Exchange-rate risk mitigation with price-level-adjusting mortgages: The case of the mexican UDI

Journal of Real Estate Research, The, Jan-Mar 2003 by Lipscomb, Joseph B, Harvey, John T, Hunt, Harold

The first payment occurs one year after the loan is made. The borrower will consult the UDI conversion index to find the peso equivalent of an UDI on the day the payment is due. In the example, at the end of the first year, an UDI is worth 1.2 pesos, as indicated in Exhibit 1. Therefore the borrower will pay the lender 44,047.27 pesos (36,706.06 UDIs x 1.2 pesos per UDI). The second year, the borrower will pay 52,856.73 pesos (36,706.06 UDIs x 1.44 pesos per UDI). Following the first payment, the remaining balance of the loan is 243,293.94 UDIs. If the borrower wanted to prepay the balance at the end of the first year, he/she would pay 291,952.73 pesos (243,293.94 UDIs x 1.2 pesos per UDI). Exhibit 1 shows each of the 15 payments and their associated loan balances in terms of UDIs and in terms of peso equivalents.

Curves of the payments in UDIs and in pesos are shown in Exhibit 2. The payments are fixed at 36,706.06 UDIs over the life of the loan, but the peso value of the payments grows dramatically and peaks at the end of 15 years with a final payment of 565,531.06 pesos.

Exhibit 3 shows plots of the UDI and peso for the balances. The curve of UDI balances exhibits the typical appearance of an amortization pattern for constant-payment payment fixed-rate loans. The decline in the UDI balance is continuous and accelerating. However, in terms of pesos, the balance increases initially until it peaks at 828,373.55 pesos following the payment in year 11. Then, the peso balance begins to decline and reaches zero following the 15th payment.

As a check to verify that the mechanics of the UDI mortgage result in a 12% real peso rate of return, the peso balance after the 14th payment, 420,782.04, can be multiplied by 1.20 to adjust for 20% inflation in the final year of the loan. Then, the inflation-adjusted balance can be increased by 12% to allow for interest that has accrued for the year. The result is $565,531.06 ($420,782.04 X 1.20 x 1.12), which is the same as the final peso payment that was originally calculated by multiplying the fixed UDI payment, 36,706.06, by the current UDI conversion index, 15.4070. This comparison illustrates that the inflation-adjusting mortgage-amortization scheme employed in the UDI system does in fact yield a real return in pesos at the specified interest rate. Thus, the lender has received a repayment of 250,000 real-pesos and a real-rate of return of 12%.

Simulation of Returns Using Mexico's Historical Inflation

The UDI system is modeled after the price-level adjusting mortgages (PLAMs) used in Brazil in the past, as described by Anderson and Lessard in Lessard and Modigliani (1975). The UDI mortgage loan process begins with the origination of the loan for a specified number of pesos. The loan originator establishes the term of the loan, the payment frequency and the real rate of interest, all of which are fixed for the life of the loan. The real rate is a combination of a real interest rate in the classic sense plus a risk premium appropriate to the particular mortgage loan. On the day the loan is originated, the peso value of the principal is translated into UDIs using the UDI Index. From that time forward, the principal balance of the loan is denominated in UDIs, and payments and the amortization schedule are calculated in UDIs. When payment is due, the number of UDIs owed is translated back into pesos, using the current value of the UDI Index. The UDI's value was initially set at one-to-one with the peso on April 4, 1995, and continues to increase over time with the Mexican Consumer Price Index. On the 10th and 26th of each month, the Bank of Mexico publishes the index of an UDI's value for the next 15 days. The value of an UDI changes daily. The UDI value as of October 25, 2002 was 3.18 pesos/UDI.