Collateral Debt Obligations. Thought of the Day 111.0

A CDO is a general term that describes securities backed by a pool of fixed-income assets. These assets can be bank loans (CLOs), bonds (CBOs), residential mortgages (residential- mortgage–backed securities, or RMBSs), and many others. A CDO is a subset of asset- backed securities (ABS), which is a general term for a security backed by assets such as mortgages, credit card receivables, auto loans, or other debt.

To create a CDO, a bank or other entity transfers the underlying assets (“the collateral”) to a special-purpose vehicle (SPV) that is a separate legal entity from the issuer. The SPV then issues securities backed with cash flows generated by assets in the collateral pool. This general process is called securitization. The securities are separated into tranches, which differ primarily in the priority of their rights to the cash flows coming from the asset pool. The senior tranche has first priority, the mezzanine second, and the equity third. Allocation of cash flows to specific securities is called a “waterfall”. A waterfall is specified in the CDO’s indenture and governs both principal and interest payments.

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1: If coverage tests are not met, and to the extent not corrected with principal proceeds, the remaining interest proceeds will be used to redeem the most senior notes to bring the structure back into compliance with the coverage tests. Interest on the mezzanine securities may be deferred and compounded if cash flow is not available to pay current interest due.

One may observe that the creation of a CDO is a complex and costly process. Professionals such as bankers, lawyers, rating agencies, accountants, trustees, fund managers, and insurers all charge considerable fees to create and manage a CDO. In other words, the cash coming from the collateral is greater than the sum of the cash paid to all security holders. Professional fees to create and manage the CDO make up the difference.

CDOs are designed to offer asset exposure precisely tailored to the risk that investors desire, and they provide liquidity because they trade daily on the secondary market. This liquidity enables, for example, a finance minister from the Chinese government to gain exposure to the U.S. mortgage market and to buy or sell that exposure at will. However, because CDOs are more complex securities than corporate bonds, they are designed to pay slightly higher interest rates than correspondingly rated corporate bonds.

CDOs enable a bank that specializes in making loans to homeowners to make more loans than its capital would otherwise allow, because the bank can sell its loans to a third party. The bank can therefore originate more loans and take in more origination fees. As a result, consumers have more access to capital, banks can make more loans, and investors a world away can not only access the consumer loan market but also invest with precisely the level of risk they desire.

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1: To the extent not paid by interest proceeds.

2: To the extent senior note coverage tests are met and to the extent not already paid by interest proceeds. If coverage tests are not met, the remaining principal proceeds will be used to redeem the most senior notes to bring the structure back into compliance with the coverage tests. Interest on the mezzanine securities may be deferred and compounded if cash flow is not available to pay current interest due.

The Structured Credit Handbook provides an explanation of investors’ nearly insatiable appetite for CDOs:

Demand for [fixed income] assets is heavily bifurcated, with the demand concentrated at the two ends of the safety spectrum . . . Prior to the securitization boom, the universe of fixed-income instruments issued tended to cluster around the BBB rating, offering neither complete safety nor sizzling returns. For example, the number of AA and AAA-rated companies is quite small, as is debt issuance of companies rated B or lower. Structured credit technology has evolved essentially in order to match investors’ demands with the available profile of fixed-income assets. By issuing CDOs from portfolios of bonds or loans rated A, BBB, or BB, financial intermediaries can create a larger pool of AAA-rated securities and a small unrated or low-rated bucket where almost all the risk is concentrated.

CDOs have been around for more than twenty years, but their popularity skyrocketed during the late 1990s. CDO issuance nearly doubled in 2005 and then again in 2006, when it topped $500 billion for the first time. “Structured finance” groups at large investment banks (the division responsible for issuing and managing CDOs) became one of the fastest-growing areas on Wall Street. These divisions, along with the investment banking trading desks that made markets in CDOs, contributed to highly successful results for the banking sector during the 2003–2007 boom. Many CDOs became quite liquid because of their size, investor breadth, and rating agency coverage.

