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# Mortgages and Mortgage-Backed Securities

After completing this reading, you should be able to:

• Describe the various types of residential mortgage products.
• Calculate 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 mortgage-backed securities (MBS), particularly the formation of mortgage pools, including specific pools and TBAs.
• Describe the process of trading of pass-through agency MBS.
• Explain the mechanics of different types of agency MBS products, including collateralized mortgage obligations (CMOs), interest-only securities (IOs), and principal-only securities (POs).
• Describe a dollar roll transaction and how to value a dollar roll.
• Understand what nonagency mortgage-backed securities are the mechanics of trading them.
• Explain prepayment modeling and its four components: refinancing, turnover, defaults, and curtailments.
• Describe the steps in valuing an MBS using Monte Carlo simulation.
• Define Option Adjusted 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 ’70s and ’80s, 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 mortgage-backed 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 pass-through structure.

### Lien Status

A first-lien mortgage is more desirable than a second-lien mortgage from the perspective of the lender. In the event of liquidation, a first-lien status would give the lender the right to submit the first claim on the proceeds of the liquidation process.

### Original Loan Term

Long-term mortgages have a maturity period of 30 years, with medium-term ones ranging between 10-20 years. In recent years, however, borrowers increasingly prefer medium-term loans to long-term ones. Most borrowers want to repay their mortgages as soon as possible.

### Credit Classification

Prime (A-grade) loans take the 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 loan-to-value ratios, typically far less than 95%. Borrowers are individuals with stable and sufficient income.

Sub-Prime (B-grade) loans have higher rates of default and delinquency compared to prime loans. They are associated with loan-to-value ratios of 95% or more. Borrowers may be individuals with lower income levels and marginal/poor credit histories.

Alternative A-loans lie in between prime and subprime loans. In essence, they are prime loans, but certain characteristics 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

Fixed-rate mortgages are associated with a fixed rate of interest up to maturity.

Adjustable-rate 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 fixed-rate 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 fixed-rate mortgages include:

• It consists of equal payments over the life of the mortgage.
• A loan is amortized over its term such that each scheduled payment goes toward the 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.

$$\text{Principal}=\text{PMT} \frac{1-(1+r)^{-n}}{r}$$

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: 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 What is the remaining principal at the end of each of the first 3 months? #### Solution r = 0.045/12 = 0.00375, n = 12 × 10 = 120 \begin{align*} \text{PMT} & = \frac{\text{Principal}} {\frac{1-(1+r)^{-n}}{r}}\\ \\ & = \frac{250,000} {\frac{1-(1+0.00375)^{-120}}{0.00375}} \\ \\ & = 2,590.96 \\ \end{align*} On a financial calculator, N = 120; I/Y = 0.375 (0.045/12); PV = -250,000; FV = 0; CPT => PMT = 2,590.96 We can now create an amortization schedule: ##### Month 1 Interest $$= 0.00375 × 250,000 = 937.50$$ Repayment of principle will therefore be $$2,590.96 – 937.50 = 1,653.46$$ The remaining principal at the beginning of the second month $$= 250,000 – 1,653.46 = 248,346.54$$ ##### Month 2 Interest $$= 0.00375 × 248,346.54 = 931.30$$ Repayment of principal will therefore be $$2,590.96 – 931.30 = 1,659.66$$ The remaining principal at the beginning of the third month $$= 248,346.54 – 1,659.66 = 246,686.88$$ ##### Month 3 Interest $$= 0.00375 × 246,686.88=925.08$$ Repayment of principal will therefore be $$2,590.96 – 925.08 = 1,665.88$$ The remaining principal at the beginning of the fourth month $$= 246,686.88 – 1,665.88 = 245,021$$ $$\small{\begin{array}{l|c|c|c|c} & \textbf{Month 1} & \textbf{Month 2} & \textbf{Month 3} & \\ \hline \textbf{Total Payment} & 2,590.96 & 2,590.96 & 2,590.96 & <<\text{ Equal}\\ \textbf{Principal} & 1,653.46 & 1,659.66 & 1,665.88 & \text{<< Increasing} \\ \textbf{Interest} & 937.50 & 931.30 & 925.08 & \text{<< Decreasing} \\ \textbf{Loan Balance} & 248,346.54 & 246,686.88 & 245,021.00 & \text{<< Decreasing}\\ \end{array}}$$ 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. #### Example: Calculating a Payment using the Remaining Cash Flows The outstanding principal can also be calculated by discounting the remaining cash flows using the following formula: $$\text{Outstanding principal} = \frac{\text{PMT}}{r} × (1-\frac{1}{(1+r)^{n}})$$ Assuming that the mortgage in the previous example has five years left, the outstanding principal (in USD) assuming that there have been no prepayments is: \begin{align*} & \frac{2,590.96}{0.00375} × (1-\frac{1}{(1+0.00375)^{5×12}}) \\ \\ & = 690,922.67×0.2011 \\ \\ & = 138,944.5483 \end{align*} ## Factors that Determine the Value of an MBS ### Weighted Average Maturity Weighted average maturity (WAM) is the weighted average amount of time until the maturities on mortgages in an MBS. To compute WAM, 1. 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 each mortgage percentage compared to the total value. 2. Multiply each percentage by the number of years to maturity. 3. Add together the subtotals. #### Example of Weighted Average Maturity A mortgage-backed 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.

