Financial Engineering - PowerPoint Presentation

Slide1

Financial Engineering

Lecture 11Slide2

Mortgage Backed Securities

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 loansSlide3

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)Slide4

Mortgage Backed Securities

Cash Flow Pattern for

BondsSlide5

Mortgage Backed Securities

Cash Flow Pattern for

MORTGAGES

Reflecting PREPAYMENTSlide6

Prepayment Analysis Benchmarks

Maturity

Half Life

Avg. Life

Duration

Secondary Mortgage MarketSlide7

Secondary Mortgage MarketSlide8

Prepayment Factors

Seasoning **

Refinancing **

Economic Activity

Trading up

Default

Disaster

Legal structure

Geographical region

Season of year

Secondary Mortgage MarketSlide9

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

Secondary Mortgage MarketSlide10

Secondary Mortgage MarketSlide11

Mortgage Backed Securities

MBS Valuation

MBS Value = PV of cash flows

Steps

Determine the monthly payment

Use prepayment assumption to derive maturity

Calculate the PV of the monthly payment at the YTM.Slide12

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 prepaymentSlide13

MBS Valuation

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?Slide14

MBS Valuation

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 = - 92,682Slide15

MBS Valuation

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 = $ 12,064,114Slide16

MBS Valuation

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. Slide17

MBS Valuation

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 = 92,682Slide18

MBS Valuation

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 i = 0.54 % ( .065 / 12 )

PV = 13,000,000

n = 180 (15 x 12)solving for the FVFV = - 6,241,454Slide19

MBS Valuation

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

i = 0.6167 % ( .074 / 12 )

FV = - 6,241,454 n = 180 (15 x 12)solving for the PVPV = $ 12,123,449Slide20

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. Slide21

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

6 yr prepay 12yr prepay 18yr prepay

10% yield 1 mil 1 mil 1 mil9 % yield 1,045,429 1,070,401 1,083,33411% yield 956,960 935,947 926,279

Secondary Mortgage MarketSlide22

Mortgage Strips

REMIC - real estate mortgage investment conduits

Variable maturity tranche

Variable/Fixed rate tranche

IO

POSlide23

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

Monthly REMIC Values

Tranche PMT 12 yr prepay 18yr prepay

9% cpn 4023 466,683 461,24711%cpn 4761 533,765 539,495Secondary Mortgage MarketSlide24

Stripped Mort backed Securities (SMBS)

Principal Only (PO)

Interest Only (IO)

Pricing

Risk

Secondary Mortgage MarketSlide25

Annual Prepayment Rates for Seasoned GNMA

Prepayment % per Year

Change from Base interest rate

12% loan

10% loan

8% loan

Base rate = 9 %Slide26

Value of Stripped Seasoned SMBS

Value

Change from Base interest rate

- 0 +

Mortgage

IO

PO

Base rate = 7 %

Coupon = 5%Slide27

Value of Stripped Seasoned SMBS

Value

Change from Base interest rate

- 0 +

Mortgage

IO

PO

Base rate = 7 %

Coupon = 9%Slide28

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.

Secondary Mortgage MarketSlide29

SMBS

vs

CMO

vs

REMIC

SMBS Uses

1 - predict interest rates

2 - Hedge prepayment

3 - Hedge Interest Rate Risk

Secondary Mortgage MarketSlide30

Value at Risk (VaR)

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 intervalSlide31

Value at Risk (

VaR

)

Standard Measurements

10 days

99% confidence interval

VaRSlide32

Value at Risk (VaR)

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.Slide33

Value at Risk (VaR)

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?