Lesson 9.4: Famous failures: LTCM and the 2007 quant quake
Learn what went wrong at LTCM in 1998 and in the August 2007 quant quake: leverage, crowding, liquidity spirals and the lessons for risk.
By the end of this lesson you will be able to explain what Long-Term Capital Management did and why it failed in 1998, say how leverage turns a small adverse move into a total loss, describe the August 2007 episode in which many quantitative equity funds lost money together, model a simple liquidity spiral in which forced selling pushes prices against the sellers, see why the correlations that models assume in calm times break down in a crisis, and list the practical lessons for risk. You will show that a fund with 25 times leverage is wiped out by a fall of 4 per cent in its assets, that a fund with leverage L that loses a fraction s of its assets must sell (L − 1) times its loss to restore its leverage, that in a toy model of five identical funds a 2 per cent shock grows to a 4.8 per cent fall in prices at 3 times leverage and 28.7 per cent at 10 times, with all five funds failing, when the market is thin. You should have read Lessons 4.4, 5.3, 8.4 and 9.2. The mathematics is leverage arithmetic and simple iteration. This course is education about how markets and research work, not investment advice.
A course that teaches how to build strategies would be dishonest if it did not also teach how they die. Some of the best-known failures in finance were not run by amateurs. They were run by people with doctorates, Nobel prizes, large capital and careful models. They failed for reasons that were not exotic: too much leverage, positions too large for the market, a belief that diversification would hold in a crisis, and an inability to stay solvent long enough to be right. The same patterns repeat, which is why they are worth learning. Facts about the cases below come from public accounts, and figures differ somewhat by source, so treat the numbers as approximate.
Long-Term Capital Management, 1998
Long-Term Capital Management (LTCM) was a hedge fund founded in 1994 in Greenwich, Connecticut, by John Meriwether, a bond trader who had led an arbitrage group at Salomon Brothers. Its partners included traders from that group and two academics, Myron Scholes and Robert Merton, who shared the 1997 Nobel Prize in economics for the option pricing work of Lessons 6.2 and 7.2. It was a symbol of the idea that mathematical finance could tame risk.
What it did
LTCM's core business was relative value, or convergence, trading, the kind described in Lesson 9.2. It looked for pairs of securities that were similar in nature but priced slightly differently, bought the cheap one and sold the dear one, and waited for the gap to close. Examples were:
On-the-run against off-the-run government bonds: the most recently issued bond of a maturity is more liquid and trades at a slightly higher price than an older, nearly identical one.
Swap spreads and other curve trades, in several currencies.
Convergence of European government bond yields before the euro.
Equity pairs such as the two listings of a dual-listed company (the Royal Dutch and Shell shares), and some merger arbitrage.
Selling volatility: it sold long-dated equity index options at high implied volatilities (Lesson 6.3).
Each trade made a small profit, a few tenths of a percentage point, with a statistical expectation that it would be positive. To turn those into a high return on capital, LTCM used very high leverage.
The numbers
At the start of 1998, public accounts put LTCM's equity at about $4.7 billion, supporting a balance sheet of more than $100 billion of assets, a leverage of about 25 to 1, and derivative positions with a notional value above $1 trillion. A fund like that is exposed to the market for the whole of the assets, though it has only the equity to absorb a loss.
The arithmetic is simple. With assets A and equity E, the leverage is L = A ÷ E. If the assets fall by a fraction x, the equity falls by L × x, and it is wiped out when x reaches 1 ÷ L.
Leverage · 2× · 5× · 10× · 25× · 50×Fall in assets that wipes out the equity · 50% · 20% · 10% · 4% · 2%
Worked example 1. A fund has equity of 4 supporting assets of 100, a leverage of 25. It holds bonds with a modified duration of about 8, financed by borrowing. A convergence trade makes money if a yield spread narrows, but if the spread widens by 50 basis points, the bonds fall by about 8 × 0.5 = 4 per cent of their value: a loss of 4 on assets of 100. That equals the entire equity. A spread widening of 50 basis points is not extraordinary in a crisis, and in 1998 some spreads moved by far more. The trade was not wrong in the long run, since spreads did eventually converge, but the fund could not survive the interval.
Leverage works the same way on the upside. The return on equity is L times the return on assets, less the cost of the borrowing on the extra L − 1: equity return = L × asset return − (L − 1) × cost of borrowing. A modest edge becomes a handsome return, and the track record of LTCM in its first years, with returns reported at roughly 40 per cent in each of 1995 and 1996 after fees, seemed to confirm that the edge was real.
