Long-Term Capital Management, L.P.

Long-Term Capital Management, L.P.
Jiao Yunfan Peng Xiaoli Jin Long Yu Shuoning

Outline Background Information about LTCM Trading Strategies
Selling Volatility Risk Arbitrage Swap Spread- Convergence Strategy Yield-Curve relative-value trades A uniform analysis frame A recent empirical case Portfolio Risk Management The Fail Where did LTCM Go Wrong Rescuing LTCM

Background Information

Established in early 1994 with a initial capital size of $1 billion. Led by Mr. John Meriwether, once the Vice Chairman of Salomon Brothers in charge of the fixed income business. Engaged in trading strategies that would exploit market pricing discrepancies. Relied heavily on sophisticated analytical models. Capital doubled after three and a half years in 1997. Then, what happened?

What Happened to LTCM in Aug.,1998 ?! On 23 Aug.,1998,LTCM lost $553 million, 15% of its capital Correlations of all trades = 1 “Don’t ever call me at home again!” They must sell something -- in a market WITHOUT A BUTER…

Trading Strategies Selling Volatility Risk Arbitrage
Swap Spread- Convergence Strategy Yield-Curve relative-value trades A uniform analysis frame A recent empirical case

SAMPLE TRADE 1: Selling Volatility
Trade Introduction Risks

Selling Volatility The market expected that the implied volatility was higher than that of LTCM’s perception. So LTCM thought that the option price was overvalued according to B/S model. They bet that option prices would fall in the future. So LTCM sold options to earn the price discrepancy. LTCM simultaneously sold long-term puts and calls on an index.

Selling Volatility: profit and loss
If the stock volatility was small, that is to say, the price was near the strike price K, LTCM would make a large profit. However, if the stock price moved largely in either direction---the volatility was large, LTCM would suffer a loss. The smaller the volatility was, the more profit LTCM would gain. But if the index level moved outside the lower limit or the upper limit, a loss would occur. P Short put Short call K S K was equal to the forward price of the index.

Selling Volatility: Risks
Daily settlement needed a lot of working capital. This was difficult to maintain over five years. It was difficult to predict the market volatility. Using historical data was risky. And the model did not include extreme event. Incorrect comparison of volatility (Heston and Nandi, 2000) Someone comparing the implied volatility with the simple measure of historical volatility might often be tempted to sell straddles. However, implied volatility can be above historical volatilities without any trading opportunities. (Implied volatility reflects the drift or the expected value of the variance under the risk-neutral distribution, which tends to be higher than the drift of the variance under the data-generating distribution, under negative correlation between returns and volatility.)

Selling Volatility: Risks (continue)
skew (smirk) implied volatilities In-the-money call has higher implied volatility than a near-the-money call correlation between return and volatility Negative correlation between equity market returns and implied volatilities could make the straddle values highly sensitive to the direction of the market. rebalancing the straddle to maintain minimal exposure to the direction of the market is theoretically feasible, the rebalancing process exposes a trader to model risk and may not always help.

SAMPLE TRADE 2: Risk Arbitrage

Risk arbitrage Risk arbitrage / merger arbitrage
Risk arbitrageurs would attempt to capture the spread by purchasing the shares of the target company and selling short of the shares of the acquirer. Tend to provide stable returns (about twice the T-bills index) in most market environments. In 1997, the fund’s risk arbitrage portfolio: contained about $5 billion of long position involved over 30 different merger situations, most of which US companies A 5% net spread on these positions represent $250 million of expected annual incremental profits

Risk arbitrage: rationale
Following the announcement of a acquisition, the target’s shares tended to trade at a discount to the consideration offered – usually the shares of the acquirer or cash. Only some of the discount could explained by the time value of the money or the risk of the acquisition not being consummated. LTCM believed the spread exist because there were fewer natural holders of the target’s shares while the merger was being completed, many of target’s shareholders preferred to take profits and not bear the risk of a deal break.

Risk arbitrage: strategy
Participate in situations where the risk of a break was manifestly very small avoided hostile takeovers avoided mergers that faced significant regulatory hurdles Preferred stock deals to cash deals Cash deals were more likely to break or be renegotiated Stock deals tended to have higher expected profits because selling short was difficult and/or costly for many investors

Risk arbitrage: could it profit?
Less risky deals had lower spread. Could the fund still profit? The fund could finance the trades very efficiently. ( zero haircuts) For any particular merger, LTCM considered the risk of a break to be nearly uncorrelated with its other strategies. The spreads therefore did not have to be large in order for risk arbitrage to enhance the Sharpe Ratio of the fund.

