Lesson 3 of 25 · 7 min

A convergence fund, 1998: leverage multiples and why they compounded

A twenty-five to one balance sheet turns a two percent price move into a forty-five percent loss of capital.

The reported figures for Long-Term Capital Management at the start of 1998 were roughly five billion dollars of capital against a balance sheet widely reported at around one hundred billion, with derivative notional reported at well over a trillion. The multiple matters less than what a multiple does to a small price move.

Balance-sheet leverage is assets divided by equity. Its effect is mechanical: the percentage change in equity equals the multiple times the percentage change in assets. At twenty-five to one, a 1 percent decline in the value of the assets removes 25 percent of the capital. Nothing about that requires a crisis; it is the definition working.

equity change % = (assets ÷ equity) × asset change %

assets: The gross market value of everything held, before subtracting what is owed.
equity: Assets minus borrowings. The capital that absorbs losses.
asset change %: The percentage move in the value of the assets, of either sign.
equity change %: The percentage move in capital that results. The multiple is the amplifier.

The compounding has two sources. First, losses shrink the denominator, so the multiple rises as the position falls, and each further percent of decline costs a larger share of what is left. Second, financing terms tighten in the same conditions: the haircut on repo financing rises, which forces asset sales even when the balance is unchanged. Leverage therefore climbs at the moment it most needs to fall.

In 1998 there was a third layer. Several of the positions were themselves financed positions in instruments whose prices already embedded borrowing, and the same risk factor sat underneath the lot. The reported loss for August 1998 alone was roughly 44 percent of capital, and roughly 90 percent for the year to late September.

Key terms

Balance-sheet leverage: Gross assets divided by equity. A multiple that says how much a small price move is magnified before anything else happens.
Haircut: The share of an asset's value a financier refuses to lend against. Raising it forces a sale without any change in the balance owed.
Notional: The reference amount a derivative is written on. It is not money at risk, but it does set how much the contract moves per unit of price.

Worked example

What two ordinary days do at twenty-five to one

Illustrative figures scaled down so the arithmetic is followable; they are not the reported amounts. Assets of $3,150,000 against equity of $126,000, and two consecutive 1.8 percent declines in asset value.

Leverage at the start: 25.0x
Assets after the first 1.8 percent fall: $3,093,300
Equity after the first fall: $69,300
Leverage after the first fall: 44.6x
Equity after a second 1.8 percent fall: $13,620.60
Capital remaining: 10.8%

Two days that a newspaper would not report removed 89.2 percent of the capital. The second day cost more than the first because the multiple had risen to 44.6x on its own.

Check yourself

A book holds $2,400,000 of assets against $96,000 of equity. Asset values fall 3 percent. What is left of the equity, and what is the new leverage multiple?

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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.