What went wrong in 1998
In August 1998, Russia defaulted on its domestic debt, a surprise that few models had assigned much probability. Investors around the world ran to safety. They bought the most liquid government bonds and sold everything else, and spreads between liquid and less liquid assets, which LTCM was short, widened sharply and not just in one market but in many at once. The fund lost heavily: public accounts put its losses at about $4.6 billion in less than four months, most of its capital.
Four things combined.
1. Leverage left no margin for error. The trades were individually sound, but the capital could not carry them through a widening.
2. Correlation went to one. LTCM's positions were spread across many markets, and its risk models had treated them as largely independent, so that a loss in one would be offset by gains elsewhere. In the crisis, all the trades were exposed to the same underlying factor, the price of liquidity, and they lost together. The diversification that the models counted on disappeared when needed (compare Lesson 9.3's pods).
3. Size. LTCM's positions were so large that, when it tried to reduce them, it moved the prices against itself (Lesson 4.4), and other traders who knew or guessed its positions traded ahead of its sales.
4. Financing and the short history. The fund's risk models used a history of a few years of calm markets, which had no event like August 1998, and its funding rested on short-term borrowing that lenders could withdraw or reprice. As losses grew, margin demands grew, forcing more sales.
By September the fund was close to failing, with positions so large and so entangled with the big banks that its default threatened to disrupt markets. The Federal Reserve Bank of New York convened its creditors, and a group of 14 banks and securities firms contributed about $3.6 billion to take over the fund and wind it down in an orderly way. The Fed did not lend money. The investors, including the partners, lost most of what they had put in.
The lessons
Leverage kills the ability to wait. A convergence trade is right if you can hold it until it converges, and leverage takes away that option.
A model fitted to calm data understates the tail. The Value at Risk numbers of LTCM implied a loss of the kind that occurred in August 1998 to be so rare as to be practically impossible, which is a sign of a model that does not allow for fat tails and regime change (Lesson 2.2). Stress tests that assume correlations of one are more useful.
Liquidity is a risk factor in its own right. The price of liquidity moves, and positions that are hard to sell are the ones that lose most when everyone needs to sell.
Size is a risk. If you cannot leave without moving the market, you do not have the liquidity your risk model assumes.
Funding is part of the strategy. Long-term financing and lock-ups for investors reduce the risk of being forced to sell, and cost money.
The quant quake, August 2007
On 6 to 10 August 2007, many quantitative equity market-neutral funds, the kind of strategy described in Lesson 5.3, suffered large and unexpected losses over a few days, with no news about the stocks involved and no big move in the overall market. The funds that were affected typically had low volatility and relied on leverage to turn small, diversified edges into acceptable returns. Amir Khandani and Andrew Lo of MIT studied the episode in papers published in 2007 and 2011. They found that losses were concentrated around 7 to 9 August, and that on 10 August a good part of them reversed, a pattern that looks less like a change in the value of the stocks and more like a temporary price pressure from forced selling.
The unwind hypothesis
The explanation most commonly given, often called the unwind hypothesis, runs as follows. Many quantitative funds held similar positions, since they used similar factor models, built on similar data and common ideas such as value, momentum and earnings revisions, and used leverage. At the time, credit markets were already under stress from the first losses on US subprime mortgages. Some fund or funds, possibly because of losses elsewhere in the firm and margin calls, had to liquidate large portfolios quickly. Their sales pushed down the stocks they were long and pushed up those they were short. Other funds with the same positions then suffered losses on both sides, which cut their capital and forced them to reduce leverage, which meant selling more, and so on. The whole process was a liquidity spiral: selling pushes prices down, the losses force more selling. When the forced selling stopped, prices partly recovered, as the reversal on 10 August suggests. The exact identity of the sellers was not confirmed in public, so this remains a hypothesis consistent with the evidence rather than an established fact.
The episode was particularly striking because a market-neutral fund has no exposure to the market, and its managers could reasonably believe that a market fall was not the danger. The danger instead came from other participants holding the same trades: a risk of crowding.
