Lecture 11

History of banks and spread Federal National Mortgage Association (FNMA) ◦ Fannie Mae ◦ C hartered 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

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)

Cash Flow Pattern for Bonds Bonds 12 10 8 6 4 2 0 1 2 3 4 5 6 Years 7 8 9 10 Interest Principal

Cash Flow Pattern for MORTGAGES Reflecting PREPAYMENT Mortgages 12 10 8 6 4 2 0 Interest Principal 1 2 3 4 5 6 Years 7 8 9 10

 Prepayment Analysis Benchmarks     Maturity Half Life Avg. Life Duration

1 Half Life = 6.5yrs

Avg. Life=8.2 yrs Years 30

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

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 30mt PSA 102 = quicker prepay PSA 96 = slower prepay

10 SMM=0% SMM=2% SMM=0.3% 0 2 5 8 11 14 17 Years 20 23 26 29

 MBS Valuation MBA Value = PV of cash flows Steps 1.

2.

3.

Determine the monthly payment Use prepayment assumption to derive maturity Calculate the PV of the monthly payment at the YTM.

 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

Example A mortgage pool contains $13,000,000 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?

Example A mortgage pool contains $13,000,000 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 = $ 13,000,000 FV = 0 n = 264 (22 x 12) i = 0.54 % ( .065 / 12 )

solving for the PMT PMT = - 92,682

Example A mortgage pool contains $13,000,000 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 = $ 12,061,114

Example A mortgage pool contains $13,000,000 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.

Example A mortgage pool contains $13,000,000 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

Example A mortgage pool contains $13,000,000 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 = 13,000,000 i = 0.54 % ( .065 / 12 ) n = 180 (15 x 12)

solving for the FV FV = - 6,241,454

Example A mortgage pool contains $13,000,000 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

Example - Analysis

Notice the MBS value drops 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.

example • • $ 1mil, 30year 10% mortgage How is the value changed by prepayment assumptions • • • Monthly payment is $8,775.72

Balance due: 6yr=956,597 12yr=877,708 18yr=734,321 MBS values YTM 10% yield 9 % yield 11% yield 6 yr prepay 1 mil 1,045,429 956,960 12yr prepay 1 mil 1,070,401 935,947 18yr prepay 1 mil 1,083,334 926,279

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

example REMICs (use previous MBS example data) 10% avg coupon - convert to 9% and 11% tranche (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 PMT 4023 4761 REMIC Values 12 yr prepay 466,682 533,768 18yr prepay 461,236 539,433

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

12% loan Base rate = 9 % 10% loan 8% loan

Change from Base interest rate

Mortgage Base rate = 7 % Coupon = 5% IO PO 0 +

Change from Base interest rate

Mortgage Base rate = 7 % Coupon = 9% PO IO 0 +

Change from Base interest rate

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, 2NB can buy IO SMBSs.

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

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

Standard Measurements • 10 days  10  

day

 10 • 99% confidence interval 99 %    2 .

33 • VaR

VaR



(

 10 

2 .

33 )

 

asset valu e



Example You own a $10 mil portfolio of IBM stock. IBM has a daily volatility of 2%. Calculate the VaR over a 10 day time period at a 99% confidence level.

 10  .

02   6 .

32 % 10 99 %(  )  .

0632  2 .

33  14 .

74 %

VaR



.

1473



10 , 000 , 000



$ 1 , 473 , 621

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 VaR of AT&T and the combined portfolio?

VaR

IBM

VaR

AT

&

T

 $ 1 , 473 , 621  $ 368 , 405

VaR AT

&

T



IBM

 $ 1 , 842 , 026

VaR Portfolio

 $ 1 , 751 , 379

Diversific ation

Benefit

 $ 90 , 647