After completing this reading, you should be able to:
 Describe the various types of residential mortgage products.
 Calculate a fixed rate mortgage payment, and its principal and interest components.
 Describe the mortgage prepayment option and the factors that influence prepayments.
 Summarize the securitization process of mortgagebacked securities (MBS), particularly the formation of mortgage pools including specific pools and TBAs.
 Calculate weighted average coupon, weighted average maturity, and conditional prepayment rate (CPR) for a mortgage pool.
 Describe a dollar roll transaction and how to value a dollar roll.
 Explain prepayment modeling and its four components: refinancing, turnover, defaults, and curtailments.
 Describe the steps in valuing an MBS using Monte Carlo simulation.
 Define OptionAdjusted Spread (OAS), and explain its challenges and its uses.
Types of Residential Mortgage Products
A mortgage is a loan that has a specific piece of property as collateral. In the 70’s and 80’s, mortgages existed solely in the primary market where banks would issue mortgage products to customers who would, in turn, repay the principal plus interest. In modern times, however, mortgage lenders now repackage mortgages for sale in secondary markets as securitized investments.
In the secondary market, mortgages are pooled together and repackaged to form a mortgagebacked security. The principal and interest payments pass through the bank before the bank hands them over to the MBS investor. Such a mechanism is referred to as the passthrough structure.
Lien Status
A firstlien mortgage is more desirable than a secondlien mortgage from the perspective of the lender. In the event of liquidation, a firstlien status would give the lender the right to submit the first claim on the proceeds of the liquidation process.
Original Loan Term
Longterm mortgages have a maturity period of 30 years, with mediumterm ones ranging between 1020 years. In recent years, however, borrowers increasingly prefer mediumterm loans to longterm ones. Most borrowers want to repay their mortgages as soon as possible.
Credit Classification
Prime (Agrade) loans take top spot as the most desirable loans from the lender’s perspective. They are associated with low rates of delinquency and default thanks to low loantovalue ratios, typically far less than 95%. Borrowers are individuals with stable and sufficient income.
Subprime (Bgrade) loans have higher rates of default and delinquency compared to prime loans. They are associated with loantovalue ratios of 95% or more. Borrowers may be individuals with lower income levels and marginal/poor credit histories.
Alternative Aloans lie in between prime and subprime loans. In essence, they are prime loans, but there are certain characteristics that make them riskier than prime loans. For instance, there may be less documentation available to support income levels, however impressive the actual figures might be.
Interest Rate Type
Fixedrate mortgages are associated with a fixed rate of interest up to maturity.
Adjustablerate mortgages are associated with a floating rate of interest. For example, the rate could be LIBOR + 100 bps. In such an arrangement, the rate would change every six months.
Fixed Rate Mortgages: Principal and Interest Payments
A fixedrate mortgage is a mortgage loan that has a fixed interest rate for the entire term of the loan. It is based on the creditworthiness of the borrower and uses residential real estate as collateral. The level of interest depends in part on the creditworthiness of the borrower whereby the riskier the borrower, the higher the interest rate.
Other notable characteristics of fixedrate mortgages include:
 Consists of equal payments over the life of the mortgage
 Loan is amortized over its term such that each scheduled payment goes toward settlement of both principal and interest
 As the loan matures, the amortization schedule works in such a way that the borrower pays more principal and less interest with each payment
Calculating the amount of each payment
To determine the amount of each scheduled payment, PMT, we customize the formula for the present value of an annuity.
$$ Principal=PMT \frac{1(1+r)^{n}}{r} $$
Where:
r = monthly interest rate (annual rate/12)
n = total number of months
Making PMT subject of the formula,
$$ PMT=\frac{Principal} {\frac{1(1+r)^{n}}{r}} $$
Example of calculating a payment
 Consider the following loan:
 Loan amount: $250,000
 Annual rate of interest: 4.5
 Term: 10 years
 Start date: 01/01/2019
r = 0.045/12 = 0.00375, n = 12 * 10 = 120
$$ PMT=\frac{Principal} {\frac{1(1+r)^{n}}{r}} $$
$$ PMT=\frac{250,000} {\frac{1(1+0.00375)^{120}}{0.00375}} $$
On a financial calculator,
N = 360; I/Y = 0.00375 (0.045/12); PV = 250,000; FV = 0; CPT » PMT = 2,590.96
We can now create an amortization schedule:
Month 
Month 1 
Month 2 
Month 3 

Total payment 
$2,590.96 
$2,590.96 
$2,590.96 
<< Equal 
Principal 
$1,653.46 
$1,663.18 
$1,672.89 
<< Increasing 
Interest 
$937.50 
$927.78 
$918.07 
<< Decreasing 
Loan balance 
$248,346.54 
$246,693.08 
$245,039.62 
<< Decreasing 
Note 1: Interest payable is based on the amount of loan outstanding. Therefore, we will always see an increase in the principal paid on each payment.
