Measuring the Effects of Prepayments on Mortgage-Backed Securities

Mortgage-backed securities differ from corporate and government bonds in that their cash flows cannot be estimated with certainty, since homeowners often prepay their mortgages. Prepayments may include sale of the property, refinancing, curtailments, or liquidation of the property due to foreclosure. Standard fixed-income measurements, which allow investors to compare different types of bonds, include price, yield, average life, duration and convexity. Exact bond measurements cannot be calculated for mortgage backed securities because the underlying cash flows are dependent upon the prepayment rate, which is a random variable. However, prior information about the distribution of prepayment rates allows one to estimate a bond measurement by defining it as a function of the prepayment rate. Simulating prepayment rates can provide information about the probable yield, average life and other measurements of mortgage-backed securities. Computer implementation is not difficult because the calculations involve matrix algebra, which can easily be translated into an array-based programming language such as APL. Amortization Schedule and Cash Flows Each loan has an amortization schedule. A typical amortization schedule contains the beginning balance, scheduled principal and interest payments for each period (usually monthly). Let the scheduled balance ( ) 0 1 1 , , , N B B B − = B L . (Since the balance at the end of period N is defined to be zero, we will leave it out.) If we know the original balance, term and interest rate, it is easy to calculate the payment, principal and interest amounts for each period. To represent the scheduled cash flows we will construct a matrix whose rows represent time periods and whose columns represent cash flows. The sum of each row equals the total cash received each period. For a fixed-rate mortgage with no prepayments, these amounts are equal. The first two columns of the matrix represent principal—scheduled and prepayment respectively. Note that prepayments are set to zero. The last two columns represent gross interest, which is divided into net interest, and servicing fees respectively.