Rating agencies helped bring liquidity to the CDO market. They analyzed each tranche of a CDO and assigned ratings accordingly. Equity tranches were often unrated. The rating agencies had limited manpower and needed to gauge the risk on literally thousands of new CDO securities. The agencies also specialized in using historical models to predict risk. Although CDOs had been around for a long time, they did not exist in a significant number until recently. Historical models therefore couldn’t possibly capture the full picture. Still, the underlying collateral could be assessed with a strong degree of confidence. After all, banks have been making home loans for hundreds of years. The rating agencies simply had to allocate risk to the appropriate tranche and understand how the loans in the collateral base were correlated with each other – an easy task in theory perhaps, but not in practice.

The most difficult part of valuing a CDO tranche is determining correlation. If loans are uncorrelated, defaults will occur evenly over time and asset diversification can solve most problems. With low correlation, an AAA-rated senior tranche should be safe and the interest rate attached to this tranche should be close to the rate for AAA-rated corporate bonds. High correlation, however, creates nondiversifiable risk, in which case the senior tranche has a reasonable likelihood of becoming impaired. Correlation does not affect the price of the CDO in total because the expected value of each individual loan remains the same. Correlation does, however, affect the relative price of each tranche: Any increase in the yield of a senior tranche (to compensate for additional correlation) will be offset by a decrease in the yield of the junior tranches.

(Il)liquid Hedge Lock-Ups. Thought of the Day 107.0

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Hedge funds have historically limited their participation in illiquid investments, preferring to match their investment horizon to the typical one-year lock-up periods that their investors agree to. However, many hedge funds have increasingly invested in illiquid assets in an effort to augment returns. For example, they have invested in private investments in public equity (PIPEs), acquiring large minority holdings in public companies. Their purchases of CDOs and CLOs (collateralized loan obligations) are also somewhat illiquid, since these fixed income securities are difficult to price and there is a limited secondary market during times of crisis. In addition, hedge funds have participated in loans, and invested in physical assets. Sometimes, investments that were intended to be held for less than one year have become long-term, illiquid assets when the assets depreciated and hedge funds decided to continue holding the assets until values recovered, rather than selling at a loss. It is estimated that more than 20% of total assets under management by hedge funds are illiquid, hard-to-price assets. This makes hedge fund asset valuation difficult, and has created a mismatch between hedge fund assets and liabilities, giving rise to significant problems when investors attempt to withdraw their cash at the end of lock-up periods.

Hedge funds generally focus their investment strategies on financial assets that are liquid and able to be readily priced based on reported prices in the market for those assets or by reference to comparable assets that have a discernible price. Since most of these assets can be valued and sold over a short period of time to generate cash, hedge funds permit investors to invest in or withdraw money from the fund at regular intervals and managers receive performance fees based on quarterly mark-to-market valuations. However, in order to match up maturities of assets and liabilities for each investment strategy, most hedge funds have the ability to prevent invested capital from being withdrawn during certain periods of time. They achieve this though “lock-up” and “gate” provisions that are included in investment agreements with their investors.

A lock-up provision provides that during an initial investment period of, typically, one to two years, an investor is not allowed to withdraw any money from the fund. Generally, the lock-up period is a function of the investment strategy that is being pursued. Sometimes, lock-up periods are modified for specific investors through the use of a side letter agreement. However, this can become problematic because of the resulting different effective lock-up periods that apply to different investors who invest at the same time in the same fund. Also, this can trigger “most favored nations” provisions in other investor agreements.

A gate is a restriction that limits the amount of withdrawals during a quarterly or semi- annual redemption period after the lock-up period expires. Typically gates are percentages of a fund’s capital that can be withdrawn on a scheduled redemption date. A gate of 10 to 20% is common. A gate provision allows the hedge fund to increase exposure to illiquid assets without facing a liquidity crisis. In addition, it offers some protection to investors that do not attempt to withdraw funds because if withdrawals are too high, assets might have to be sold by the hedge fund at disadvantageous prices, causing a potential reduction in investment returns for remaining investors. During 2008 and 2009, as many hedge fund investors attempted to withdraw money based on poor returns and concerns about the financial crisis, there was considerable frustration and some litigation directed at hedge fund gate provisions.