Note 2: The loan balance only decreases by the principal amount on each payment since the interest payable portion of the payment is paid to the financial institution issuing the loan.
Prepayment Risk
Prepayment risk is the risk involved with the premature return of principal on a mortgage. A prepayment effectively renders the borrower free of mortgage obligations. A mortgage prepayment option works much like a call option for the borrower.
Mortgage prepayments take one of two forms:
 Increasing the amount/frequency of payments
 Repaying/refinancing the entire outstanding balance.
Prepayments are more likely to occur following a drop in interest rates. In such circumstances, the borrower may decide to refinance their existing mortgages at the lower rates.
Some of the other factors that influence prepayment include:
 Seasonality: Housing turnover increases at certain periods during the year, e.g., over summer when the weather is favorable
 Age of mortgage pool: Borrowers prefer to refinance a significant number of years into the mortgage to minimize penalties and administrative charges that are usually tied to principal outstanding
 Housing prices: An increase in home prices may spur prepayments as borrowers scramble to take out some of the increased equity for personal use
 Refinancing burnout: Prepayment risk decreases following a sustained period of refinancing activity
The Securitization Process
To reduce the risk from holding a potentially undiversified portfolio of mortgage loans, a number of originators (financial institutions) work together to pool residential mortgage loans. The loans pooled together have similar characteristics. The pool is then sold to a separate entity, called a special purpose vehicle (SPV), in exchange for cash. An issuer will purchase those mortgage assets in the SPV and then use the SPV to issue mortgagebacked securities to investors. MBSs are backed by the mortgage loans as collateral.
The simplest MBS structure, a mortgage passthrough, involves cash (interest, principal, and prepayments) ﬂowing from borrowers to investors with some short processing delay. Usually, the issuer of MBSs may enlist the services of a mortgage servicer whose main mandate is to manage the flow of cash from borrowers to investors in exchange for a fee. MBSs may also feature mortgage guarantors who charge a fee and in return guarantee investors the payment of interest and principal against borrower default.
Factors that Determine the Value of a MBS
Weighted Average Maturity
Weighted average maturity (WAM) is the weighted average amount of time until the maturities on mortgages in a MBS. To compute WAM,
 Compute the percentage value of each mortgage or debt instrument in the portfolio. This is achieved by adding the current principal value of all the mortgages together and then calculating the percentage of each mortgage in comparison to the total value.
 Multiply each percentage by the number of years to maturity
 Add together the subtotals
Example of Weighted Average Maturity
A mortgagebacked portfolio includes four mortgage investments as follows:
Mortgage 1: $100,000 in current value, maturity in 5 years
Mortgage 2: $10,000 in current value, maturity in 2 years
Mortgage 3: $50,000 in current value, maturity in 6 years
Mortgage 4: $40,000 in current value, maturity in 3 years
Determine the WAM of the portfolio:
Solution
Total value of portfolio = $100,000 + $10,000 + $50,000 + $40,000 = $200,000
We then compute the percentage value of each mortgage:
Mortgage 1: %value = $100,000/$200,000 = 50%
Mortgage 2: %value = $10,000/$200,000 = 5%
Mortgage 3: %value = $50,000/$200,000 = 25%
Mortgage 4: %value = $40,000/$200,000 = 20%
The percentage values of each mortgage are then multiplied by the remaining duration until maturity:
 50% * 5 years = 2.5 years
 5% * 2 years = 0.1 years
 25% * 6 years = 1.5 years
 20% * 3 years = 0.6 years
The resulting figures are then totaled to produce a WAM of 4.7 years.
