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Why borrowed money in finance magnifies outcomes — the math of leverage

June 28, 2026 · 5 min

David Sterling & Megan Skiendel

At 100-to-1 leverage, a 1% price move erases your entire stake — but the real danger is the margin call that arrives before the loss completes, forcing liquidation at the worst price and cascading into correlated positions. LTCM and Archegos both proved that understanding the math isn't the same as acting on it.

Leverage is the use of borrowed capital to control a larger financial position than one's own equity alone would permit. The mechanism is purely arithmetical: gains and losses are calculated on the full position size, not just the investor's contributed equity.

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About this episode

Leverage is one of those concepts that looks deceptively simple on paper — borrow money, multiply your exposure, multiply your outcomes. But as this episode makes clear, the arithmetic is the easy part. The dangerous part is everything the spreadsheet doesn't show. The episode works through two landmark collapses to trace what actually goes wrong. Long-Term Capital Management in 1998 had Nobel laureates running fixed-income arbitrage at roughly 25-to-1 leverage on equity. The positions weren't wrong in theory. What collapsed them was a liquidity crisis triggered by Russia's debt default — not because LTCM's thesis failed, but because every correlated trade moved against them simultaneously, and there were no buyers. The Federal Reserve then orchestrated a $3.6 billion private-sector bailout, and as the episode notes, who was in that room mattered as much as the leverage ratio. Archegos in 2021 is the same movie with intentional opacity layered on top. Bill Hwang's fund held $160 billion in notional exposure on $10 billion of equity through total return swaps — instruments that fell outside the disclosure thresholds regulators applied to direct equity positions. A risk officer flagged the concentration before the collapse. The number was visible. Nobody acted while the fees were good. What the episode keeps returning to is the gap between understanding and action. We've understood leverage every time it's caused a crisis. The next blowup won't turn on whether someone can do the math.

Frequently asked

How does leverage work in trading and investing?

Financial leverage lets traders control a position larger than their own capital — at 100-to-1, a $5,000 stake controls $500,000 in exposure. A 1% adverse price move then wipes out the entire $5,000. Gains are amplified by the same ratio, making leverage a multiplier on both profits and losses.

What is a margin call and why is it dangerous?

A margin call occurs when a leveraged position's losses reduce equity below the broker's required minimum. The broker liquidates the position immediately — often at the worst available price — before the full loss plays out. That forced selling can push prices lower, triggering margin calls across other traders holding correlated positions.

What caused the Long-Term Capital Management collapse?

Long-Term Capital Management collapsed in 1998 running roughly 25-to-1 leverage on equity. Russia's August 1998 debt default caused every correlated fixed-income position to move against LTCM simultaneously, and liquidity vanished — no one would buy the positions. The Federal Reserve then orchestrated a $3.6 billion private-sector bailout to prevent broader market contagion.

How did Archegos Capital hide its leverage from regulators?

Archegos held $160 billion in notional exposure on $10 billion of equity — 16-to-1 leverage — almost entirely through total return swaps. Regulators never saw it because total return swaps fell outside the disclosure thresholds that direct equity holdings of equivalent size would have triggered, a gap ESMA's post-mortem explicitly identified.

What is the difference between leverage ratio and notional exposure?

Notional exposure is the total market value controlled; equity is the capital actually at risk. Archegos's $160 billion notional on $10 billion equity illustrates the gap — the full $160 billion was invisible to regulators because the swap structure carried different disclosure obligations than direct share ownership of the same size would have required.

Grounded in 9 sources
FinTech-amplified credit risk: excess leverage and regulatory discipline in China’s real estate crisis · doi.org
The effect of leverage manipulation on real estate firms’ financial risk: Based on the interest conflicts perspective · doi.org
Leverage and derivatives – the case of Archegos · esma.europa.eu
A210729 ex992.htm · sec.gov
Black Swans and Financial Stability · federalreserve.gov
Long-Term Capital Management (LTCM) Collapse: Causes and U.S. Intervention · investopedia.com
Capital Note: The Unwinding of Bill Hwang’s Archegos Has Few Systemic Implications | National Review · nationalreview.com
Why LTCM Lost $4.6B in 4 Months — And How Margin Spirals Repeat the Pattern | Quant Decoded · quantdecoded.com
The 27 Biggest ODD Failures That Shook Finance | Resonanz Capital · resonanzcapital.com
Read transcript

David Sterling: Five thousand dollars. That's your stake. You've got 100-to-1 leverage, so you control $500,000 in exposure. A single 1% price move — that's it, one percent — your $5,000 is gone. Completely. And the spreadsheet makes that look like a clean, symmetric fact. It goes up 1%, you doubled. Goes down 1%, you're out. Neat arithmetic.

