**PSA Standard Benchmark**

The Public Securities Association’s (now known as the Bond Market Association) established convention for expressing prepayments on a mortgage pass-through.

The PSA Benchmark is expressed as a series of monthly prepayment rates. It’s also referred to as a prepayment model suggesting that it can be used to estimate prepayment rates.

It assumes the following prepayment rates for a 30-year mortgage.

The first month prepayments = 1/30^{th} of 6% (0.2%), then prepayments rise at a linear rate for 30 months. In the 30^{th} month the prepayment rate reaches 6%. After that it maintains a 6% CPR for the remaining life of the mortgage. This benchmark is referred to as 100% PSA.

“100 PSA”: investor expectations that mortgage principal repayments in a security pool will all (100%) follow the PSA Benchmark.

The prepayment speeds can be made slow or fast by altering the percentage. If a mortgage pool is 50 PSA, then half of the mortgage prepayments are expected to follow the PSA Benchmark, i.e., 0.1% prepayment in the first month that will linearly increase to 3% in the first 30 months after which it will remain constant at 3%. 150 PSA means 1.5 times the speed of PSA benchmark (i.e., based on 9% – 6% * 1.5).

The following chart illustrates the PSA for 50 PSA, 100 PSA, and 150 PSA.

**Calculating SMM and CPR using PSA**

PSA benchmark can be used to calculate SMM and CPR. The following examples illustrates this.

**Example 1**

Using the PSA benchmark, CPR = 6% * t/30

For month 10,

CPR = 6% * 10/30 = 2%

SMM = 1 – (1 – 2%)^(1/12) = 0.17%

**Example 2**

Using 150 PSA, CPR = 9% * t/30

For month 5,

CPR = 9% * 5/30 = 1.5%

SMM = 1 – (1 – 1.5%)^(1/12) = 0.126%

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