Mortgage 
Current Value 
% value of mortage in portfolio 
% value × Remaining duration 
Mortgage 1 
$100,000 
$100,000/$200,000 = 50% 
50% * 5 years = 2.5 years 
Mortgage 2 
$10,000 
$10,000/$200,000 = 5% 
5% * 2 years = 0.1 years 
Mortgage 3 
$50,000 
$50,000/$200,000 = 25% 
25% * 6 years = 1.5 years 
Mortgage 4 
$40,000 
$40,000/$200,000 = 20% 
20% * 3 years = 0.6 years 
Total 
$200,000 
WAM = 2.5 + 0.1 + 1.5 + 0.6 = 4.7 years 
How is WAM useful? It helps to determine the interest rate sensitivity of mortgagebacked portfolios. The larger the WAM, the longer the period of exposure to interest rate movements, and the greater the chances of a material effect on portfolio value relative to other investment alternatives.
Weighted Average Coupon
The weighted average coupon (WAC) is the weightedaverage interest rate of mortgages that underlie a mortgagebacked security (MBS) at the time the securities were issued. It represents the average interest rate of a pool of mortgages with varying interest rates.
To compute WAC,
 Compute the percentage value of each mortgage or debt instrument in the portfolio Just like under WAM, this is done by adding the current principal value of all the mortgages together and then calculating the percentage of each mortgage in comparison to the total value.
 Multiply each percentage by the gross interest rate of the mortgage
 Add together the subtotals
Example of Weighted Average Coupon
A mortgagebacked portfolio includes four mortgage investments as follows:
Mortgage 1: $100,000 in current value, 5% interest rate
Mortgage 2: $10,000 in current value, 4% interest rate
Mortgage 3: $50,000 in current value, 6% interest rate
Mortgage 4: $40,000 in current value, 3% interest rate
Determine the WAC of the portfolio:
Solution
Total value of portfolio = $100,000 + $10,000 + $50,000 + $40,000 = $200,000
We then compute the percentage value of each mortgage:
Mortgage 1: %value = $100,000/$200,000 = 50%
Mortgage 2: %value = $10,000/$200,000 = 5%
Mortgage 3: %value = $50,000/$200,000 = 25%
Mortgage 4: %value = $40,000/$200,000 = 20%
The percentage values of each mortgage are then multiplied by their respective interest rates:
 50% * 5% = 2.5%
 5% * 4% = 0.2%
 25% * 6% = 1.5%
 20% * 3% = 0.6%
The resulting figures are then totaled to produce a WAC of 4.8%.
Modeling the Prepayment Rate
Prepayment is undoubtedly one of the key issues an investor in MBSs would want to keep an eye on. Prepayments speed up principal repayments and also reduce the amount of interest paid over the life of the mortgage. Thus, they can adversely affect the amount and timing of cash flows.
Markets have adopted two main benchmarks that are used to track prepayment risk – the conditional prepayment rate (CPR) and the Public Securities Association (PSA) prepayment benchmark.
Conditional Prepayment Rate (CPR)
The CPR is a proportion of a loan pool’s principal that is assumed to be paid off ahead of time in each period. It measures prepayments as a percentage of the current outstanding loan balance. It is always expressed as a percentage, compounded annually. For example, a 5% CPR means that 5% of the pool’s outstanding loan balance pool is likely to prepay over the next year. It is estimated based on historical prepayment rates for past loans with similar characteristics as well as future economic prospects.
The CPR can be converted to a single monthly mortality rate (SMM) as follows:
$$ SMM=1(1CPR)^{1/12}$$
SMM is in effect the amount of principal on mortgagebacked securities that is prepaid in a given month.
Note: This also implies that:
$$ CPR=1(1SMM)^{12}$$
Prepayment for month i (in $) = SMM(beginning balance – scheduled principal repayment in month i)
Public Securities Association (PSA) Prepayment Benchmark
The Public Securities Association model prepayment benchmark is one of the models used to estimate the monthly rate of prepayment. It is based on the assumption that rather than remaining constant, the monthly repayment rate gradually increases as a mortgage pool ages. The PSA is expressed as a monthly series of CPRs. The model assumes that:
 CPR = 0.2% for the first month after origination, increasing by 0.2% every month up to 30 months
 CPR = 6% for months 30 to 360
A mortgage pool whose prepayment speed (experience) is in line with the assumptions of the PSA model is said to be 100% PSA. Similarly, a pool whose prepayment experience is two times the CPR under the PSA model is said to be 200% PSA (or 200 PSA).
