Lesson 25 of 25 · 8 min

One unchanged portfolio, through one tightening cycle

Nothing is bought and nothing is sold, and nine months later four fifths of the headroom has gone.

The only way to see how much of a tightening is environmental is to take the borrower out of the experiment. So: five holdings, fixed quantities, nine months, and not one transaction of any kind.

The account holds 9,400 units of a broad equity index fund at $146.20, 4,850 shares of a large-company stock at $83.40, 17,900 shares of a mid-sized company at $31.75, 21,600 units of an investment-grade bond fund at $47.90 and 38,500 shares of a thinly traded small company at $7.40. That is $3,666,635 of market value and, at advance rates of 70, 65, 50, 80 and 30 percent, $2,422,259 of lending value. Against a $1,340,000 balance the headroom is $1,082,259, or 44.7 percent of lending value. A 42 percent concentration cap applies; the largest contributor is at 39.71 percent.

Four readings, nine months apart end to end, on identical holdings:

Month three, spreads widen. The bond holding falls 3.9 percent on the spread move alone and equities drift. No advance rate changes. The quarter costs $24,484.78 in interest, and headroom is $981,459.37.
Month six, the schedule is republished. Prices are lower and four rows are reduced: 70 to 62, 65 to 58, 50 to 38, 80 to 76, 30 to 20. Headroom is $418,260.18.
Month nine, two thresholds. The small holding closes at $4.35, below a $5 floor, and is credited at nothing; two further rows are trimmed.
Month nine, the cap. The bond holding, having fallen least, now contributes 44.87 percent of lending value against the 42 percent cap, so $48,047.35 of it is disallowed. Headroom is $207,312.51.

The reconciliation is the point of the exercise. Lending value fell $794,579.11 in total: $446,135.75 from prices, $266,901.00 from advance rate revisions, $33,495.00 from the reclassification, and $48,047.35 from the concentration cap. Headroom fell $874,946.49, which is that $794,579.11 plus $80,367.39 of interest accrued across the three quarters. Every dollar is accounted for and no share changed hands.

Three figures describe the same nine months for the same five holdings. Market value fell 20.8 percent. Lending value fell 32.8 percent. Headroom fell 80.8 percent. The distance between the first of those numbers and the last is the entire subject of this track.

Key terms

Attribution: Splitting a total change into the separate causes that produced it, in an order that sums back to the total.
Environmental change: A change in a position that no decision by the holder produced. Prices, schedules, thresholds and limits all qualify.
Headroom decay: The steady erosion of borrowing room from the balance side, through accrued interest, independent of anything the collateral does.

Worked example

The same five holdings at four moments

Illustrative figures throughout. Quantities are constant at every reading; only prices, advance rates, one reclassification, one cap and accrued interest change.

Month zero: Headroom $1,082,259
Month three, spreads widen: Headroom $981,459.37
Month six, rows reduced: Headroom $418,260.18
Month nine, floor and cap: Headroom $207,312.51
Attribution of the lending value fall: $446,135.75 + $266,901.00 + $33,495.00 + $48,047.35
Attribution of the headroom fall: $794,579.11 + $80,367.39

Market value minus 20.8 percent, lending value minus 32.8, headroom minus 80.8. The portfolio was never touched.

Check yourself

At month zero the loan-to-value against lending value is 55.32 percent; at month nine it is 87.26. How much of that 31.94-point rise came from the balance growing, and how much from lending value falling?

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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.