Hedge funds sometimes use a “side pocket” account to house comparatively illiquid or hard-to-value assets. Once an asset is designated for inclusion in a side pocket, new investors don’t participate in the returns from this asset. When existing investors withdraw money from the hedge fund, they remain as investors in the side pocket asset until it either is sold or becomes liquid through a monetization event such as an IPO. Management fees are typically charged on side pocket assets based on their cost, rather than a mark-to-market value of the asset. Incentive fees are charged based on realized proceeds when the asset is sold. Usually, there is no requirement to force the sale of side pocket investments by a specific date. Sometimes, investors accuse hedge funds of putting distressed assets that were intended to be sold during a one-year horizon into a side pocket account to avoid dragging down the returns of the overall fund. Investors are concerned about unexpected illiquidity arising from a side pocket and the potential for even greater losses if a distressed asset that has been placed there continues to decline in value. Fund managers sometimes use even more drastic options to limit withdrawals, such as suspending all redemption rights (but only in the most dire circumstances).

Credit Default Swaps.

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Credit default swaps are the most liquid instruments in the credit derivatives markets, accounting for nearly half of the total outstanding notional worldwide, and up to 85% of total outstanding notional of contracts with reference to emerging market issuers. In a CDS, the protection buyer pays a premium to the protection seller in exchange for a contingent payment in case a credit event involving a reference security occurs during the contract period.

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The premium (default swap spread) reflects the credit risk of the bond issuer, and is usually quoted as a spread over a reference rate such as LIBOR or the swap rate, to be paid either up front, quarterly, or semiannually. The contingent payment can be settled either by physical delivery of the reference security or an equivalent asset, or in cash. With physical settlement, the protection buyer delivers the reference security (or equivalent one) to the protection seller and receives the par amount. With cash settlement, the protection buyer receives a payment equal to the difference between par and the recovery value of the reference security, the latter determined from a dealer poll or from price quote services. Contracts are typically subject to physical settlement. This allows protection sellers to benefit from any rebound in prices caused by the rush to purchase deliverable bonds by protection buyers after the realization of the credit event.

In mature markets, trading is highly concentrated on 5 year contracts, and to certain extent, market participants consider these contracts a ‘‘commodity.’’ Usual contract maturities are 1, 2, 5, and 10 years. The coexistence of markets for default swaps and bonds raises the issue on whether prices in the former merely mirrors market expectations already reflected in bond prices. If credit risk were the only factor affecting the CDS spread, with credit risk characterized by the probability of default and the expected loss given default, the CDS spread and the bond spread should be approximately similar, as a portfolio of a default swap contract and a defaultable bond is essentially a risk-free asset.

However, market frictions and some embedded options in the CDS contract, such as the cheapest-to-deliver option, cause CDS spreads and bond spreads to diverge. The difference between these two spreads is referred to as the default swap basis. The default swap basis is positive when the CDS spread trades at a premium relative to the bond spread, and negative when the CDS spread trades at a discount.

Several factors contribute to the widening of the basis, either by widening the CDS spread or tightening the bond spread. Factors that tend to widen the CDS spread include: (1) the cheapest-to-deliver option, since protection sellers must charge a higher premium to account for the possibility of being delivered a less valuable asset in physically settled contracts; (2) the issuance of new bonds and/or loans, as increased hedging by market makers in the bond market pushes up the price of protection, and the number of potential cheapest-to-deliver assets increases; (3) the ability to short default swaps rather than bonds when the bond issuer’s credit quality deteriorates, leading to increased protection buying in the market; and (4) bond prices trading less than par, since the protection seller is guaranteeing the recovery of the par amount rather than the lower current bond price.

