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THIS PAPER PRESENTS an analytically rigorous method for estimating the value of an outstanding residential mortgage and for determining the error between this correct method of determining value and conventional or "rule-of-thumb" methods. It also develops a procedure for determining the likely error in the correctly estimated value associated with potential divergence between estimated and realized cash flows. The paper builds on a methodology for calculating expected mortgage yield which was described in an earlier article.' I. BACKGROUNDIt is obvious that the market price of a financial instrument is not its "true value" if the expected yield the buyer associates with that price has not been correctly calculated. This is generally the case with outstanding residential mortgages. It is only by accident that these mortgages are correctly priced, i.e., that the yield expected at the transaction price is the yield correctly implied by that price.We hasten to add that we are not discussing the several factors that may cause divergence between expected yield and realized yield, such as borrower default and variation in reinvestment rates. With an exception to be discussed later, this paper is concerned only with ex ante magnitudes. Our thesis is simply that the existing procedure used to value outstanding mortgages is defective. In some cases it leads to prices that are too high and in other cases to prices that are too low. II. THE PROBLEM OF CALCULATING YIELDWe begin with a brief summary of the main factors involved in calculating expected yield on a mortgage.2 The basic problem in calculating expected yield is that if a mortgage is acquired at a price different from par, which is almost always the case, yield depends on when the loan is terminated or "prepaid." This is illustrated in Figure 1, which shows how the yield on a 30-year 8 1/2% contract rate mortgage varies with the prepayment period, assuming discounts from par of 2 and 10 points.The prevailing method of dealing with this problem is to assume termination after a period equal to the average life of a portfolio of "comparable mortgages."

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