Value and Yield Risk on Outstanding Insured Residential Mortgages

Abstract

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."

Originators, wholesalers, and conduits: The marginal value of the contract rate on 30-year conventional mortgages

“…For a given contract rate the effective rate to the mortgagee increases as the discount increases. The effective rate increases by a much larger percent for shorter holding periods; see Curley and Guttentag (1977).…”

Pricing Fast‐pay Mortgages: Some Simulation Results

“…This paper prices the interest rate differential on default-free hypothetical early equity mortgages using yield curve data from 1970 to 1984. Studies by Curley and Guttentag (1977), Kaufman and Morgan (1980), and others have shown that conventionally computed yields on mortgages must be adjusted to make them comparable to other securities. Other studies have applied the option pricing framework to conventional mortgages [see Dunn and McConnell (1981) and Buser and Hendershott (1984)].…”

The Estimation of Mortgage Prepayment Rates

“…Only insurers, predominantly the FHA, were concerned about the timing of payments and eventual disposition of mortgages. Thus, FHA termination data have been the factual basis for several analyses, such as Curley and Guttentag (1974) and Waldman (1981). Curley and Guttentag (1974) use ordinary least squares (OLS) to regress the logarithm of the annual termination rate (defined as the number of loans that either prepay or default during the year divided by the number outstanding at the beginning of the year) against three explanatory factors: the annual average interest-rate differential, the discount (points) that prevailed during the current year, and the logarithm of the ratio of the policy year to the year of maturity.…”

“…This can be done most easily through the use of a "fixed-effects" or "covariance" model, in which dummy variables are used to allow each pool and time period to have a different intercept, but the effect of DIF and the other explanatory variables is assumed to be the same across pools and stationary 2Secause the divisor is the beginning-of-period balances, this problem is mitigated to some extent, particularly for mortgages that were outstanding for two or more years. Greater precision would result, however, if a "policy year" variable, such as that used by Curley and Guttentag (1974) and by Peters, Pinkus, and Askin (1984), could be constructed. over time.…”