An Analytical Comparison of the Durations and Price Sensitivities of Fixed-Rate, Constant Payment and Constant Amortization Mortgages

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Both open-form and closed-form formulas are developed to compute duration for two types of fixed-rate mortgages: the level or constant payment mortgage and the constant amortization mortgage. Because holding periods are often less than maturity, duration formulas are also developed for mortgages that are paid prior to maturity. The duration formulas are used to compare the risk and price behavior of the two types of mortgages. Under any scenario, the constant amortization mortgage exhibits less interest rate risk than the constant payment mortgage. The durations of both mortgage types are monotonically increasing functions of maturity when the mortgages are held to maturity. When the mortgages are subject to prepayment, however, durations may, under certain circumstances decline with original maturity.