Example of (PSA) Prepayment Benchmark
Compute the CPR and SMM for the 8^{th} and 20^{th} months, assuming 100 PSA and 200 PSA.
Solution
Case 1: Assuming 100 PSA
CPR(month 8) = 8 x 0.2% = 1.6%
100 PSA implies that CPR (month 8) = 1 x 1.6% = 1.6%
SMM = 1 – (1 – CPR)^{1/12} = 1 – (1 – 0.016)^{1/12} = 0.1343%
CPR(month 20) = 20 x 0.2% = 4%
100 PSA implies that CPR (month 20) = 1 x 4% = 4%
SMM = 1 – (1 – CPR)^{1/12} = 1 – (1 – 0.04)^{1/12} = 0.3396%
Case 2: Assuming 200 PSA
CPR(month 8) = 8 x 0.2% = 1.6%
200 PSA implies that CPR (month 8) = 2 x 1.6% = 3.2%
SMM = 1 – (1 – CPR)^{1/12} = 1 – (1 – 0.032)^{1/12} = 0.2706%
CPR(month 20) = 20 x 0.2% = 4%
200 PSA implies that CPR (month 20) = 2 x 4% = 8%
SMM = 1 – (1 – CPR)^{1/12} = 1 – (1 – 0.08)^{1/12} = 0.6924%
Important: CPR and SMM have a nonlinear relationship. The implication is that the SMM for 200% PSA does not equal two times the SMM for 100% PSA.
Dollar Roll Transaction
A dollar roll transaction is a form of repurchase agreement in which an investor sells a mortgagebacked security during one period, called the “front month,” and repurchases it in a subsequent period, called the later or “back month.” In so doing, the investor relinquishes their access to the principal and interest on the loan that is sold. However, the investor receives cash from the sale which could be reinvested and used to purchase the security later. The aim of the investor is to capitalize on a drop in price of the MBS by “selling high and buying low.” The trade counterparty benefits in that they do not have to deliver the MBS in the current month and thus get to keep the principal and interest payments that would otherwise be passed through to the holder of those securities.
A dollar roll works much like selling stocks short.
The price difference between the front month and the back month is known as the drop. When the drop is significant, the dollar roll is said to be “on special.” The size of the drop is influenced by:
 Demand for mortgage passthrough securities
 Holding period (period between the two settlement dates)
 Funding cost in the repo market
 The volume of mortgage closings in a mortgage originator’s pipeline.
Dollar rolls work in TBA (To be announced) MBS markets. To be announced is a term that describes forwardsettling mortgagebacked securities trades. The term originates from the fact that the specific mortgagebacked security to be delivered to fulfill a TBA trade is not designated at the time the trade is initiated. Rather, trade parties are required to exchange mortgage pool information 48 hours prior to trade settlement. The TBA market treats MBS pools as relatively interchangeable, a move that increases the overall liquidity of the MBS market because thousands of different MBSs with different characteristics can be conveniently traded.
Renowned institutions like Freddie Mac, Fannie Mae, and Ginnie Mae issue mortgage passthrough securities that trade in the TBA market. For example, an investor who just purchased a 30year 5% Freddie Mac (FRM) pool might sell the FRM 30year 5% May TBA and buy the FRM 30year 5% June TBA. In effect, the sale of the May TBA raises cash, while the purchase of the June TBA returns cash.
Example of a dollar roll transaction
TBA prices of the Ginnie Mae 3% for January 12 and February 12 settlements are $102.30 and $102.10, respectively. The accrued interest to be added to each of these prices is $0.125. The expected total principal paydown (scheduled principal plus prepayments) is 2% of outstanding balance and the prevailing shortterm rate is 1%. Also, assume that the actual/360 day convention is applied.
An investor wishes to roll a balance of $10 million. Determine the value of the role.
