The error in that running LTV

A running LTV is exact only when its inputs are exact. Four of those inputs go stale in different ways. The numerator goes stale if you keep last month's close and ignore accrual. The denominator goes stale if the public last sale is not the mark the lender uses. The haircuts go stale if the schedule has been revised in a letter you have not seen. The units go stale if a sale, a purchase, or a corporate action has changed a row.

The numerator error is the one you can measure from the fixture alone. Take the invented April book of $6,015,195.50 from a later lesson and divide last March's close into it: $1,858,563.47 ÷ $6,015,195.50 = 30.90 percent. The April close after thirty days at 7.22 percent is $1,869,745.83, and $1,869,745.83 ÷ $6,015,195.50 = 31.08 percent. The running ratio that forgot the interest is 0.18 percentage points light.

Eighteen hundredths of a point is small on this loan. It is also entirely mechanical. Fifteen days of the same rate is $5,591.18 of forgotten interest, a trigger understatement of $5,591.18 ÷ 0.70 = $7,987.40. The other three errors — mark versus print, silent haircut, silent unit change — do not have a size until they occur. They are named here because the running LTV treats them as zero, and zero is an assumption, not a measurement.

The reconstruction is a running estimate whose largest known bias is unpaid interest in the numerator. The unknown biases are everything the last letter cannot see.