A toy model of a liquidity spiral
We can build the mechanism in a few lines. Take five identical funds, each holding the same portfolio of 100, financed with equity E = 100 ÷ L and the rest borrowed. A shock lowers prices by 2 per cent. Each fund's equity falls, so its leverage rises above target L. Under a margin rule it must sell enough to restore leverage L. The sales push prices down by an amount proportional to the total sold: the price falls by a fraction κ times the share of all holdings that is sold. A larger κ means a thinner market. The lower price causes more losses and more selling, and the process repeats until nothing more needs to be sold, or the funds fail.
The first round has a neat property. A fund with leverage L whose assets fall by a fraction s loses sA. To restore leverage it must sell (L − 1) × sA, that is, (L − 1) times its loss. At leverage 10, a loss of 2 requires a sale of 18. At leverage 3 the sale is only 4. Higher leverage means the forced selling is a multiple of the loss.
We iterated the model until it settled. The initial shock is a 2 per cent price fall.
Leverage · Final price fall, deep market (κ = 0.1) · Final price fall, thin market (κ = 0.3)3 · 2.49% · 4.75%
5 · 3.25% · 16.89%
8 · 5.14% · 27.90%
10 · 6.76% · 28.69%, and all five funds fail
In a deep market with low leverage, the spiral hardly matters: a 2 per cent shock becomes 2.5 per cent. As leverage and the thinness of the market rise, the amplification grows sharply, and not in proportion: at 5 times leverage in a thin market the 2 per cent shock becomes 17 per cent, 8.4 times the original, and at 10 times leverage the funds fail altogether. The danger comes from the combination of leverage, many holders of the same position, and a market with limited depth.
The lessons
Crowding is a hidden risk. A fund can be hedged against every common factor and still be exposed to the other funds that hold the same positions. Positions that are popular with similar funds are exposed to a shock that has nothing to do with their fundamentals.
Market neutrality does not mean safety. The 2007 losses came to funds that were neutral to the market and to factors, and that is exactly why they were leveraged.
The correlation of strategies is not stable. Funds with different names and managers had the same trades, so they lost together, a point that applies to the multi-manager platforms of Lesson 9.3.
Leverage turns a temporary price move into a permanent loss. Without forced selling, the prices recovered within days, and funds that could hold their positions did well. Those that were forced to sell crystallised the loss.
Watch for the unwind in the data. Measures of how many funds hold the same stocks, and how strongly factor returns suddenly reverse, can give an early warning.
Other failures, briefly
Amaranth Advisors (2006). A multi-strategy fund lost about $6 billion in September 2006, mostly in natural gas futures spreads. One trader's concentrated positions had grown to a very large share of the fund's capital and a large share of the market's open interest in some contracts. When the spreads moved against it, the fund could not exit without moving prices. The lessons are concentration and liquidity.
Knight Capital (2012). On 1 August 2012, a faulty software deployment at the US market maker Knight Capital sent a flood of unintended orders into the market. In about 45 minutes the firm lost roughly $440 million, more than its available capital, and had to be rescued by new investors. The lesson is operational risk: testing, release controls, kill switches and monitoring matter as much as the strategy.
Archegos Capital (2021). A family office took very large, concentrated, leveraged positions in a few stocks through swaps with several banks. When prices fell, margin calls forced it to liquidate, and its banks, which had not seen each other's exposures, suffered losses totalling several billion dollars. The lessons are concentration, leverage and counterparty transparency.
The same patterns recur in other markets, including India's, wherever leverage, concentrated positions and thin liquidity meet.
Failure · What happened · PatternLTCM, 1998 · Convergence trades at about 25 times leverage lost most of the capital when spreads widened after the Russian default · Leverage, correlation going to one, liquidity, size
Quant quake, 2007 · Market-neutral quant funds lost together on crowded positions in a few days · Crowding, liquidity spiral, forced deleveraging
Amaranth, 2006 · A concentrated natural gas spread position lost about $6 billion · Concentration, liquidity
Knight Capital, 2012 · A software error lost about $440 million in 45 minutes · Operational risk
Archegos, 2021 · Concentrated leveraged swaps forced a liquidation that hurt banks · Concentration, leverage, opacity
## What the failures teach about risk
1. Limit leverage to what you can survive. Set it so that the worst move you can imagine, with the liquidity you will actually have, does not force a sale. Remember L − 1 times the loss.
2. Stress test for the world where correlations rise. Assume diversification fails, and that liquidity dries up at the same time.
3. Measure crowding. Know who else holds your positions, and how large the total is compared with the daily volume (Lesson 4.4).