Risk arbitrage: risks and drawbacks
Negative factor: delay of the announced deal as it reduces the annualized return Breakup of the announced deal: regulatory reasons, lack of agreement, shareholder rejection, unexpected event, counterbid… A decrease in the deal’s flow: all managers chasing the same deals

SAMPLE TRADE 3: Swap Spread
Convergence Trade

Swap Spread Trade Introduction Counterparties LTCM U.S. Treasury FUND
BOND FIX T-BOND INTEREST LIBOR Counterparties LTCM U.S. Treasury FIXED INTEREST FUND FUND REPO BOND COLLATERAL Investors Net Flow X to the Fund: X = (FIX T-BOND INTEREST – REPO) – (FIXED INTEREST – LIBOR) = (LIBOR – REPO) – (FIXED INTEREST - FIX T-BOND INTEREST ) = (LIBOR – REPO) – SWAP SPREAD =20bps-SWAP SPREAD

Swap Spread Profit and loss Counterparties LTCM U.S. Treasury FUND
BOND FIX T-BOND INTEREST LIBOR Counterparties LTCM U.S. Treasury FIXED INTEREST FUND FUND REPO BOND COLLATERAL Investors Fix T-bond Interest Falls Swap Spread Widen Betting on the Widening Bond Value Increases Unwind the Position at a PROFIT before the Maturity

Swap Spread Profit and loss Counterparties LTCM U.S. Treasury FUND
BOND FIX T-BOND INTEREST LIBOR Counterparties LTCM U.S. Treasury FIXED INTEREST FUND FUND REPO BOND COLLATERAL Investors Fix T-bond Interest Rises Swap Spread Narrow Betting on the Widening Bond Value Decreases Stay with the position or Suffer a mark-to-market LOSS

Swap Spread: Example DATA: repo swap Fixed Floating 6.77% 6.94%
Libor-20bp Libor -17bp -20bp

Swap Spread: Example Here we consider the swap-spread risk, so we will consider the to fixed cash flow’s duration, we just consider two factors’ influence: The swap spread The interest of Treasury bond. Cash flow of repo: 6.77% Libor-20bp Cash flow of swap: Libor 6.94%

Swap Spread: Example Valuation of repo

Swap Spread: Example Valuation of swap The term structure curve

Swap Spread: Example If we assume :
The definition of swap spread: If we assume : 1, The T-bond’s yield curve is flat r , ss is also flat ss. We use discrete calculation to calculate the result, so we have……

Swap Spread: Example Value of repo: Value of swap:
So the value of the portfolio:

Swap Spread: Example Only from mathematic analysis, we can get the following conclusion:

Swap Spread: Example The parameters are:
We assume that T=20 years, then we get that: From the notes of the case file, we assume T=20 is only a kind of approximation, and it works well.

Swap Spread: Example At the beginning we assume that we the principal is $100, so we can get the following conclusions: If ss (swap spread) changes 1bp, that will make the value of the portfolio change about 0.144% of the nominal principal If the interest of the Treasure bond changes 1bp, the value of the portfolio will only change about %, nearly zero. If LTCM holds a position whose nominal size is $1 billion, that means if the swap spread increase 1bp, the portfolio will increase about $1.44 million. While if the T-bond’s interest increases 1bp, the portfolio will decrease only about $14 thousand. From the case we know LTCM built the position to an exposure of $5 million per basis spread, the nominal principal size was about $5 billion, that was about 0.1%=5 million/5 billion. LTCM mainly considered the risk of SWAP SPREAD, but not the interest risk.

SAMPLE TRADE 4: Relative Value Strategy
Yield Curve Relative Value Strategy

Relative Value Strategy
The yield curve is concave in the middle terms. As a normal yield curve the curve should slope up, when you find such a curve shape, you can do arbitrage following the below strategy-Butterfly Strategy: T Y Preferences of specific maturities. Pay fixed-rate in 3 year swaps Receiving fixed-rate in 7 year swaps Pay fixed-rate in 10 year swaps. Fixed Libor Libor Fixed Libor Fixed

Time 1 2 3 4 5 6 7 8 9 10 rate 5% 5.1% 5.2% 5.5% 5.8% 5.9% 6.2% 6.1% 6.0% 5.7% dur -0.91 -1.72 -2.45 -3.06 -3.56 -4.02 -4.33 -4.70 -5.03 -5.43 If we assume that the principal of the 3 securities are all $1, and the coupon rate is 10%, then we can calculate the sensitive factor of different security. We get the following result: { The portfolio’s duration should be zero. If the yield curve moves parallel, we can got the above 2 equations. We need one more equation……