Factors that tend to tighten bond spreads include: (1) bond clauses allowing the coupon to step up if the issue is downgraded, as they provide additional benefits to the bondholder not enjoyed by the protection buyer and (2) the zero-lower bound for default swap premiums causes the basis to be positive when bond issuers can trade below the LIBOR curve, as is often the case for higher rated issues.

Similarly, factors that contribute to the tightening of the basis include: (1) existence of greater counterparty risk to the protection buyer than to the protection seller, so buyers are compensated by paying less than the bond spread; (2) the removal of funding risk for the protection seller, as selling protection is equivalent to funding the asset at LIBOR. Less risk demands less compensation and hence, a tightening in the basis; and (3) the increased supply of structured products such as CDS-backed collateralized debt obligations (CDOs), as they increase the supply of protection in the market.

Movements in the basis depend also on whether the market is mainly dominated by high cost investors or low cost investors. A long credit position, i.e., holding the credit risk, can be obtained either by selling protection or by financing the purchase of the risky asset. The CDS remains a viable alternative if its premium does not exceed the difference between the asset yield and the funding cost. The higher the funding cost, the lower the premium and hence, the tighter the basis. Thus, when the market share of low cost investors is relatively high and the average funding costs are below LIBOR, the basis tends to widen. Finally, relative liquidity also plays a role in determining whether the basis narrows or widens, as investors need to be compensated by wider spreads in the less liquid market. Hence, if the CDS market is more liquid than the corresponding underlying bond market (cash market), the basis will narrow and vice versa.

High Frequency Traders: A Case in Point.

Events on 6th May 2010:

At 2:32 p.m., against [a] backdrop of unusually high volatility and thinning liquidity, a large fundamental trader (a mutual fund complex) initiated a sell program to sell a total of 75,000 E-Mini [S&P 500 futures] contracts (valued at approximately $4.1 billion) as a hedge to an existing equity position. […] This large fundamental trader chose to execute this sell program via an automated execution algorithm (“Sell Algorithm”) that was programmed to feed orders into the June 2010 E-Mini market to target an execution rate set to 9% of the trading volume calculated over the previous minute, but without regard to price or time. The execution of this sell program resulted in the largest net change in daily position of any trader in the E-Mini since the beginning of the year (from January 1, 2010 through May 6, 2010). [. . . ] This sell pressure was initially absorbed by: high frequency traders (“HFTs”) and other intermediaries in the futures market; fundamental buyers in the futures market; and cross-market arbitrageurs who transferred this sell pressure to the equities markets by opportunistically buying E-Mini contracts and simultaneously selling products like SPY [(S&P 500 exchange-traded fund (“ETF”))], or selling individual equities in the S&P 500 Index. […] Between 2:32 p.m. and 2:45 p.m., as prices of the E-Mini rapidly declined, the Sell Algorithm sold about 35,000 E-Mini contracts (valued at approximately $1.9 billion) of the 75,000 intended. [. . . ] By 2:45:28 there were less than 1,050 contracts of buy-side resting orders in the E-Mini, representing less than 1% of buy-side market depth observed at the beginning of the day. [. . . ] At 2:45:28 p.m., trading on the E-Mini was paused for five seconds when the Chicago Mercantile Exchange (“CME”) Stop Logic Functionality was triggered in order to prevent a cascade of further price declines. […] When trading resumed at 2:45:33 p.m., prices stabilized and shortly thereafter, the E-Mini began to recover, followed by the SPY. [. . . ] Even though after 2:45 p.m. prices in the E-Mini and SPY were recovering from their severe declines, sell orders placed for some individual securities and Exchange Traded Funds (ETFs) (including many retail stop-loss orders, triggered by declines in prices of those securities) found reduced buying interest, which led to further price declines in those securities. […] [B]etween 2:40 p.m. and 3:00 p.m., over 20,000 trades (many based on retail-customer orders) across more than 300 separate securities, including many ETFs, were executed at prices 60% or more away from their 2:40 p.m. prices. [. . . ] By 3:08 p.m., [. . . ] the E-Mini prices [were] back to nearly their pre-drop level [. . . and] most securities had reverted back to trading at prices reflecting true consensus values.

