Lesson 19 of 25 · 7 min

Reconstructing last month's schedule from two statements

The second statement is a second photograph of the same table. Subtract, and the month appears.

Two consecutive statements give you two observations of units, prices and, when printed, advance rates. Last month's schedule is the earlier observation, reconstructed the same way as lesson 2, then laid beside this month's. What moved is a price, a unit count, a rate, or some combination. The reconstruction is a subtraction, not a memoir.

Take an invented February close on the same five holdings, same units, same rates, different prices. Meridian 12,400 × $146.50 = $1,816,600 at 50 percent = $908,300. Calder 3,100 × $581.00 = $1,801,100 at 35 percent = $630,385. Collective 4,150 × $211.20 = $876,480 at 70 percent = $613,536. Oakridge 8,200 × $61.80 = $506,760 at 55 percent = $278,718. Government fund 18,600 × $50.90 = $946,740 at 85 percent = $804,729.

February market value is 1,816,600 + 1,801,100 + 876,480 + 506,760 + 946,740 = $5,947,680. February lending value is 908,300 + 630,385 + 613,536 + 278,718 + 804,729 = $3,235,668. The February blend is 3,235,668 ÷ 5,947,680 = 0.54402, which is 54.40 percent. March is 54.32 percent on $6,032,795 and $3,277,251.25. Rates did not move. Prices did. The blend ticked down eight hundredths of a point because Calder, the low row, rose a little more than the others.

A rate that did move would show up as a product that cannot be explained by the price change. If February Calder had printed at 40 percent, its product would have been 1,801,100 × 0.40 = $720,440, and the March 35 percent would be a reclassification, not a mark. Two statements are enough to separate those stories, which is why a single statement cannot.

Last month's blend is not this month's starting point. It is last month's ending point, and the two meet only if you keep the table.

Key terms

Paired statements: Two consecutive period documents on the same facility, used to separate price moves from rate moves.
Unexplained product: A lending-value change that the price change cannot produce at a constant advance rate. Evidence of a reclassification.
Constant-rate month: A period in which every category rate held still, so every product change is a price or unit change.

Worked example

February beside March, rates held still

Invented February close on the same units and rates as March, different prices. March figures as in lesson 2.

February market value: $5,947,680
February lending value: $3,235,668
February blended advance rate: 54.40%
March blended advance rate: 54.32%
Change in lending value: +$41,583.25
Change in market value: +$85,115

Eighty-five thousand of new wealth produced forty-two thousand of new collateral, at a slightly worse mix, with no rate rewritten.

Check yourself

February lending value is $3,235,668 on $5,947,680 of market value, at the same five rates as March. What is the February blend, and what would a Calder product that did not match 35 percent of February's $1,801,100 tell you?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.