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Long-Term Financing in an Inflationary Environment 287
ing rate—a financial indexation—while eliminating or minimizing the tilt
problem.
The so-called “French Mortgage” eliminates the tilt by scheduling the periodic
payment exactly as in the PLAM, i.e. computing the initial payment using the
fixed long-term real rate and the chosen maturity and indexing later payment to
the price underscore. The balance outstanding at the end of a payment period is
obtained by adding to the opening balance the amount of interest due for the
period and subtracting the amount actually paid in the period. The interest due,
in turn, is obtained by applying to the initial balance, the floating short-term rate
for the period. When the balance due reaches zero the mortgage is fully paid.
How long will this take? It can be shown that if the difference between the floating
nominal and the fixed real rate coincides with the rate of inflation (which is
implied by the so-called “Fisher Law”), then the maturity will coincide with the
one embedded in the first payment. Unfortunately this condition may fail to hold,
and in this case, the time required before the debt is finally paid may be shorter
or longer. In other words, the instrument has a floating maturity. This is the major
drawback of the instrument. It should be noted that, though two distinct rates are
involved in the specification, the floating short rate is the one that is effectively
paid by the borrower while the fixed rate only controls the duration of the
instrument.
An interesting variant of the French Mortgage is the so-called “Mexican Mortgage.”
It is the same as the French Mortgage except that the periodic repayments
are indexed on a wage index rather than on the cost of living. It aims to avoid
the danger that, in the course of inflation, wages may fail to keep up with prices,
causing the periodic payment to grow faster than labor income. Under the
Mexican scheme the periodic payment cannot rise any faster than the wage index.
Of course if a decline of the real wage does occur, then it will take longer for the
debtor to fully repay his debt.
Another type of mortgage, labeled the Inflation Proof Mortgage (IPM), was
developed at MIT in the mid 70s. Like the French and Mexican, it gives the
lenders and borrowers the opportunity to replace the fixed with a floating rate but
is designed so to insure a maturity fixed in advance, as in the traditional mortgage.
To this end the real repayment schedule is not fixed in advance at a constant
level but is instead recalculated at each payment date by reamortizing the
remaining balance over the remaining life of the contract. The balance at any
point is computed as in the French Mortgage. Note that the amortization over the
balance of the contract insures that the last payment, due at the fixed maturity,
will complete the payment of the entire debt. Aside from this feature, what makes
the IPM attractive is that the periodic payment will tend to stay pretty constant
in real terms provided Fisher’s Law holds (i.e. the short-term floating rate exceeds