If the yield curve rotates around the point (0, spot)…… Year 1 2 3 4 5 6 7 8 9 10 Zero-coupon rate 5% 5.10% 5.20% 5.50% 5.80% 5.90% 6.20% 6.10% 6.00% 5.70% dur of per USD -0.91 -1.72 -2.45 -3.06 -3.56 -4.02 -4.33 -4.70 -5.03 -5.43 Cash Flow 1.13 0.1 1.1 1.22 1.32 If we assume as before when the YC rotates, we should calculate the duration from a totally new perspective: When the curve turns a very small angle, we can conclude that the interest-change should be positive proportional to the Time. The cash follow will change now, we should first decide the cash flow. T Y

Assume that the portfolio size is one dollar, and we spend dollars on each security. Then we know that we can buy Cash Flow Table: (for each share’s investment) Year 1 2 3 4 5 6 7 8 9 10 Security 1 0.088 0.973 Security 2 0.082 0.901 Security 3 0.076 0.835 krDuration -0.91 -1.72 -2.45 -3.06 -3.56 -4.02 -4.33 -4.70 -5.03 -5.43 How can we get this table? The numbers are got from the following formula In each row end, we should consider the principal.

Then we can get: That is: This should be zero, so we get the third equation.

Substitute all the data, we get: Also we know:

The result is Until now we have analyze the portfolio’s sensitive, we build the positions that will not change when the Yield Curve moves, parallel or rotate. Because the yield curve in a 2-dimension space, it can only move parallel or rotate. So we know that if the curve’s shape do not change, the portfolio will not change, only the curve moves relatively-that is the curve’s shape changes, the portfolio’s value will change~ ,so we call it Relative-Value Strategy!

Maturity Yield Risk-Free Initial Curve This will be very risky.

Uniform Analysis Frame

In fact the idea has been used in the management of the asset and liability, in Reitano ’s thesis ‘Non-parallel Yield Curve Shifts and Immunization’ (Journal of Portfolio Management 1992), he discussed the immunization strategy in the portfolio management so that the portfolio’s value will not change when the yield curve shifts nonparallel. Here we also used this kind of idea to do arbitrage, when the yield curve shifts, we make sure that the value do not change, but and only when the yield curve changes its shape, then we gain or loss.

If you find that there are n factors will influence your portfolio’s value, that means: Now we choose n securities : Each security, we hold omega i shares If we want to use the immunization strategy, we should promise that : Immunization Matrix

So we can solve the above equation, to get the immunization strategy. But our purpose is to do arbitrage, so we will find that we do not want to use this immunization strategy to hedge all the risk. So we can have the following relax-equation.

Uniform Analysis Frame: Look back!
How to use our model to analyze the relative strategy? The relative strategy should be a three factors model: 1.The parallel movement.—Delta r 2.The rotating angle.----Delta Theta 3.The curvature of the curve.—Curvature This is the relax-variable!

Uniform Analysis Frame: Look back!
Now we only have n-1 immunization equations, and n variables, so there is one variable is free! And we have another equation: So we can solve it! 1.The portfolio is also immune to the n-1 factors. 2.The factor j will influence the portfolio’s value. 3.If the factor j goes as our judgment, then we will lose This model can also be used in the Swap Spread strategy, and other multi-factors arbitrage model .

How to extend your model to a dynamic model-----consider the Time. How to add the influence of trading cost-----it might be very practical~ How to consider a continual model----very interesting in theory Whether the equations have solution? Under what condition the solutions do not exit? Whether can the extend-immunization matrix be diagonal? Why?

A Recent Empirical Case
From American Market’s Prove

A Recent Empirical Case
We prepare some data got from American market to prove the strategies illustrated are efficient. Data date: 5/19/2008 Data resource: quote.yahoo.com

US Treasury Bonds Rates
Maturity Yield Yesterday Last Week Last Month 3 Month 1.60 1.58 1.44 1.22 6 Month 1.68 1.66 1.63 1.46 2 Year 2.24 2.21 2.45 1.76 3 Year 2.18 2.15 2.37 1.69 5 Year 2.96 2.97 3.17 2.60 10 Year 3.77 3.78 3.86 3.48 30 Year 4.52 4.54 4.58 4.32