In the ordinary course of business, HFTs use their technological advantage to profit from aggressively removing the last few contracts at the best bid and ask levels and then establishing new best bids and asks at adjacent price levels ahead of an immediacy-demanding customer. As an illustration of this “immediacy absorption” activity, consider the following stylized example, presented in Figure and described below.

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Suppose that we observe the central limit order book for a stock index futures contract. The notional value of one stock index futures contract is $50. The market is very liquid – on average there are hundreds of resting limit orders to buy or sell multiple contracts at either the best bid or the best offer. At some point during the day, due to temporary selling pressure, there is a total of just 100 contracts left at the best bid price of 1000.00. Recognizing that the queue at the best bid is about to be depleted, HFTs submit executable limit orders to aggressively sell a total of 100 contracts, thus completely depleting the queue at the best bid, and very quickly submit sequences of new limit orders to buy a total of 100 contracts at the new best bid price of 999.75, as well as to sell 100 contracts at the new best offer of 1000.00. If the selling pressure continues, then HFTs are able to buy 100 contracts at 999.75 and make a profit of $1,250 dollars among them. If, however, the selling pressure stops and the new best offer price of 1000.00 attracts buyers, then HFTs would very quickly sell 100 contracts (which are at the very front of the new best offer queue), “scratching” the trade at the same price as they bought, and getting rid of the risky inventory in a few milliseconds.

This type of trading activity reduces, albeit for only a few milliseconds, the latency of a price move. Under normal market conditions, this trading activity somewhat accelerates price changes and adds to the trading volume, but does not result in a significant directional price move. In effect, this activity imparts a small “immediacy absorption” cost on all traders, including the market makers, who are not fast enough to cancel the last remaining orders before an imminent price move.

This activity, however, makes it both costlier and riskier for the slower market makers to maintain continuous market presence. In response to the additional cost and risk, market makers lower their acceptable inventory bounds to levels that are too small to offset temporary liquidity imbalances of any significant size. When the diminished liquidity buffer of the market makers is pierced by a sudden order flow imbalance, they begin to demand a progressively greater compensation for maintaining continuous market presence, and prices start to move directionally. Just as the prices are moving directionally and volatility is elevated, immediacy absorption activity of HFTs can exacerbate a directional price move and amplify volatility. Higher volatility further increases the speed at which the best bid and offer queues are being depleted, inducing HFT algorithms to demand immediacy even more, fueling a spike in trading volume, and making it more costly for the market makers to maintain continuous market presence. This forces more risk averse market makers to withdraw from the market, which results in a full-blown market crash.

Empirically, immediacy absorption activity of the HFTs should manifest itself in the data very differently from the liquidity provision activity of the Market Makers. To establish the presence of these differences in the data, we test the following hypotheses:

Hypothesis H1: HFTs are more likely than Market Makers to aggressively execute the last 100 contracts before a price move in the direction of the trade. Market Makers are more likely than HFTs to have the last 100 resting contracts against which aggressive orders are executed.

Hypothesis H2: HFTs trade aggressively in the direction of the price move. Market Makers get run over by a price move.

Hypothesis H3: Both HFTs and Market Makers scratch trades, but HFTs scratch more.

To statistically test our “immediacy absorption” hypotheses against the “liquidity provision” hypotheses, we divide all of the trades during the 405 minute trading day into two subsets: Aggressive Buy trades and Aggressive Sell trades. Within each subset, we further aggregate multiple aggressive buy or sell transactions resulting from the execution of the same order into Aggressive Buy or Aggressive Sell sequences. The intuition is as follows. Often a specific trade is not a stand alone event, but a part of a sequence of transactions associated with the execution of the same order. For example, an order to aggressively sell 10 contracts may result in four Aggressive Sell transactions: for 2 contracts, 1 contract, 4 contracts, and 3 contracts, respectively, due to the specific sequence of resting bids against which this aggressive sell order was be executed. Using the order ID number, we are able to aggregate these four transactions into one Aggressive Sell sequence for 10 contracts.

