# Residential Mortgage-backed Securities

Residential Mortgage-backed Securities (RMBS) are securities derived from the pooling of mortgages and their subsequent sale to investors. The section discusses the different types of RMBS, including mortgage pass-through securities, non-agency RMBS, and collateralized mortgage obligations.

## Mortgage Pass-through Securities

Mortgage Pass-Through Securities result from lenders combining multiple mortgages and selling these as securities to investors. The arising monthly payments of principal, interest, and prepayments from the mortgage pool are passed to the investors.

### Features of Mortgage Pass-through Securities

1. Cash Flows: These depend on monthly flows from the underlying mortgage pool. They cover both amounts passed to holders and administrative fees for servicing the pool.
2. Administrative Charges: These arise from tasks such as collecting payments from borrowers, maintaining mortgage records, and initiating foreclosure if necessary. These charges and any guarantee fees from the issuer are a fraction of the mortgage rate.
3. Pass-Through Rate: It is the coupon rate of the mortgage pass-through security. It is lower than the weighted average mortgage rate due to administrative costs.
4. Heterogeneous Nature: Mortgages in the pool differ in outstanding principal, interest rates, and maturities. The formula below calculates the weighted coupon rate (WAC) and the weighted average maturity (WAM) for each security.

WAM represents the average time until the mortgages in a pool are expected to be repaid, while WAC indicates the weighted average interest rate of the mortgages in the pool.

$\text{WAC} = \sum_{}^{}\left( \frac{\text{Current balance of each mortgage}}{\text{Total current balance}\text{ of all mortgages}} \times \text{Interest rate of each mortgage} \right)$

$\begin{matrix} & \\ & WAM = \sum_{}^{}\left( \frac{\text{Current balance of each mortgage}}{\text{Total current balance}\text{ of all mortgages}} \times \text{Number of Months to Maturity of each mortgage} \right) \end{matrix}$

The pass-through rate is the interest rate received by the RMBS investors. This is less than the WAC due to administrative charges.

$Pass – Through\ Rate = WAC – Administrative\ Charges$

#### Example: Calculating WAC and WAM

Given the information in the table below, calculate the weighted average coupon rate (WAC) and the weighted average maturity (WAM).

$$\begin{array}{l|c|c|c|c|c} \textbf{Mortgage} & \textbf{Interest} & \textbf{Beginning} & \textbf{Current} & \textbf{Original Term} & \textbf{Number of Months} \\ & \textbf{rate} & \textbf{Balance (EUR)} & \textbf{Balance (EUR)} & \textbf{(months)} & \textbf{to Maturity} \\ \hline A & 2.8\% & 450,000 & 408,000 & 360 & 288 \\ \hline B & 3.5\% & 370,000 & 340,000 & 600 & 516 \\ \hline C & 3.0\% & 210,000 & 185,000 & 288 & 216 \\ \hline D & 4.1\% & 500,000 & 240,000 & 480 & 192 \\ \hline E & 3.4\% & 270,000 & 252,000 & 384 & 288 \\ \hline & & \textbf{1,800,000} & \textbf{1,425,000} & & \\ \end{array}$$

### Solution

Weighted Average Coupon Rate (WAC):

${WAC}_{A} = \left( \frac{408,000}{1,425,000} \times 2.8\% \right) = 0.8017\%$

${WAC}_{B} = \left( \frac{340,000}{1,425,000} \times 3.5\% \right) = 0.8351\%$

${WAC}_{C} = \left( \frac{185,000}{1,425,000} \times 3.0\% \right) = 0.3895\%$

${WAC}_{D} = \left( \frac{240,000}{1,425,000} \times 4.1\% \right) = 0.6905\%$

${WAC}_{E} = \left( \frac{252,000}{1,425,000} \times 3.4\% \right) = 0.6013\%$

$Total\ WAC = 0.8017\%\ + \ 0.8351\% + \ 0.3895\%\ + \ 0.6905\%\ + \ 0.6013\% = 3.3180\%$

Weighted Average Maturity (WAM):