Municipal Bonds Maturity Yield Yesterday Last Week Last Month 2yr AAA
2.40 2.28 2.45 2.32 2yr AA 2.39 2.34 2.33 2yr A 2.81 2.59 2.64 2.76 5yr AAA 2.99 2.88 3.07 5yr AA 2.89 3.11 3.03 5yr A 3.30 3.40 3.45 3.24 10yr AAA 3.65 3.60 3.72 3.58 10yr AA 3.62 3.63 4.06 3.49 10yr A 3.69 4.13 3.75 20yr AAA 4.38 4.47 4.82 4.34 20yr AA 4.46 4.48 4.59 4.70 20yr A 4.37 4.43 4.73 4.64

Corporate Bonds Maturity Yield Yesterday Last Week Last Month 2yr AA
4.02 4.04 3.97 4.08 2yr A 3.81 3.86 3.72 5yr AAA 4.14 3.66 4.21 4.34 5yr AA 4.76 4.66 4.60 4.64 5yr A 4.98 4.95 4.81 5.29 10yr AAA 5.02 5.04 5.53 5.30 10yr AA 6.00 5.73 5.83 5.98 10yr A 5.48 5.56 5.50 5.54 20yr AAA 6.09 6.07 6.04 6.69 20yr AA 5.97 6.08 5.74 5.75 20yr A 6.35 6.33 6.30 6.55

US Treasury Bonds Rates
Black : One month ago Green: One week ago Red : One day ago Blue : Today

Municipal Bonds

Municipal Bonds: Notes
First row: aaa~aa; Column: Different time point; Second row: aaa~a; Column: Different time point; Third row: aa~a; Column: Different time point; Time Point: 2y, 5y, 10y, 20y; Red line has a higher credit quality; Green one is lower.

Corporate Bonds (No AAA)
AA~A; Red is AA, Green is A

Portfolio Risk Management
How did the Fund manage its overall portfolio risk? What is liquidity? How did LTCM manage its liquidity risk?

100% financing and long-short structure implications for how the firm should think about risk management: No explicit equity investment and it is impossible to work directly with measures such as return on equity; Risk could not be measured by the notional sizes of the positions. In particular, the risk of a long-short position depended entirely on the degree to which the profits on the long position could deviate from the profits on the short position.

Value-at-risk Measures Pricing Discrepancies Belief Economic Stress Testing Positions Correlation Long term vs Short term Risk Risk Estimation

Value-at-risk (VaR) Measures VaR can be defined as the worst loss that can happen under normal market conditions over a specified horizon at a specified confidence level. More formally, VaR measures the shortfall from the quantile of the distribution of trading revenues. As before VaR is interpreted as the largest acceptable loss the bank is willing to suffer over a specified period. To cover this loss, the bank must maintain adequate equity capital. In other words, VaR is the amount of capital a firm allocated to self-insurance.

Equity Capital as a VaR measure VaR Example1: swap-spread trade Notional position: $5 billion Gain or loss 5 million for 1 b.p. spread change Expected: 23 b.p. widen in swap spread with a standard deviation of 7 b.p. Results: VaR= $25 million, standard deviation= $35 million. The amount of equity capital that needs to be set aside to cover most of the potential losses is $25 million.

VaR Example 2: Setting the VaR confidence level in relation to the desired rating LTCM capital: $4.7 billion Assuming: Daily standard deviation of profits and losses is $100 million 252 trading days per year Annual volatility:

VaR Example 2: In fact… Targeting at Aa2 Credit rating Distribution of losses normally distributed Distribution of losses with fatter tails than normal distribution ﹥﹥$4.7 billion

Pricing Discrepancies Belief As pricing discrepancies became more pronounced, trades based on these discrepancies would attract more capital from arbitrageurs and other investors, and thus the downside risk of a trade generally diminished as valuations became more extreme. Therefore, the larger the discrepancies are, the more investors and arbitrageurs will join in the trade and the more active and effective the market will be. In other words, finding large pricing discrepancies will reduce the risk the fund is exposed to.

Economic Stress Testing Analyzing how the Fund’s positions would perform if a low probability, high impact event occurred. For example, the Fund had many positions that would be affected by a breakup of EMU that was scheduled to be completed on January 1,1999 in Europe. LTCM would regularly estimates the profit and loss implications of such an event, and if the expected net outcome were a loss, it might restructure the position to reduce the risk.

Positions Correlation At the margin, a position that was uncorrelated with the reminder of the portfolio contributed relatively little risk, and therefore could be held in large size. The Exhibit in the next slide illustrates that the risk of a portfolio increases with the number of positions, depending on the correlation between the profits of the individual positions. Thus, the LTCM control the portfolio risk by holding positions with profits that are uncorrelated as much as possible.