$$\small{\begin{array}{l|c|c|c}\textbf{Mortgage}& \textbf{Current Value} & \textbf{ % Value of Mortgage } & \textbf{ % Value×Remaining}\\ &{}&\textbf{in Portfolio}&\textbf{Duration}\\ \hline\text{Mortgage1} & 100,000 & 100,000/200,000=50\% & 50\%×\text{5 years}= \text{2.5 years} \\ \text{Mortgage 2} & 10,000 & 10,000/200,000=5\% & 5\%×\text{2 years}= \text{0.1 years} \\ \text{Mortgage 3} & 50,000 & 50,000/200,000=25\% & 25\%×\text{6 years}= \text{1.5 years} \\ \text{Mortgage 4} & 40,000 & 40,000/200,000=20\% & 20×\text{3 years}= \text{0.6 years} \\ \text{Total} & 200,000 & & {\text{WAM}=2.5+0.1+1.5\\+0.6=\text{4.7 years}}\\ \end{array}}$$

How is WAM useful? It helps to determine the interest rate sensitivity of mortgage-backed 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 weighted-average interest rate of mortgages that underlie a mortgage-backed 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,

1. Compute the percentage value of each mortgage or debt instrument in the portfolio. 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 compared to the total value.
2. Multiply each percentage by the gross interest rate of the mortgage

#### Example of Weighted Average Coupon

A mortgage-backed 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:

### 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 8th and 20th months, assuming 100 PSA and 200 PSA.

#### 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.

## The Securitization Process

To reduce the risk of holding a potentially undiversified portfolio of mortgage loans, many 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 mortgage-backed securities to investors. MBSs are backed by the mortgage loans as collateral.

The simplest MBS structure, a mortgage pass-through, 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.

### Agency Mortgage-Backed Securities

Some agencies (government agencies and government-sponsored enterprises) purchase mortgages from banks and use the cash flows from those mortgages to create mortgage-backed securities that are then sold to investors. By doing so, the agencies enable banks to give out new loans and not keep the loans on their books. The agencies also ensure that banks do not run out of money to give out to potential new homeowners.

To protect their investors against default risk, such agencies charge a fee on their mortgages. The agencies do not, however, protect their investors from prepayment risk. An example of an agency Mortgage-backed security is pass-through security.

In a pass-through, all investors in the pool get the same return. The return is equivalent to the investor’s share of the cash flow in the pool minus the agency fee. Despite being risk-free investments, still, pass-throughs have prepayment risk.

Pass-through agency securities can be traded either as specified pools (traders agree to trade a specified pool at a specified price) or as to be announced (TBAs), which are traded in the forward markets.

#### Dollar Roll Transactions

A dollar roll transaction is a form of repurchase agreement in which an investor sells mortgage-backed 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 the 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 those securities holders.