Solution
Proceeds from selling the January 12 TBA are: $10m × (102.30 + 0.125)/100 = $10,242,500
Investing these proceeds to February 12 at 1% interest earns interest of: $10,242,500 × 31/360 × 1% = $8,820
Purchasing the February TBA, which has experienced a 2% paydown, will cost: $10m × (1 – 2%) × (102.10 + 0.125)/100 = $10,018,050
Net proceeds from the roll therefore are: $10,242,500 + $8,820 – $10,018,050 = $233,270
If the investor does not roll, the net proceeds are the coupon plus principal paydown: $10m × (3%/12 + 2%) = $225,000
Value of the roll = net proceeds from the roll – net proceeds without roll: = $233,270 – $225,000 = $8,270
Monte Carlo simulation in the valuation of mortgagebacked securities
A popular method for valuing MBSs is called the Monte Carlo Methodology. The simulation creates thousands of interest paths that the MBS could follow over its life. The process recognizes the fact that there is a probability distribution of the possible outcomes of a MBS. Taking into account multiple interest rate paths is important because interest rates impact repayments and will therefore impact the amount and timing of cash flows to the investor.
There are four steps required to value a mortgage security using the Monte Carlo methodology:
Step 1: Simulate shortterm interest rate and refinancing rate paths;
Step 2: Project the cash flow on each interest rate path;
Step 3: Determine the present value of the cash flows on each interest rate path;
Step 4: Compute the theoretical value of the mortgage security.
OptionAdjusted Spread
When modeling the value of a mortgagebacked security, the optionadjusted spread (OAS) is the spread that, when added to all the spot rates of all the interest rate paths will make the average present value of the paths equal to the actual observed market price plus accrued interest. In other words, we purpose to find a single spread such that shifting the paths of short term rates by that spread results in a model value equal to the market price. OAS is the most popular measure of relative value for mortgagebacked securities.
Mathematically, OLS is determined by the following relationship:
$$ Market price= \frac{PV[path(1)]+PV[path(2)]+…+PV[path(n)]}{n} $$
Where N = number of interest rate paths
While the LHS of the equation above gives the current market price of the MBS, the RHS of the equation is the Monte Carlo model’s output of the average theoretical value of the MBS. The OAS is determined iteratively, that is, if the average theoretical value determined by the model is higher (lower) than the MBS market value, the spread is increased (decreased).
We can view the OAS as a measure of MBS returns that takes into account two types of volatility: changing interest rates and prepayment risk.
The OAS should not be confused with a Zspread. The Zspread is the yield that equates the present value of the cash flows from the MBS to the price of the MBS discounted at the Treasury spot rate plus the spread. However, it does not include the value of the embedded options (prepayments), which can have a big impact on the present value.
The difference between the Zspread and the OAS gives the option cost, which we can interpret as a measure of prepayment risk.
Option cost = Zerovolatility spread – OAS
OAS is a byproduct of Monte Carlo simulation, not the traditional value approaches used to value options. This makes it have several limitations:
 It is dependent on some type of a prepayment model, e.g., the PSA model. As established earlier, most of these models are based on historical data which may not always reconcile with actual future results.
 It is subject to all modeling risks associated with simulation
 The process of adjusting interest rate paths is subject to modeling error.
 OAS assumes that the investor holds the securities to maturity while in reality, most investors hold securities for a finite period
Question
A mortgagebacked portfolio includes four mortgage investments as follows:
 Mortgage 1: $140,000 in current value, 5% interest rate, 5 years remaining duration
 Mortgage 2: $100,000 in current value, 4% interest rate, 6 years remaining duration
 Mortgage 3: $50,000 in current value, 6% interest rate, 3 years remaining duration
 Mortgage 4: $60,000 in current value, 3% interest rate, 2 years remaining duration
The weighted average coupon of the portfolio is closest to:
 4.5%
 5.1%
 4.9%
 4.0%
The correct answer is A.
The weighted average coupon (WAC) is the weightedaverage interest rate of mortgages that underlie a mortgagebacked security (MBS) at the time the securities were issued. It represents the average interest rate of a pool of mortgages with varying interest rates.
Total value of portfolio = $140,000 + $100,000 + $50,000 + $60,000 = $350,000
We then compute the percentage value of each mortgage:
 Mortgage 1: %value = $140,000/$350,000 = 40%
 Mortgage 2: %value = $100,000/$350,000 = 28.6%
 Mortgage 3: %value = $50,000/$350,000 = 14.3%
 Mortgage 4: %value = $60,000/$350,000 = 17.1%
The percentage values of each mortgage are then multiplied by their respective interest rates:
 40% * 5% = 2%
 6% * 4% = 1.1%
 3% * 6% = 0.9%
 1% * 3% = 0.5%
The resulting figures are then totaled to produce a WAC of approx. 4.5%.