Number of positions (N) Portfolio risk if position profits are perfectly correlated Incremental Risk Portfolio Risk if Position Profits are Uncorrelated 1 100 2 200 141 41 3 300 173 32 4 400 27 5 500 224 24 6 600 245 21 7 700 265 20 8 800 283 28 9 900 17 10 1000 316 16 $100N $100N1/2

Long term vs Short term Risk One-year horizon (long horizons) One-month horizon (short horizons) Financial instruments Prices Determinant Fundamental value Traders’ short-term liquidity needs Risk Lower Higher Correlation Structure Base the correlations on the correlations of the fundamental factors that affected the trades Assume that the various categories of trades in the portfolio were always positively correlated because many other institutions had the same trades on.

LTCM’s stated intention was to take on an amount of risk corresponding to a standard deviation of NAV of 20% per annum. In practice, however, the Fund’s actual and estimated volatility had been much less than 20%. In September, 1997, the Fund had a an annualized standard deviation of $720 million, which represented only a 10.7% risk level. LTCM estimated that its positions had expected annual trading profits of $750 million which did not include about $350 million in annual interest that the Fund would earn on its equity capital. These figures implied that it would take more than a “ten sigma” event for the Fund to lose all of its investor capital in one year, or a thirty-sigma event for the Fund to lose all of its capital in one month.

What is liquidity? What does it mean?
1. The degree to which an asset or security can be bought or sold in the market without affecting the asset's price. Liquidity is characterized by a high level of trading activity. 2. The ability to convert an asset to cash quickly. Also known as "marketability". Examples: 1. It is safer to invest in liquid assets than illiquid ones because it is easier for you to get your money out of the investment. 2. Examples of assets that are easily converted into cash include blue chip and money market securities.

What is liquidity? Our understanding:
For a liquid asset, it can be sold (1) rapidly, (2) with minimum loss of value, (3) anytime within market hours. For obligations, enough liquid assets can be used to meet the payment. The liquidity of a product can be measured as how often it is bought and sold which is known as volume.

Market Liquidity Market liquidity is a business, economics or investment term that refers to an asset's ability to be easily converted through an act of buying or selling without causing a significant movement in the price and with minimum loss of value. The essential characteristic of a liquid market is that there are ready and willing buyers and sellers at all times. Speculators and market makers are key contributors to the liquidity of a market, or asset.

Liquidity Management “Two-way mark to market”
Example: swap-spread trade The Fund would have to post an additional $10 million of collateral Value of the Bond fell to $240 million Initial Long Position of $250 million Treasury bonds Two-way mark to market The bond position appreciated to $260 million The Counterparty would send the Fund $10 million of collateral

Liquidity Management “Two-way mark to market” for contractuals
Contractuals were structured similarly. That is, contractuals were revalued daily, and collateral would flow into or out of the Fund dollar for dollar commensurate with the change in the values of the contractuals. The use of two-way mark to market for contractuals essential for liquidity management. In the swap-spread example, if the value of the Treasury bond position fell by $10 million, the value of the offsetting swap agreement would rise by $10 million (unless the swap spread had widened or narrowed)and LTCM would be able to use the collateral inflow related to the swap to fund the collateral outflow related to the bond. The only flow of capital would be related to net mark-to-market gains or losses on its positions.

Liquidity Management Working Capital Uses Working Capital Resources
Financing haircuts on bond positions Margin requirements for equity and futures positions Working Capital Resources Unsecured term debt, its line of credit and its investor equity. In managing the Fund’s liquidity, LTCM’s chief concern was with the possibility that secured financing might become difficult to obtain or prohibitively expensive, which could occur in the event of an external market disruption or if the Fund found itself in some type of difficulty.

Liquidity Management Managing the Fund’s liquidity:
Estimate the theoretical “worst case” haircuts Eg. 2% on German government bonds Estimate a worst case schedule of potential liquidity needs over time Carefully structure its financing so that the Fund would not be forced to liquidate positions rapidly solely due to disruptions in the financing market In September 1997, although the Fund’s sources of working capital totaled of $7.63 billion, its uses of working capital were less than $1.7 billion- $200 million for haircuts on bond positions, $500 million for margin requirements on equity positions, $780 million for margin on futures positions, and about $200 million for miscellaneous operational purposes.

