Lesson 16 of 25 · 7 min

Why a leveraged path cannot be summarised by its endpoint

The units sold at the bottom do not participate in the recovery, so two identical return sequences end differently.

Track 4 lesson 13 showed that the order of returns matters under leverage. The mechanism is worth doing in full, because it is not a statement about volatility drag — it is a statement about units leaving the portfolio permanently.

Take the facility from lesson 13 and a three-step path of −26 percent, −9 percent, then +48 percent. The collateral's round trip is 0.74 × 0.91 × 1.48 = 0.99664, so it finishes 0.34 percent below where it started, at $1,465,049. With no maintenance rule the equity is $1,465,049 − $742,000 = $723,049.

Now apply the rule. After the first move the collateral is $1,087,800 and the loan-to-value is 68.21 percent, past the 65 percent threshold. Curing it requires selling S where the post-sale ratio returns to 65 percent, so S = ($742,000 − 0.65 × $1,087,800) ÷ 0.35 = $34,930 ÷ 0.35 = $99,800. After the second move the collateral is $899,080 and the ratio is 71.43 percent, requiring a further ($642,200 − $584,402) ÷ 0.35 = $165,137. Total sold: $264,937.

The remaining $733,943 then rises 48 percent to $1,086,235 against a balance of $477,063, so the equity is $609,173. The same returns in the same order produced $723,049 without the rule and $609,173 with it — a gap of $113,876, or 15.75 percent, on a path whose collateral finished 0.34 percent down. Across the 200,000 simulated paths that touched the trigger and then recovered above it, the average cost of the rule was $80,258 of terminal equity.

The endpoint of a leveraged path is not a function of the returns. It is a function of the returns, the order, and how many units were removed while the order was unfavourable.

Key terms

Absorbing action: A sale triggered by a threshold, which cannot be undone when prices recover. It converts a temporary decline into a permanent change in the position.
Cure multiple: The collateral that must be sold per dollar of shortfall, equal to one divided by one minus the threshold. At 65 percent it is 2.857.
Terminal equity: Collateral value minus balance at the end of the period. The quantity an endpoint summary reports, and the one the path silently rewrites.

Worked example

One return sequence, two portfolios

Collateral $1,470,000, balance $742,000, threshold 65 percent. Path: −26 percent, −9 percent, +48 percent.

Collateral round trip: −0.34%
First breach and cure: Sell $99,800
Second breach and cure: Sell $165,137
Equity with no rule applied: $723,049
Equity with the rule applied: $609,173
Difference: $113,876

The collateral finished a third of a percent down and the leveraged holder finished 15.75 percent behind an identical holder who was never asked to sell.

Check yourself

Collateral falls 26 percent, then 9 percent, then rises 48 percent, finishing 0.34 percent below where it began. Why does a borrower at a 65 percent threshold end $113,876 behind someone who held the same assets unleveraged through the same path?

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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.