Testing Hypothesis H1. Aggressive removal of the last 100 contracts by HFTs; passive provision of the last 100 resting contracts by the Market Makers. Using the Aggressive Buy sequences, we label as a “price increase event” all occurrences of trading sequences in which at least 100 contracts consecutively executed at the same price are followed by some number of contracts at a higher price. To examine indications of low latency, we focus on the the last 100 contracts traded before the price increase and the first 100 contracts at the next higher price (or fewer if the price changes again before 100 contracts are executed). Although we do not look directly at the limit order book data, price increase events are defined to capture occasions where traders use executable buy orders to lift the last remaining offers in the limit order book. Using Aggressive sell trades, we define “price decrease events” symmetrically as occurrences of sequences of trades in which 100 contracts executed at the same price are followed by executions at lower prices. These events are intended to capture occasions where traders use executable sell orders to hit the last few best bids in the limit order book. The results are presented in Table below

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For price increase and price decrease events, we calculate each of the six trader categories’ shares of Aggressive and Passive trading volume for the last 100 contracts traded at the “old” price level before the price increase or decrease and the first 100 contracts traded at the “new” price level (or fewer if the number of contracts is less than 100) after the price increase or decrease event.

Table above presents, for the six trader categories, volume shares for the last 100 contracts at the old price and the first 100 contracts at the new price. For comparison, the unconditional shares of aggressive and passive trading volume of each trader category are also reported. Table has four panels covering (A) price increase events on May 3-5, (B) price decrease events on May 3-5, (C) price increase events on May 6, and (D) price decrease events on May 6. In each panel there are six rows of data, one row for each trader category. Relative to panels A and C, the rows for Fundamental Buyers (BUYER) and Fundamental Sellers (SELLER) are reversed in panels B and D to emphasize the symmetry between buying during price increase events and selling during price decrease events. The first two columns report the shares of Aggressive and Passive contract volume for the last 100 contracts before the price change; the next two columns report the shares of Aggressive and Passive volume for up to the next 100 contracts after the price change; and the last two columns report the “unconditional” market shares of Aggressive and Passive sides of all Aggressive buy volume or sell volume. For May 3-5, the data are based on volume pooled across the three days.

Consider panel A, which describes price increase events associated with Aggressive buy trades on May 3-5, 2010. High Frequency Traders participated on the Aggressive side of 34.04% of all aggressive buy volume. Strongly consistent with immediacy absorption hypothesis, the participation rate rises to 57.70% of the Aggressive side of trades on the last 100 contracts of Aggressive buy volume before price increase events and falls to 14.84% of the Aggressive side of trades on the first 100 contracts of Aggressive buy volume after price increase events.

High Frequency Traders participated on the Passive side of 34.33% of all aggressive buy volume. Consistent with hypothesis, the participation rate on the Passive side of Aggressive buy volume falls to 28.72% of the last 100 contracts before a price increase event. It rises to 37.93% of the first 100 contracts after a price increase event.

These results are inconsistent with the idea that high frequency traders behave like textbook market makers, suffering adverse selection losses associated with being picked off by informed traders. Instead, when the price is about to move to a new level, high frequency traders tend to avoid being run over and take the price to the new level with Aggressive trades of their own.

Market Makers follow a noticeably more passive trading strategy than High Frequency Traders. According to panel A, Market Makers are 13.48% of the Passive side of all Aggressive trades, but they are only 7.27% of the Aggressive side of all Aggressive trades. On the last 100 contracts at the old price, Market Makers’ share of volume increases only modestly, from 7.27% to 8.78% of trades. Their share of Passive volume at the old price increases, from 13.48% to 15.80%. These facts are consistent with the interpretation that Market Makers, unlike High Frequency Traders, do engage in a strategy similar to traditional passive market making, buying at the bid price, selling at the offer price, and suffering losses when the price moves against them. These facts are also consistent with the hypothesis that High Frequency Traders have lower latency than Market Makers.