4. Size positions against the market's liquidity, not against your own risk model alone.
5. Secure your funding. Term financing, longer lock-ups for investors and conservative margin terms are insurance against forced selling.
6. Do not trust a short history. A risk model fitted to years of calm data will say that a crisis is nearly impossible (Lessons 2.2 and 4.2).
7. Control operations. Test software, separate duties, use limits and a kill switch.
8. Keep risk independent. The risk function must be able to say no to the people who make money.
9. Respect model risk. Every model is a simplification (Lesson 8.4), and the failure comes where the model is silent.
Module 11 develops the tools for measuring and managing these risks.
The code below reproduces the leverage arithmetic and runs the toy liquidity spiral.
python
import numpy as np
1. leverage: the fall in assets that wipes out equity, and the forced sale after a loss
for lev in (2, 5, 10, 25, 50):
print(f"leverage {lev:>2}: equity wiped out by a fall in assets of {100 / lev:.0f}%")
assets, equity = 100.0, 4.0
duration, spreadmove = 8.0, 0.005
loss = assets duration spreadmove
print("a spread widening of 50 bp on a duration of 8 costs", loss, "on assets of", assets, "with equity of", equity)
def forcedsale(leverage, shock, assets=100.0):
equity = assets / leverage
loss = shock assets
newassets, newequity = assets - loss, equity - loss
return loss, newassets - leverage newequity # sale needed to restore the target leverage
for lev in (3, 10):
loss, sale = forcedsale(lev, 0.02)
print(f"leverage {lev}: a 2% shock loses {loss:.1f}; the sale needed is {sale:.1f} = {sale / loss:.0f} times the loss (L - 1 = {lev - 1})")
2. a toy liquidity spiral with five identical funds that sell to restore their leverage
def spiral(leverage, funds=5, shock=0.02, kappa=0.3, assets0=100.0, rounds=60):
equity0 = assets0 / leverage
debt = np.full(funds, assets0 - equity0)
units = np.full(funds, assets0) # units of the asset, at a price of 1
price = 1.0 - shock
totalunits0 = funds assets0
failed = np.zeros(funds, dtype=bool)
for in range(rounds):
equity = units price - debt
sell = np.zeros(funds)
for i in range(funds):
if units[i] <= 1e-9:
continue
if equity[i] <= 0: # the fund has failed: everything is sold
sell[i], failed[i] = units[i], True
else:
sell[i] = max(units[i] - leverage equity[i] / price, 0)
if sell.sum() < 1e-6:
break
debt = np.maximum(debt - sell price, 0) # sale proceeds repay borrowing
units = units - sell
price = 1 - kappa sell.sum() / totalunits0 # selling pushes the price down
return 1 - price, int(failed.sum())
print("final price fall after a 2% shock (and the number of funds that fail):")
for kappa, label in ((0.1, "deep market"), (0.3, "thin market")):
row = []
for lev in (3, 5, 8, 10):
fall, failed = spiral(lev, kappa=kappa)
row.append(f"leverage {lev}: {fall 100:5.2f}% ({failed} failed)")
print(f" {label} (kappa = {kappa}): " + " | ".join(row))
Common mistakes
Treating high leverage as a free multiplier of an edge. It multiplies the chance of ruin as well as the return.
Believing diversification will hold in a crisis. Correlations rise, and the factor that all positions share, such as liquidity, dominates.
Judging risk by a short, calm history. A crisis is not in the sample.
Ignoring other people's positions. A crowded trade is exposed to the actions of those who hold it with you.
Assuming market neutrality means safety. Neutral funds can still be exposed to forced selling and crowding.
Sizing positions to the risk model and not to the market's liquidity. You cannot sell what the market cannot absorb.
Relying on short-term financing for long-term positions. The lender can withdraw at the worst time.
Neglecting operational controls. A software error can be as costly as a bad trade.
Learning only from your own failures. The patterns above recur across firms, markets and decades.
Key takeaways
LTCM, founded in 1994 with Nobel laureates among its partners, ran convergence trades at about 25 times leverage: roughly $4.7 billion of equity on more than $100 billion of assets. A fall of 1 ÷ L in the assets wipes out the equity, so 4 per cent at 25 times, which a spread widening of 50 basis points on a duration of 8 produces.