-----Charles Smithson (1999), reporting LTCM information
Risk Management LTCM believed the combination of its structure of long-term financing, its careful management of liquidity, its large capital base, the transparency created by mark-to-market accounting, and the low risk of its portfolio all combined to give dealers a high degree of comfort. In turn, this resulted in the Fund receiving favorable financing terms relative to other market participants. LTCM asserts that the portfolio was managed so that its target risk was no larger than the risk of an unleveraged position in the S&P 500. -----Charles Smithson (1999), reporting LTCM information

Main Trades and How They Failed
THE FAIL What Happened in 1998 Main Trades and How They Failed Main Risk Concerns

？ Between Jan. to Aug.,1998 > Bank of Volatility
From early in 1998,LTCM began to sell volatility to the market Opportunity Option implied Vol. in 5 years (20%) > Observed historical Vol. (15%) Near-term index option implied Vol. ？ Profit Index Value Short Put Short Call Position Simultaneously sell both put and call in S&P500 and other index in Europe (Net position Hedged) Position Size: Vega=$30m by Sep. 1997, thus 1% option imp.Vol when converged worth $30m An Arbitrage Opportunity? LTCM’s belief: The past can predict the future, history will repeat Option market’s inherent premium: Tailored product with less liquidity Behavior finance: Not only bet on Realized Vol. but also Inferred Vol. Leverage: B-S might be right in long-terms but LTCM faced daily settling

LTCM’s trades were indeed correlated, exposing to similar factors
Between Jan. to Aug.,1998 Some other trades U.S.treasury market: Believe market be inefficient-credit spread would narrow over time Short simple swap rate against LIBOR expressed as T-B+XXbp Europe: Bet spread between spreads of Germany and GB would narrow Exotic bonds: Brazil and Russia without comparative advantage Equity: Buying high-tech firm’s put hedging with S&P500 LTCM’s betting on directions, to be more a speculator than an arbitrageur LTCM’s trades were indeed correlated, exposing to similar factors

Between Jan. to Aug.,1998 Other risks besides volatility: Not pure arbitrage! 1998: A good start U.S bond market’s confidence: historical low credit spread Peak in April: LTCM earned 3% with 285% increase in 50 month

？ Between Jan. to Aug.,1998 Turning downwards: A chain of reaction
From May -Asia’s insatiability began to raise concern -MBS market down -Speculators rushed to Russia, pushing interest high enough to cause a crash U.S. treasuries market -Confidence was dispelled by panic of risk, treasuries become preferred thus spread widened -Only LTCM shorted T-B: A loss ？ A general Credit Problem -Not specified to any security, spread in all markets widened altogether -LTCM lost money in every trade Other markets - Stock market got nervous, more volatile (27%) - European market: Spread and spread of spreads widened for anxiety - Simple swap rate against LIBOR rose for fear Other players retreated -Salomon exited swap market, a shock to both investors’ confidence and liquidity -But LTCM remained optimistic: Selling directional position adding converge position to reduce Model Risk. View the world in rearview mirror again! Other bet in Russia -“Russia wouldn't let the currency fall” -Rely purely on experience and model without considering particularity of Russia

The Fail August 18-21, 1998 On 18, Russia announced a bond moratorium, but the market expected a bailout. While Asia incurred a down fall, Dow went up by 150p On 21, since there was’t any bailout activities, financial market around the world was shocked with panic of general investors Barclays exited its short position in U.K swap market, which pushing the it even higher-bad for still-in LTCM Everyone wanted to be out. Equity market Dow fell 280p before noon. LTCM betting volatility going down, lost a lot. Credit market “All over the world run to credit”: spread in all the market rose Uniform expectation and uni-directional transaction: selling high yield bonds and buying treasuries

The Fail LTCM: Simultaneously loss in all other trades
Off-the-run value up-short sold by LTCM Russian and Brazilian bonds plunged for riskiness-held by LTCM M&A transaction was postponed due to unsteady market environment-risk arbitrage strategy failed Loss with a remote chance did happen In early 1998, their models said the maximum that LTCM were likely to lose in a single trading day was $45m-totally tolerable It was a 10-sigma odds that LTCM could loss all capital in a year On 23 Aug.,1998,LTCM lost $553 million, 15% of its capital In the past, the greatest loss in a single day was 2.9%

Conclusion: Far from liquidity strain ?!
Risk Concerns A over view of operational risk: Aug., Rely on other investors’ decision Still-substantial liquidity A concern of go-on-declining NAV Multiple collateral flows with the same dealer Unable to net Nerves could spread: Extra WC Declining trading volume: Mid-market price is? Covenants on $900m term credit WC $4.08b Equity $2.95b ？ Tied-up $2.1b Unsecured Term Debt $230m Credit Facility $900m Conclusion: Far from liquidity strain ?!