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 pass-through securities.
• Holding period (the 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 forward-settling mortgage-backed securities trades. The term originates from the fact that the specific mortgage-backed 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, which increases the MBS market’s overall liquidity because thousands of different MBSs with different characteristics can be conveniently traded.

Renowned institutions like Freddie Mac, Fannie Mae, and Ginnie Mae issue mortgage pass-through securities that trade in the TBA market. For example, an investor who just purchased a 30-year 5% Freddie Mac (MBS) pool might sell the MBS 30-year 5% May TBA and buy the MBS 30-year 5% June TBA. In effect, the sale of the May TBA raises cash, while the purchase of the June TBA returns cash.

#### Example: 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 the outstanding balance, and the prevailing short-term 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 roll.

#### 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 ### Other Agency Products 1. Collateralized Mortgage Obligation: It involves creating tranches – classes of security that bear different amounts of prepayment risk. Assume that there are two tranches, A and B. Tranche A investors finance 60% of the principal while tranche B investors finance 40% of the principal. In this example, tranche B bears most of the prepayment risk. Each tranche will get interest on its outstanding principal; however, principal payments will only be paid to tranche B after paying tranche A investors. 2. Interest-Only Securities (IOs): Interest payments from mortgage securities will be directed to the interest-only securities. 3. Principal Only Securities (POs): Principal payments from mortgage securities will be directed to the principal-only securities. ### Non-Agency Mortgage-Backed Securities Non-agency mortgage-backed securities are issued by private corporations, like financial institutions, and are not guaranteed by government-sponsored institutions. Banks sell a mortgage portfolio to a special purpose vehicle (SPV). The SPV then creates securities and passes the cash-flows to the securities it has created. Investors in non-agency mortgage-backed security are not protected against the default risk. ## Modeling Prepayment Behavior Prepayment risk is the risk involved with the premature return of principal on a mortgage. 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; or • Repaying/refinancing the entire outstanding balance. The four reasons for prepayment are refinancing, turnover, defaults, and curtailment. ### Refinancing As the name suggests, refinancing occurs when the borrower of a loan wishes to refinance a property. Reasons for refinancing include: • A decrease in interest rates, since refinancing when the interest rates are low reduces the monthly payments of the borrower; • An increase in the value of the property qualifying the borrower for a higher loan; or • An improved credit rating of the borrower, enabling him/her to obtain a lower rate. The incentive function measures the extent of prepayment. The incentive function is equal to $$WAC-R$$, where $$WAC$$ is the weighted average coupon, and $$R$$ is the mortgage rate available to borrowers. Generally, the prepayment rate increases with a decrease in mortgage rates, and the older a mortgage pool is, the lesser the chances of refinancing. ### Turnover Turnover prepayments are made following the sale of a house. Housing turnover increases at certain periods during the year, e.g., over summer when the weather is favorable. The rate of turnover payments is usually dependent on the age of a mortgage holder and on his/her geographical location. 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. ### Defaults Defaults occur to agency MBSs. The agency will pay the outstanding loan amount of any defaulter of an agency MBS. This payment is treated as a prepayment. ### Curtailments Curtailments occur when a mortgage holder pays back part of the mortgage earlier. More often, curtailments occur when the mortgage is relatively old/ when the mortgage balance is relatively low. ## Monte Carlo Simulation in the Valuation of Mortgage-Backed 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 an 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 short-term 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. ## Option-Adjusted Spread When modeling the value of a mortgage-backed security, the option-adjusted 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 mortgage-backed securities. Mathematically, OLS is determined by the following relationship: $$\text{Market price}= \frac{\text{PV}[\text{path}(1)]+\text{PV}[\text{path}(2)]+…+\text{PV}[\text{path}(n)]}{n}$$ 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 Z-spread. The Z-spread 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 Z-spread and the OAS gives the option cost, which we can interpret as a measure of prepayment risk. Option cost = Zero-volatility 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 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 ## Practice Question A mortgage-backed 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: 1. 4.5% 2. 5.1% 3. 4.9% 4. 4.0% The correct answer is A. The weighted average coupon (WAC) is the weighted-average interest rate of mortgages that underlie a mortgage-backed 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%.

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