration the time of year. It is believed that prepayments peak in the fall and decrease in the winter Monthly Multiplier Months 20

22 Burnout Multiplier Burnout Multiplier (BM(t)) Premium Burnout takes into account the tendency for prepayment to diminish over time. In our simulation, the Burn% is calculated as a function of the pool factor Months 21

23 Prepayment rate Prepayment rate with a random interest rate path (all four factors are considered) 50% Prepayment rate=ri(t) x SM(t) x MM(t) x BM(t) 40% 30% 20% 10% 0% Months 22

24 2.2 Interest Rate Risks In reality, the interest rate path is not fully predictable. We use certain stochastic processes to model the interest rates Equilibrium Models Vasicek Model: Cox, Ingersoll, and Ross (CIR) model: Courtadon Model: dr t c(r t r )dt dw t dr t c(r t r )dt r t dw t dr t c(r t r )dt r t dw t 23

25 More interest rate models No Arbitrage Models Ho-Lee Model Hull-White Model: Black-Karasinski (B-K) Model: Other models Heath-Jarrow-Morton (HJM) Model: Modeling forward rate instead of short rates dr t (t)dt dw t dr t c(r t (t))dt dw t dln r t c(lnr t (t))dt dw t LIBOR Market Model: Easy to implement using market data 24

26 An interest rate path generated using Vasicek Model 14% 12% 10% 8% 6% 4% 2% 0% Months 25

27 2.3 Default Risks Mortgage borrowers tends to default when House value is less than the principal balance (if the house price drop dramatically) No sufficient income to pay monthly payments (Mortgage rate increases, loss jobs, live expense increases, etc.) When mortgage borrowers default, all (pass-through) MBS bond investors will face the same default risk: partial of their bond principal can not be repaid. To decrease default risks, mortgage lenders should use higher standard when issuing new mortgage loans 26

28 3. Price MBS bonds 3.1 Basic Idea Present Value of a payment of X payable at a future time T: Present value = where is the interest rate. For a bond with payments c 1, c 2,, c n which are payable at t 1, t 2,,t n the current price is the total present value of the cash flow: P = e rt 1c 1 + e rt 2c e rt nc n Due to random interest rates and random prepayment, e rt X the cash flow for MBS bond is not pre-deterministic. Price is given by taking expectations: r P E Q n k 1 e r k t k c k 27

29 3.2 Monte-Carlo Simulation Law of large numbers: Let Then be i.i.d. r.v. s. Important tool in the pricing of complex financial instruments. Advantage: the convergence speed does not depend of the dimension of. Drawback: The convergence speed is very slow ( ) 1 N lim N X 1 X 2 L X N N X E[X 1 ] X 1,X 2,L,X N 28

30 3.3 Steps to pricing a MBS product The expectation can be evaluated by Monte Carlo Simulation Specify an interest rate model Generate interest rate paths Generate cash flows for each interest rate path using the prepayment model Calculate the total present values for cash flows for each interest rate path Take average for all possible present values to get the price 29

31 4. Subprime Mortgage Crisis: ABS CDOs or Mezz CDOs (Simplified) Assets Senior Tranche (80%) AAA The mezzanine tranche is repackaged with other mezzanine tranches Mezzanine Tranche (15%) BBB Senior Tranche (65%) AAA Mezzanine Tranche (25%) BBB Equity Tranche (5%) Not Rated Equity Tranche (10%) Note: The slides of this section are mainly from the materials accompanied with John Hull s book, Options, Futures and Other Derivatives, 8th Edition. 30

32 Losses to AAA Senior Tranche of ABS CDO (Table 8.1, page 184) Losses on Subprime portfolios Losses on Mezzanine Tranche of ABS Losses on Equity Tranche of ABS CDO Losses on Mezzanine Tranche of ABS CDO Losses on Senior Tranche of ABS CDO 10% 33.3% 100% 93.3% 0% 13% 53.3% 100% 100% 28.2% 17% 80.0% 100% 100% 69.2% 20% 100% 100% 100% 100% 31

33 U.S. Real Estate Prices, 1987 to 2010: S&P/Case-Shiller Composite-10 Index Jan 87 Jan 90 Jan 93 Jan 96 Jan 99 Jan 02 Jan 05 Jan 08 32

34 What happened Starting in 2000, mortgage originators in the US relaxed their lending standards and created large numbers of subprime first mortgages. This, combined with very low interest rates, increased the demand for real estate and prices rose. To continue to attract first time buyers and keep prices increasing they relaxed lending standards further Features of the market: 100% mortgages, ARMs, teaser rates, liar loans, non-recourse borrowing Mortgages were packaged in financial products and sold to investors 33

35 What happened... Banks found it profitable to invest in the AAA rated tranches because the promised return was significantly higher than the cost of funds and capital requirements were low In 2007 the bubble burst. Some borrowers could not afford their payments when the teaser rates ended. Others had negative equity and recognized that it was optimal for them to exercise their put options. Foreclosures increased supply and caused U.S. real estate prices to fall. Products, created from the mortgages, that were previously thought to be safe began to be viewed as risky Many banks incurred huge losses 34

36 What Many Market Participants Did Not Realize Default correlation goes up in stressed market conditions The BBB tranches used to create ABS CDOs were typically about 1% wide and had all or nothing loss distributions. This is quite different from the loss distribution for a BBB bond from a BBB bond 35

37 Regulatory Arbitrage The regulatory capital banks were required to keep for the tranches created from mortgages was less than that for the mortgages themselves 36

38 Incentives The crisis highlighted the dysfunctional incentives of Mortgage originators (Their prime interest was in in originating mortgages that could be securitized) Valuers (They were under pressure to provide high valuations so that the loan-to-value ratios looked good) Traders (They were focused on the next end-of year bonus and not worried about any longer term problems in the market) 37

39 The Aftermath A huge amount of new regulation including: Banks required to hold more capital Banks required to satisfy liquidity ratios More emphasis on stress testing and the use of historical data from stressed market conditions Clearing houses for OTC derivatives Taxes on bonuses (UK) Limits to proprietary trading 38

40 Thanks! 39