Megan Skiendel: But the spreadsheet isn't what kills you.

David Sterling: No. And that's — well, that's the whole episode, frankly. The margin call arrives before the loss completes. Your broker isn't waiting for the full 1% to settle. They're liquidating your position now, at the worst possible price, and that sale pushes prices lower, which hits everyone else holding the same correlated book.

Megan Skiendel: It's like a mortgage, honestly. The bank doesn't care that your house dropped in value — they care whether you can make the payment this month. The equity shrinking is your problem. The cash flow stopping is theirs.

David Sterling: Right. And leverage shows up in places most people never see. Margin accounts, yes. But also total return swaps, options, corporate debt — each one a different level of opacity to regulators.

Megan Skiendel: So if the arithmetic is this simple — and it really is, it's just multiplication — why do sophisticated institutions keep getting destroyed by it?

Megan Skiendel: Long-Term Capital Management. Nobel Prize-winning economists. Fixed-income arbitrage that looked, on paper, like it couldn't lose. They were running roughly 25:1 leverage on equity — and the trades weren't wrong, that's the part people skip over.

David Sterling: The positions were theoretically sound.

Megan Skiendel: Right. And then Russia defaults on its debt, August 1998, and — actually, wait, it's not even that the default proved LTCM wrong. It's that every correlated fixed-income position moved against them simultaneously. Liquidity just... vanished. You can't close what no one will buy.

David Sterling: The Russia default was the match. But frankly, any sufficiently large shock triggers the same cascade at 25:1. The powder keg was already built. The specific trigger is almost arbitrary.

Megan Skiendel: I don't entirely disagree — but then the Federal Reserve orchestrates a $3.6 billion private-sector bailout to stop contagion. And that's where I push back, because that's not arithmetic. That's a room full of people deciding Long-Term Capital Management deserved rescue. Who's in that room matters.

David Sterling: The institutional relationships determined the outcome, not the leverage ratio. That's — well, that's the tension, isn't it. Leverage built the condition. Humans decided the consequence.

Megan Skiendel: Which brings us to Bill Hwang. Because Archegos is — honestly, it's the same movie but the opacity is intentional this time. Ten billion in actual equity. A hundred and sixty billion in notional exposure through total return swaps. Sixteen-to-one effective leverage. And none of it visible to regulators because swaps just... weren't counted the same way as owning shares directly.

David Sterling: ESMA's post-mortem was explicit on that — total return swaps fell outside the disclosure thresholds that direct equity positions trigger. Structurally identical exposure, completely different reporting obligation.

Megan Skiendel: Right, but — wait, that's not actually the part that gets me. The prime brokers saw it. March 2021, a risk officer flags internally that Archegos's concentration has gotten large enough that a ten-percent move forces simultaneous selling across multiple counterparties. The number is on a screen. And the desk does nothing.

David Sterling: Because the swap spreads were running.

Megan Skiendel: Credit Suisse, Nomura — they ate over ten billion in losses combined. That's not a disclosure gap. Someone chose to stay quiet while the fees were good.

David Sterling: So the regulatory design failure and the culture failure are — I mean, they're not the same claim. One says fix the rule. The other says the rule wouldn't have mattered.

Megan Skiendel: The opacity wasn't accidental. It was tolerated. That's the uncomfortable part.

David Sterling: The arithmetic hasn't changed since 1998. Twenty-five-to-one, sixteen-to-one — the multiplication is the same. LTCM, Archegos, the next one. And I keep turning over the same question, which is — well, it's not whether we understand leverage. We do. We've understood it every time. It's whether someone in that room decided to look at the number on the screen and actually act on it.

Megan Skiendel: And they usually didn't. Because looking costs something.

David Sterling: That's what I can't — I mean, structurally, leverage is durable. It doesn't need a specific interest rate or asset price to stay dangerous. It just sits there. But the next blowup won't turn on whether we can calculate the exposure. It'll turn on whether the institution holding it is too interconnected to be allowed to fail, and whether anyone upstream actually wanted to see it before it moved.