Financial Engineering Lecture 11 Mortgage Backed Securities History

Financial Engineering Lecture 11

Mortgage Backed Securities History of banks and spread Federal National Mortgage Association (FNMA) ◦ Fannie Mae ◦ Chartered 1938 & 1968 Federal Home Loan Mortgage Corp. (FHLMC) ◦ Freddie Mac ◦ Chartered in 1970 Freddie and Fannie have same mandate Ginnie Mae ◦ Govt agency ◦ Guarantees VHA an d VA loans

Valuing MBS Valued similar to bonds (fixed incomes) Factors Prepayment Weighted average coupon (WAC) ◦ The monthly payment derived from the interest rate charged on the loans. Weighted average maturity (WAM) Required yield (YTM) Default (similar to prepayment)

Mortgage Backed Securities Cash Flow Pattern for Bonds

Mortgage Backed Securities Cash Flow Pattern for MORTGAGES Reflecting PREPAYMENT

Secondary Mortgage Market Prepayment Analysis Benchmarks Maturity Half Life Avg. Life Duration

Secondary Mortgage Market

Secondary Mortgage Market • • • Prepayment Factors Seasoning ** Refinancing ** Economic Activity Trading up Default Disaster Legal structure Geographical region Season of year

Secondary Mortgage Market Pre-Payment Models • 30 -12 Convention • Single Monthly Mortality (SMM) & Constant Prepayment Rate (CPR) • Public Securities Association Standard (PSA Model) -0% CPR in month 0 -. 2% CPR months 1 -30 -6% CPR annual after 30 mt PSA 102 = quicker prepay PSA 96 = slower prepay

Secondary Mortgage Market

Mortgage Backed Securities MBS Valuation MBS Value = PV of cash flows Steps 1. Determine the monthly payment 2. Use prepayment assumption to derive maturity 3. Calculate the PV of the monthly payment at the YTM.

Mortgage Backed Securities MBS Valuation Using present value terminology PV = Price of MBS Pmt = monthly coupon payment from MBS i = Yield to Maturity n = t = Prepayment year assumption FV = Balance of mortgage at prepayment

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool?

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool? Assume NO prepayment. Step 1 – Find the monthly payment PV = $ 13, 000 FV = 0 n = 264 (22 x 12) i = 0. 54 % (. 065 / 12 ) solving for the PMT = - 92, 682

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool? Assume NO prepayment. Step 2 – Find Present Value of the monthly payments at the YTM PMT = - 92, 682 FV = 0 n = 264 (22 x 12) i = 0. 6167 % (. 074 / 12 ) solving for the PV PV = $ 12, 064, 114

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15.

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Step 1 – Same as before. Calculate the monthly payment PMT = 92, 682

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Step 2 – NEW – Calculate the balance at the end of year 15. PMT = - 92, 682 PV = 13, 000 i = 0. 54 % (. 065 / 12 ) n = 180 (15 x 12) solving for the FV FV = - 6, 241, 454

MBS Valuation Example A mortgage pool contains $13, 000 in loans made to homeowners. The weighted average maturity of these mortgages is 22 years. The weighted average interest rate charged on the loans is 6. 5%. If the mortgage pool requires a risk adjusted yield to maturity of 7. 4%, what is the value of the mortgage pool? Instead, assume the loans are completely prepaid at the end of year 15. Step 3 – NEW – Calculate the PV of the new cash flows. PMT = - 92, 682 FV = - 6, 241, 454 i = 0. 6167 % (. 074 / 12 ) n = 180 (15 x 12) solving for the PV PV = $ 12, 123, 449

MBS Valuation Example - Analysis Notice the MBS value increase from $ 12, 061, 114 to $ 12, 123, 449 when the prepayment assumption is added. Why? The MBS selling at a discount because the YTM was higher than the coupon. By getting the money sooner, the discount is reduced.

Secondary Mortgage Market example • • • $ 1 mil, 30 year 10% mortgage How is the value changed by prepayment assumptions Monthly payment is $8, 775. 72 Balance due: 6 yr=956, 597 12 yr=877, 708 18 yr=734, 321 MBS values YTM 10% yield 9 % yield 11% yield 6 yr prepay 1 mil 1, 045, 429 956, 960 12 yr prepay 1 mil 1, 070, 401 935, 947 18 yr prepay 1 mil 1, 083, 334 926, 279

Mortgage Strips REMIC - real estate mortgage investment conduits Variable maturity tranche Variable/Fixed rate tranche IO PO

Secondary Mortgage Market example (use previous MBS example data) 10% avg coupon - convert to 9% and 11% tranche REMICs (reality would dictate that the upper tranche be slightly below 11%, but we will round for simplicity sake) Each tranche will hold $500, 000 in principal Tranche 9% cpn 11%cpn Monthly REMIC Values 4023 4761 466, 683 533, 765 PMT 12 yr prepay 18 yr prepay 461, 247 539, 495

Secondary Mortgage Market • • • Stripped Mort backed Securities (SMBS) Principal Only (PO) Interest Only (IO) Pricing Risk

Prepayment % per Year Annual Prepayment Rates for Seasoned GNMA Base rate = 9 % 12% loan 10% loan 8% loan Change from Base interest rate

Value of Stripped Seasoned SMBS Base rate = 7 % Coupon = 5% Value Mortgage PO IO - 0 + Change from Base interest rate

Value of Stripped Seasoned SMBS Base rate = 7 % Coupon = 9% Value Mortgage PO IO - 0 + Change from Base interest rate

Secondary Mortgage Market Example • Second National Bank owns a large volume of LT fixed rate loans @ D =8 • They are financed with CDs @ D=3 • To hedge a rise in interest rates, 2 NB can buy IO SMBSs.

Secondary Mortgage Market SMBS vs CMO vs REMIC SMBS Uses 1 - predict interest rates 2 - Hedge prepayment 3 - Hedge Interest Rate Risk

Value at Risk (Va. R) Value at Risk = Va. R • • Newer term Attempts to measure risk Risk defined as potential loss Limited use to risk managers Factors • Asset value • Daily Volatility • Days • Confidence interval

Value at Risk (Va. R) Standard Measurements • 10 days • 99% confidence interval • Va. R

Value at Risk (Va. R) Example You own a $10 mil portfolio of IBM stock. IBM has a daily volatility of 2%. Calculate the Va. R over a 10 day time period at a 99% confidence level.

Value at Risk (Va. R) Example You also own $5 mil of AT&T, with a daily volatility of 1%. AT&T and IBM have a. 7 correlation coefficient. What is the Va. R of AT&T and the combined portfolio?