Mortgages and Mortgage-Backed Securities

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 mortgage-backed 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 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 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 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 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 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

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:

• 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 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. 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, 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 the percentage of each mortgage in comparison 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.

 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 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 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. 2. Multiply each percentage by the gross interest rate of the mortgage 3. Add together the subtotals 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: 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:

$$SMM=1-(1-CPR)^{1/12}$$

SMM is in effect the amount of principal on mortgage-backed securities that is prepaid in a given month.

Note: This also implies that:

$$CPR=1-(1-SMM)^{12}$$

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 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 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.

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:

$$Market price= \frac{PV[path(1)]+PV[path(2)]+…+PV[path(n)]}{n}$$

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 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 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 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%

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%