After Russia's default in August 1998, liquidity-related spreads widened in many markets at once. The fund's apparently diversified positions all lost together, it lost about $4.6 billion in less than four months, and a group of 14 firms put in about $3.6 billion under the Federal Reserve Bank of New York's coordination.
The lessons are the cost of leverage, correlation going to one, liquidity as a risk, size, and the dependence on short-term funding and a short history.
In August 2007, many quantitative equity market-neutral funds lost together over a few days and partly recovered afterwards. The leading explanation, the unwind hypothesis, is forced deleveraging of crowded, similar positions, which is a liquidity spiral.
A fund with leverage L that loses a fraction s of its assets must sell (L − 1) times its loss to restore its leverage. In a toy model of five identical funds, a 2 per cent shock becomes a 4.75 per cent fall at 3 times leverage and 28.7 per cent at 10 times in a thin market, with every fund failing.
Other failures show other patterns: Amaranth (concentration and liquidity), Knight Capital (operational risk) and Archegos (concentration, leverage and opacity).
Limit leverage, stress test with rising correlations and drying liquidity, measure crowding, size to market liquidity, secure funding, control operations and keep risk independent.
Check yourself
1. A fund has equity of 8 and assets of 160. What is its leverage, and what fall in the assets wipes out its equity?
Leverage = 160 ÷ 8 = 20. The equity is wiped out by a fall of 1 ÷ 20 = 5 per cent.
2. The fund's assets fall 2 per cent. How much must it sell to restore its leverage of 20?
The loss is 3.2. The required sale is (L − 1) × loss = 19 × 3.2 = 60.8, so about 39 per cent of the remaining assets.
3. Why did LTCM's positions, spread across many markets, lose together in August 1998?
They were all exposed to the same underlying factor, the price of liquidity. In the flight to safety, the spreads on less liquid assets widened in every market at once, so the diversification that the risk models counted on disappeared.
4. Why can a market-neutral fund be hurt by a crowding unwind even if its beta and factor exposures are zero?
Because the losses come from other funds' forced selling in the same stocks, not from the market or the factors. The risk is in who else holds the position.
5. A risk model is fitted to three years of calm data and says that a loss of 10 per cent is a one-in-a-million event. What should you conclude?
That the model is probably wrong about the tail: three years cannot support a claim about a one-in-a-million event, calm data lacks crises, and fat tails and rising correlations are left out. Stress tests with plausible crisis scenarios are needed.
Try this
Set aside forty-five minutes. You need Python and the code in this lesson.
1. Run the code. Check the leverage table, the forced sales and the spiral table.
2. Change the shock to 1 per cent and to 4 per cent. How does the final price fall change at each leverage in the thin market?
3. Change the number of funds from 5 to 20 with the same total market size, so that each fund holds less. Does the spiral get better or worse, and why?
4. Add a condition that funds only sell half of what is needed each round. What does that do to the final fall and the number of failures?
5. Use the leverage simulator to find the leverage at which a 3 per cent fall in assets wipes out the equity.
6. Read a public account of LTCM, such as Roger Lowenstein's When Genius Failed, and list three decisions that, taken differently, would have let the fund survive.
7. Write a short note: for a strategy you know, what its version of "the spread widens 50 basis points" is, what its leverage is, and how it would survive it.
A good result is a leverage table you can do from memory, a liquidity spiral whose amplification you can explain and a list of survival rules for your own strategy. This completes the module on hedge funds. The next module turns to the formal tools of risk management: value at risk, expected shortfall, portfolio theory and stress tests.
Read more
Roger Lowenstein's When Genius Failed: The Rise and Fall of Long-Term Capital Management is the standard narrative account, and Philippe Jorion's 2000 paper "Risk Management Lessons from Long-Term Capital Management" in the European Financial Management journal analyses the risk failures. Amir Khandani and Andrew Lo's 2011 paper "What Happened to the Quants in August 2007? Evidence from Factors and Transactions Data" in the Journal of Financial Markets is the main study of the quant quake. Markus Brunnermeier and Lasse Pedersen's 2009 paper "Market Liquidity and Funding Liquidity" in the Review of Financial Studies models liquidity spirals. Scott Patterson's The Quants tells the story of 2007, and Nassim Taleb's The Black Swan discusses why models fail in the tail. For operational failures, the SEC's 2013 order on Knight Capital describes the software error.
Tags: Quant Trader LTCM Quant quake Leverage Liquidity risk