Risk Concerns Liquidity risk Leverage risk
Small hedge funds, copycats, arbitrageurs exited, few players remained Exit was impossible when market lost liquidity-no buyers, people had the same expectation about price, wanted the same products Fund’s size even make block trades more difficult The model assuming other “rational” investors and arbitrageurs to enter the market but fear and risk aversion won ration in a panic 31 Aug., Vol. Went above 30% while credit spread reached 162bp-a inferred spread since no one traded at all. Leverage risk In a no-buyer-market, price went out of the bell curve in LTCM’s model Maybe the damagingly huge spread was short-term, but levered investor might not survive to the day converge came

Risk Concerns Cash flow risk: Global margin call Correlation risk
LTCM(partners’ personal owned management company): Banks became risk averse and might require repayments due to the bad performance The fund: Pressure from Bear Stearns-no agreement and could be terminated at any time Multiple counterparties: LTCM’s original intention was to get best execution In a panic, non of them got the whole picture of a trade, neither did they know the position were in pairs and hedged, thus each demanding more margin than otherwise would. Correlation risk Every bet was losing simultaneously, correlations among trades were 1.

？？ Risk Concerns Effort to refinancing
Partners turned to their customers (e.g.JPMorgan, UBS, ML) for a $500m turn-around capital and to friends (e.g.Buffett) intended to sell a $5 billion worth of merger position To invest or not? Benefits Risks Mispricing Market overreacted to the panic, spreads were widened to an unmoral level and would be converge Information Chance of knowing something about LTCM’s portfolio information Liquidity Transactions would be infeasible in current market situation, investment might be locked on Market behavior “When you lose half, people figure you to down all the way and push the whole market against you.” Probability of bankruptcy and agency cost Managers would take advantage of liquidity to save their own positions due to asymmetric information ？？

Risk Concerns Whether or not invest?-Additional concern of different people Investors and special concerns Large financial institutions (LTCM’s current clients and counterparties) Greater risk: Extra loss if LTCM went bankrupt Greater capital: To be able to ensure LTCM’s turn-around Wealthy individuals <4% Less capital: More uncertainty whether LTCM could refinance the rest $300m Weaker negotiating power: Forced to suffer a loss Super investors More independent decision-making Who would invest under such a situation: Other factors Risk tolerance Expectations Time Horizon

The Model Using of Leverage Correlation and Risk Trading Strategies
WHERE DID LTCM GO WRONG? The Model Using of Leverage Correlation and Risk Trading Strategies

Where Did LTCM Go Wrong? The Model Bell curve
Shape of equity volatility smile is consistent to a “left-side fat tailed” distribution: extremely bad things more probable to happen Fama (1960s) “If the population of price changes is strictly normal, on the average for any stock an observation more than five sigma from mean should be observed about once every 7000 years. In fact such observations seem to occur about one every 3-4 years.” Excluded a risk of a “outlier” The length of sample were too short to encompass black Mondays in history again ruled out extremes Implied Vol. In-the-money Call Out-of-money Put In-the-money Put Out-of-money Call Strike Price

Where Did LTCM Go Wrong? The Model B-S assumption: Constant Vol.
The basic logic of “History would repeat itself” and methods like VAR were not realistic Implied Vol. has fat-tail Realized Vol. were far from a constant number and some times not continuous A ideal market Always assume a continuous price (and other parameters), in reality there were always jumps A liquidity market and rational investor only applied to normal conditions

Where Did LTCM Go Wrong? Using of leverage
Leverage is determined by nature of deep arbitrage-spread were to small and so was risk according to model Risk inherent in lever A leverage of times Different from others, leveraged investor are forced to liquid some of its equities in case of loss to avoid loss overwhelming themselves Leverage position is very sensitive to exposures and other factors When market is not continuous even in short time, leveraged investors may not survive to the day converge comes

Where Did LTCM Go Wrong? Correlation and Risk
Correlations among markets LTCM execute trades in the same kinds in different markets (e.g, buying off-the-run in both U.S.and Europe market), with high correlations Development of derivatives connected varied markets Correlations among trades Leverage made the whole portfolio subjected to some similar risk factors Correlations among events Market has memory. Correlation among crashes are positive. Correlations among fundamental factors Correlations among hedge funds: Copiers and followers

Where Did LTCM Go Wrong? Trading strategies Other Risks Arbitrage
Liquidity is the greatest risk for arbitrageurs which could not be measured by traditional risk management methods Market disruption, political risk(e.g. Russia), credit risk can make an arbitrage risky Deep arbitrage requires a favor financing cost and efficient market Multiple conterparties and transaction risks Caused more demanding margins than pair transaction Huge scale made block trading difficult, not price taker Other Risks Agency problem and human factors Behavior finance:over-optimistic and panic Crash in bond market in 1998 did not cause economic stress. It was evoked by panic of the street rather than macroeconomic factors

