Many homeowners prepay for multiple reasons;
- They must pay when they sell their home
- They can refinance at a lower interest rate
- They may default on their payments, so the insurer prepays the mortgage
- The home may be destroyed by flooding or fire, so the insurer pays the mortgage
Therefore, prepayment modeling is an important part of pricing MBSs.
We then talked about the simplest type of MBS - the mortgage pass-through. In practice, mortgages are usually sold on to third parties that can pool these mortgages together through securitization. Such third parties are Ginnie Mae, Freddie Mac, or Fannie Mae, along with others. MBSs that are issued by the three government agencies above are guaranteed against default, while MBSs that are issued by other third parties (non-agency mortgages) are not. This alters the modeling of MBSs. The simples type of MBS is the pass-through security where a group of mortgages is pooled together, then sold to investors, and investors receive monthly payments representing the interest and principal payments of the underlying mortgages. The pass-through rate coupon, however, is strictly less than the average coupon rate of the underlying mortgages. This is due to fees associated with servicing mortgages, as well as profit margins.
WAC - Weighted Average Coupon Rate is a weighted average of the coupon rates in the mortgage pool with weights equal to mortgage amounts still outstanding
WAM - Weighted Average Maturity is a weighted average of the remaining months to maturity of each mortgage in the mortgage pool with weights equal to the mortgage amounts outstanding.
They are prepayment conventions that are used by market participants when quoting yields and prices of MBSs.
CPR - Conditional Prepayment Rate is the annual rate at which a given mortgage pool prepays. It is expressed as percentage of the current outstanding principal level in the underlying mortgage pool
SMM - Single-Month Mortality Rate is the CPR converted to a monthly rate assuming monthly compounding.
These are related as follows:
In reality, the CPR is stochastic and depends on many economic variables. However, market participants often use deterministic prepayment schedules as a mechanism to quote MBS yields and option-adjusted spreads.
The standard benchmark for CPR is the Public Securities Association (PSA) benchmark.
The PSA benchmark assumes:
for 30 year mortgages. In this case t is the number of months since the mortgage pool originated. Slower and faster prepayment rates are then given as some percentage or multiple of the PSA benchmark.
Given a particular prepayment schedule, the average life of an MBS is defined as:
where P(k) is the principal (scheduled and projected) paid at time t, TP is the total principal, T is the total number of months, and we divide by 12 so that the average life is measured in years instead of months. Average life decreases as PSA increases.
In practice, the price of an MBS is observed in the market place and a yield-to-maturity interest rate can be determined. This rate is the rate that will make the present value of the expected cash flow equal to the market price. The expected cash flows are determined based on some underlying prepayment assumptions such as 100 PSA, 200 PSA, 300 PSA, etc. When the yield is quoted as an annual rate based on a semi-annual compounding, it is called a bond-equivalent yield. These are very limited when evaluating an MBS and fixed income securities in general.
An investor in a pass-through is exposed to interest rate risk in the fact that any fixed set of cash flows decreases as interest rates increase. However, a pass-through investor is also exposed to prepayment risk, contraction risk and extension risk.
When interest rates decline, prepayments tend to increase and the additional prepaid principal can only be invested at lower interest rates.
When interest rated increase, prepayments tend to decreased and sot there is less prepaid principal that can be invested at higher rates.
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