LTCM is a hedge fund founded by the bond arbitrage group from Salomon, plus Nobel laureate economists (Merton and Scholes) from Harvard.
They operated from 1994 to 1998, culminating in $1 turning into over $4 for each dollar invested in 1993 (and a $4.5 billion total capital), and losing it all (each $1 worth 33 cents) in 5 weeks in 1998. The Fed organized a bailout operation to ingest capital to LTCM from major Wall Street banks, out of fear of LTCM collapsing triggering a series of crises.
LTCM specialized in spread trades (usually betting the spreads to converge), a field of expertise inherited from their days at Salomon, whose arbitrage unit was its main source of income.
Spread trade is identifying (usually) a pair of instruments, with one or both instruments thought as mispriced (due to short term market inefficiency, or psychology). E.g. two 10yr US treasury bond issues within a 6-month time period, the new issue (on the run) after its issuance usually has a lower yield and higher price compared with the old issue (off the run), due to the new issue more actively traded (thus considered more liquid than the old issue), although the chance of US govt defaulting within this 6-month period is practically 0, meaning over time the two bonds aren't that different and the yields and prices should converge, thus they long the cheaper one and short the more expensive one, and no matter if the prices of both go up or down, as long as spread narrows LTCM makes money. This trade, albeit fairly safe, only pays pennies since the spreads usually aren't that large to start with. To make a fair profit (compared to its capital) LTCM borrows a lot to put in these trades, building a leverage of 30:1 (for each dollar of their capital (the money they raised from investors), they borrow 30 dollars from banks at a really low sometimes none haircut to invest in their trades. LTCM was able to do so in a bullish market where banks were actively looking for parties to invest money in, and were afraid of losing LTCM's business to another).
Similarly, such opportunities can be found in mortgage PO (principal only) / IO (interest only) strips: if interest rate (borrowing cost) goes down, people tend to refinance their mortgages and pay back early, thus IO yields will go down and PO yields go up, treasury bond yields go up. (Making these proxies to bet on interest rate movement). Another example being the yield difference between Italian and German bonds. Italian bonds, typically considered higher credit risk, yields higher than German bonds. Yet with EU and their unification of currencies on the horizon, this spread should narrow.
LTCM's phenomenal gains were from such trades, achieved with very high leverage.
Such opportunities are found and analyzed via models assuming markets are / will become efficient over time, market prices are continuous, volatility is an innate constant of a particular instrument, and volatility of today / tomorrow's can be predicted with those of the past.
For LTCM partners themselves, they invest their money in the fund, and charge a ridiculous fee to their investors. They were able to entice investors with such fees due to the high profile fund managers (raising 2 billion in 1993). The details of their trades are not disclosed to investors.
As others gradually catch up and utilize similar methods to identify mispriced opportunities, LTCM resorts to more (risky) trades in equity volalitity trading, merger arbitrage, and directional bets. And usually such are done via derivative contracts with major banks. The fund had 60K such contracts, and is deeply entangled with financial institutions world-wide by the time of collapse. Such contracts (made over the counter) do not show up in their statements / sheets. Usually to keep their trades secret they pick different counterparties for the same trade. E.g. to do a spread trade on Italian and German bonds, Goldman may see one leg and JP Morgan another, making it difficult also for banks to identify their risk and exposure via LTCM.
As for the more risky trades, equity vol bets on markets becoming more efficient, and in a turbulent time volatility should go down to a more stable level. The higher the volatility, the higher the price of equity options (you'd pay more to be able to buy something at a fixed price, in a more turbulent environment). Thus LTCM shorted equity options (again, with a huge leverage).
Merger arbitrage is a bet that an annouced merge will work out, causing the stock price of either party to move towards an expected level. LTCM does not have expertise or information advantage in this area.
Directional bets are plain gambles without hedging, e.g. buying high yield junk bonds, emerging markets, etc hoping they won't default.
The triggering event was Russian govt bond defaulting in 1998 (before that crisis in Asian currencies, and shortly afterwards turbulence in South America). LTCM had Russian bonds (directional bets) but that by itself could not have brought down the fund. The real problem is its effect on investor psychology: nuclear powers don't default, or do they? Investors flocked to more secure instruments (US treasury bonds), and quickly dragging down the prices of everything else. Treasury yields dropped to historical low, and high credit risk instruments yields grew extraordinarily high. The spreads widened, for a prolonged period of time. In the long run LTCM's trade would have made money, but the company's capital has to be able to survive the spread widening period (given its leverage ratio, the pressure was big even with a small percentage, and LTCM could not afford to be wrong for long). For that the company is forced to sell some of its positions, but there are no buyers (no liquidity) as everyone only trades treasury. Spread kept widening for 5 weeks, and LTCM lost most of its capital, and it was either a sell, bail out or a bankruptcy. Govt agencies (the regulators) should not meddle in the lives and deaths of hedge funds (prevention as opposed to intervention), however in the case of LTCM, to prevent a further disaster, the Fed did intervene by having major Wall Street banks form a consortium, put money in LTCM and take over.
A predecessor event that hurt LTCM's capital was that they returned some outside investor's money (against those investors' will) in late 1997 when the fund was doing extremely well, reasoning being the investing opportunities aren't as many. The fund wishes to maintain its level of leverage, so it returned some capital. (and the founders are the ones getting hit hardest when the ensuing crisis came: in the losing streak leverage soared to 100:1.)
How about diversifying their portfolio? LTCM is diversified, bonds, equities, derivatives, geolocations, currencies, etc. In form, but not in essence: in different geolocations / currencies they invest in junk bonds, or make the same bet that spreads should converge, market should head towards the direction of more liquidity and higher efficiency. When the global market doesn't head in that direction? They lose. How likely is this to happen on a global scale? Perhaps more likely than LTCM's models foretold.
What about risk management meetings LTCM has every week? The partners do assess their exposures very often, yet there is no independent body dedicated to risk management. It always ends up being the star traders getting their way, putting bets on areas LTCM has little advantage in, or placing their trust in models whose assumptions might not hold in a crisis.
Understanding the models: what assumptions do they make, are they reasonable assumptions, would they be able to account for a real crisis, in which investors are no longer rational? Understand their limitations.
Liquidity and leverage: a high leverage means you can't afford to be wrong continuously for long. This plus a market whose liquidity can be questionable in times of a crisis, is like playing Russian roulette with yourself.
Greed and hubris: being invincible in one asset class does not guarantee you'll be invincible in the next one, not even your next investment in the same asset class. Do due diligence, assess the risks, and make sure this process isn't just formality.