${WAM}_{A} = \left( \frac{408,000}{1,425,000} \times 288 \right) = 82.46\$

${WAM}_{B} = \left( \frac{340,000}{1,425,000} \times 516 \right) = 123.12\$

${WAM}_{C} = \left( \frac{185,000}{1,425,000} \times 216 \right) = 28.04\$

${WAM}_{D} = \left( \frac{240,000}{1,425,000} \times 192 \right) = 32.34$

${WAM}_{E} = \left( \frac{252,000}{1,425,000} \times 288\ \right) = 50.93$

$Total\ WAM = 82.46 + 123.12 + 28.04 + 32.34 + 50.93 = 316.88\ months$

The WAC is 3.318%, and the WAM is approximately 317 months.

### Risks Associated with Mortgage Pass-Through Securities

1. Prepayment Risk: Homeowners may choose to refinance or sell, leading to an earlier-than-expected mortgage payoff, especially in a declining interest rate environment. This can alter the anticipated cash inflows for investors.
2. Extension Risk: In a scenario of rising interest rates, homeowners may postpone refinancing, which can extend the timing of expected cash inflows.
3. Administrative Risk: Costs related to administrative tasks, such as payment collections or initiating legal actions for defaults, can influence the net earnings of investors.

## Collateralized Mortgage Obligations (CMOs)

CMOs transform mortgage pass-through securities or various loan pools into securitized forms. They are structured with multiple classes or tranches, each having different priority levels for the receipt of principal and interest payments. Principal and interest payments are directed to the tranches and then released to investors. The tranching structure enables prepayment risk to be allocated across the different tranches. This reduces the uncertainty on the amount and timing of payments received by investors. The higher the tranche level, the lower its exposure to prepayment and default risks.

### Collateralized Mortgage Obligations Structures

The structures result from the various methods of organizing cash flows from a mortgage pool.

1. Sequential-Pay CMO Structure: In this structure, each tranche is settled in order, where one class gets principal payments only after the prior class is fully settled.
2. Z-Tranches: Also known as accrual or accretion bonds. These tranches do not disburse interest until a pre-set date. They accrue interest during an initial period and then start distributing interest and principal payments only after other specified tranches (often referred to as support or companion tranches) have been paid off. They are usually the final tranche in a sequence, making them riskier and more challenging to value.
3. Principal-Only (PO) Securities: Investors receive only principal repayments from the mortgage pool for these securities. This makes their value sensitive to prepayment and interest rates.
4. Interest-Only (IO) Securities: These securities disburse only interest payments from the pool and have no par value. The cash flows to the holders of this security are reduced with increased prepayments.
5. Floating-Rate Tranches: These tranches bear variable interest rates tied to an index. They can be structured as inverse floaters, where the interest paid varies inversely with interest rate changes.
6. Residual Tranches: These tranches collect any leftover cash flow after settling other tranches.
7. Planned Amortization Class (PAC) Tranches: They are an evolution of sequential-pay CMOs and provide greater cash flow predictability. They ensure fixed principal payments over a set period if prepayment rates remain within specified bounds.

### Risks Associated with CMOs

1. Prepayment Risk: CMOs distribute the prepayment risk across tranches. While they do not eradicate this risk entirely, they can vary its impact across different tranches.
2. Default Risk: The seniority of a tranche in a CMO structure determines its exposure to default risk. More senior tranches have reduced exposure.
3. Interest Rate Risk: Depending on the structure, some tranches might be more susceptible to changes in interest rates, affecting their returns.

### Question

Which of the following is the most accurate definition of a collateralized mortgage obligation (CMO)?

1. A security that pools together multiple mortgages and is structured to direct interest and principal payments to different classes of bondholders.
2. A debt security issued by banks, backed only by the general creditworthiness of the issuing bank.
3. A mortgage-backed security solely based on commercial real estate loans.

A collateralized mortgage obligation (CMO) is a type of mortgage-backed security that pools multiple mortgages and directs bondholders’ interest and principal payments to different classes (or tranches) in a predefined order.

B is incorrect: This describes a bank’s unsecured debt, not a CMO.

C is incorrect: While mortgage-backed securities are based on commercial real estate loans, this does not accurately describe a CMO’s specific structure and nature.

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