Cost-Benefit Tradeoff: An Empirical Study
LTCM Rescue Who Rescued LTCM? Why to Rescue LTCM? Cost-Benefit Tradeoff: An Empirical Study

Who Rescued LTCM? On 23th September, the Fed Reserve Bank of New York organized a rescue plan to avoid a systemic risk. The rescue plan required creditors, investment banks and institutions to supply an additional $3.625 billion of funds. 11 banks agreed to invest $300m each in Long-Term Capital Management as part of the bail-out of the struggling fund that include Merrill Lynch, Morgan Stanley, and Deutsch Bank. The Federal Reserve reduced interest rates on Tuesday, September 29, the very day after the bailout.

Who Rescued LTCM? INVESTMENT BANKING: Wall Street firms defend LTCM rescue (New York Times, 1998) Some of Wall Street's biggest investment banks inject $3.5bn bail-out of hedge fund Long-Term Capital Management, as it emerged that a number of leading Wall Street executives had personal investments in the hedge fund. Merrill Lynch, one of the inner circle of investment banks most closely linked to the fund, confirmed that its chairman, David Komansky, had put $400,000 of his personal wealth into the fund. Merrill Lynch said the bank's decision to help support the fund had been taken with the overall stability of the financial system in mind. "Any suggestion that his [Mr Komansky's] very small investment affected the decision is nonsense,"

Why to Rescue LTCM? As is well known, the Federal Reserve played a key role in organizing and hosting meetings for the institutions that would ultimately recapitalize the hedge fund. This quote emphasizes that much of what was driving the Fed’s involvement with LTCM was the uncertainty regarding the consequences of doing the alternative, namely, letting the fund collapse and having its financial contracts unwound in a forced liquidation. “The abrupt and disorderly closeout of Long-Term Capital’s positions would pose unacceptable risks to the US economy” William J. McDonough, Federal Reserve Bank of New York president, 1998,

Why to Rescue LTCM? What would be the results if the LTCM were liquidated? Contraparties Financial institutions could lose money on their direct credit exposures to the ailing hedge fund, even if these exposures were supposedly “fully collateralized.” Collateral could become insufficient to cover credit losses both at the directly exposed institutions and also at a much broader set of financial institutions holding the same financial instruments. Followers Losses could arise from banks’ proprietary trading operations that were taking financial positions like those of LTCM. Thus when markets moved against LTCM, they simultaneously moved against the institutions that were following similar strategies.

Possible benefits of Fed intervention: First, such policy maker action would limit the market disruption arising from a forced liquidation of LTCM. Second, Fed intervention would prevent the failure of any major commercial or investment bank, thereby avoiding the disruptions to economic activity that such a failure might cause. “We do not have the choice of accepting the benefits of the current system [of a wide safety net] without its costs” Greenspan (1998, 1050)

Possible costs of Fed intervention: Facilitating a private-sector rescue of a failing hedge fund was TBTF in disguise. In other words, since the Fed’s action prevented major commercial and investment banks from having to pay the full costs of a market-imposed failure of LTCM, the central bank may have set a damaging precedent that implicitly extends the safety net. LTCM’s chief executive officer John Meriwether intentionally involved the Fed with the fund’s troubles to secure a better outcome for the firm. Meriwether had been a successful bond trader at Salomon Brothers when that firm underwent investigation for submitting false bids at Treasury bond auctions. At that time, the viability of Salomon came into question since the magnitude of the Fed’s punishment of the firm was uncertain.

The Costs and Benefits of Moral Suasion: Evidence from the Rescue of Long-Term Capital Management, C Furfine, Journal of Business, 2006, vol. 79, no. 2 The study examines the level of unsecured borrowing done by the firms that ultimately rescued Long-Term Capital Management in the days leading up to the hedge fund’s rescue. Although these banks borrowed less at the height of the crisis, evidence suggests that this reduction in borrowing was demand driven and did not result from rationing by the market. Further, it is shown that large banks that were not involved with the LTCM rescue saw the rates they pay for unsecured funds decline following the hedge fund’s resolution. This finding is consistent with an increase in the strength of a too-big-to-fail policy.

Ultimately, the findings in the paper cannot lead one to conclude whether the Fed should have intervened in the way in which it did because the benefits and costs of Fed action are neither measured in their entirety nor weighted by an appropriate social welfare function. Nevertheless, the results suggest that the benefits of Fed intervention may have been lower and the costs higher than perceived at the time！ Empirical Study: 14 Rescuer, 9 in the tracking sample set.

Thank You ! Q & A

Long-Term Capital Management, L.P.

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