Lesson 2 of 25 · 7 min
A convergence fund, 1998: what the positions were
The trades were individually small bets on spreads narrowing, and almost every one of them widened at once.
Long-Term Capital Management, which began trading in 1994 and was wound down after 1998, is remembered as a leverage story. The leverage is the next lesson. This one is about what it actually held, because the shape of the positions is what the size was built on.
The trades were relative value. A relative-value position holds two closely related instruments, one long and one short, and earns money if the price gap between them narrows. Widely reported examples from the fund's book include recently issued government bonds against slightly older ones, government bonds against interest-rate swaps, mortgage securities against government bonds, and long positions in bonds of countries expected to converge into a single currency.
Each such trade has a small expected gain, because the gap between two nearly identical instruments is small. That is the whole reason for the size: a spread worth a fraction of a point per year only becomes a business if it is held in enormous notional. The economics of the strategy require leverage by construction, not as an add-on.
The other property mattered more in 1998. Every one of those spreads widens when holders of the cheaper, less liquid side need cash, and they need cash at the same times. The book looked like dozens of independent trades and behaved, under stress, like one trade held dozens of times. Track 7 lesson 10 makes the general point: correlated positions are a single position for collateral purposes.
Diversification across instruments is not diversification across causes. These spreads had different names and one driver.
Key terms
- Relative-value trade
- A long position in one instrument paired with a short position in a closely related one, profitable if the gap between them narrows.
- Spread
- The price or yield difference between two related instruments, usually quoted in basis points or in points of par.
- Convergence
- The expectation that two prices which ought to be nearly identical will become nearly identical. The trade earns the gap; the risk is that the gap widens first.
Worked example
Why a small spread needs a large notional
Illustrative figures scaled down so the arithmetic is followable; they are not the reported amounts. One bond bought at 98.20 and a nearly identical one sold short at 99.05, $60,000,000 of notional per leg, supported by $1,200,000 of equity.
- Spread at entry
- 0.85 points
- Equity as a share of one leg
- 2.0%
- Gain if the spread narrows to 0.35
- $300,000
- That gain on equity
- +25.0%
- Loss if the spread widens to 1.45
- $360,000
99.05 − 98.20.
$1,200,000 ÷ $60,000,000.
0.0050 × $60,000,000.
$300,000 ÷ $1,200,000.
0.0060 × $60,000,000, or −30.0 percent of equity.
Half a point of convergence was a 25 percent year. Six tenths of a point of divergence was a 30 percent loss. The instrument barely moved in either case.
Check yourself
You hold a convergence position of $45,000,000 of notional per leg against $900,000 of equity. The spread moves 0.40 points against you. What happens to the equity?
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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.