Introduction

In this chapter, we delve into the critical analysis of mortgage pools, which are at the core of the mortgage-backed securities (MBS) market. As investors and financial professionals, understanding the metrics that characterize mortgage pools is crucial for making informed decisions. We will explore key measures like the weighted average coupon, weighted average maturity, single monthly mortality rate (SMM), and conditional prepayment rate (CPR) that offer insights into the performance and risk profiles of these securities.

Weighted Average Coupon (WAC)

The weighted average coupon is a vital indicator of the interest rate level of the loans within a mortgage pool. It is calculated as the weighted average of the interest rates of the individual loans in the pool, where the weights are based on the outstanding loan balances. The formula for calculating WAC is:

$$\sum_{i=1}^n \text{ Loan Balance }_i $$

$$ WAC = \frac{ \sum_{i=1}^n\left(\text{ Loan Balance }_i \times \text{ Coupon }_i\right) }{ \sum_1^n \text{ Loan Balance }_i }$$

Here, $\text{Loan Balance}_i$ represents the outstanding balance of the ith loan, and $Coupon_i$ is the coupon rate (interest rate) of the ith loan.

Weighted Average Maturity (WAM)

Weighted average maturity provides an insight into the expected timing of cash flows from the mortgage pool. It is the weighted average time until the principal of the underlying loans is expected to be repaid. The formula for calculating WAM is:

$$ WAM=\frac{\sum_{i=1}^n\left(\text { Loan Balance }_i \times \text { Remaining Term }_i\right)}{\sum_1^n \text { Loan Balance }_i} $$

Here, $\text{Remaining Term}_i$ represents the remaining term to maturity of the ith loan.

Single Monthly Mortality Rate (SMM)

SMM measures the rate at which principal payments are received on a monthly basis relative to the remaining principal balance in the mortgage pool. It is used to estimate prepayment speeds. The formula for calculating SMM is:

$$SMM=\frac{\text { Principal Repaid in Month }}{\text { Beginning Principal Balance-Scheduled Principal Payment }}$$

Conditional Prepayment Rate (CPR)

CPR represents the annualized rate at which borrowers in the mortgage pool are expected to prepay their loans. It is a critical metric in assessing prepayment risk. The formula for calculating CPR is:

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