Intuition might suggest that Fundamental Buyers would tend to place the Aggressive trades which move prices up from one tick level to the next. This intuition does not seem to be corroborated by the data. According to panel A, Fundamental Buyers are 21.53% of all Aggressive trades but only 11.61% of the last 100 Aggressive contracts traded at the old price. Instead, Fundamental Buyers increase their share of Aggressive buy volume to 26.17% of the first 100 contracts at the new price.

Taking into account symmetry between buying and selling, panel B shows the results for Aggressive sell trades during May 3-5, 2010, are almost the same as the results for Aggressive buy trades. High Frequency Traders are 34.17% of all Aggressive sell volume, increase their share to 55.20% of the last 100 Aggressive sell contracts at the old price, and decrease their share to 15.04% of the last 100 Aggressive sell contracts at the new price. Market Makers are 7.45% of all Aggressive sell contracts, increase their share to only 8.57% of the last 100 Aggressive sell trades at the old price, and decrease their share to 6.58% of the last 100 Aggressive sell contracts at the new price. Fundamental Sellers’ shares of Aggressive sell trades behave similarly to Fundamental Buyers’ shares of Aggressive Buy trades. Fundamental Sellers are 20.91% of all Aggressive sell contracts, decrease their share to 11.96% of the last 100 Aggressive sell contracts at the old price, and increase their share to 24.87% of the first 100 Aggressive sell contracts at the new price.

Panels C and D report results for Aggressive Buy trades and Aggressive Sell trades for May 6, 2010. Taking into account symmetry between buying and selling, the results for Aggressive buy trades in panel C are very similar to the results for Aggressive sell trades in panel D. For example, Aggressive sell trades by Fundamental Sellers were 17.55% of Aggressive sell volume on May 6, while Aggressive buy trades by Fundamental Buyers were 20.12% of Aggressive buy volume on May 6. In comparison with the share of Fundamental Buyers and in comparison with May 3-5, the Flash Crash of May 6 is associated with a slightly lower – not higher – share of Aggressive sell trades by Fundamental Sellers.

The number of price increase and price decrease events increased dramatically on May 6, consistent with the increased volatility of the market on that day. On May 3-5, there were 4100 price increase events and 4062 price decrease events. On May 6 alone, there were 4101 price increase events and 4377 price decrease events. There were therefore approximately three times as many price increase events per day on May 6 as on the three preceding days.

A comparison of May 6 with May 3-5 reveals significant changes in the trading patterns of High Frequency Traders. Compared with May 3-5 in panels A and B, the share of Aggressive trades by High Frequency Traders drops from 34.04% of Aggressive buys and 34.17% of Aggressive sells on May 3-5 to 26.98% of Aggressive buy trades and 26.29% of Aggressive sell trades on May 6. The share of Aggressive trades for the last 100 contracts at the old price declines by even more. High Frequency Traders’ participation rate on the Aggressive side of Aggressive buy trades drops from 57.70% on May 3-5 to only 38.86% on May 6. Similarly, the participation rate on the Aggressive side of Aggressive sell trades drops from and 55.20% to 38.67%. These declines are largely offset by increases in the participation rate by Opportunistic Traders on the Aggressive side of trades. For example, Opportunistic Traders’ share of the Aggressive side of the last 100 contracts traded at the old price rises from 19.21% to 34.26% for Aggressive buys and from 20.99% to 33.86% for Aggressive sells. These results suggest that some Opportunistic Traders follow trading strategies for which low latency is important, such as index arbitrage, cross-market arbitrage, or opportunistic strategies mimicking market making.

Testing Hypothesis H2. HFTs trade aggressively in the direction of the price move; Market Makers get run over by a price move. To examine this hypothesis, we analyze whether High Frequency Traders use Aggressive trades to trade in the direction of contemporaneous price changes, while Market Makers use Passive trades to trade in the opposite direction from price changes. To this end, we estimate the regression equation

Δyt = α + Φ . Δyt-1 + δ . yt-1 + Σi=120i . Δpt-1 /0.25] + εt

(where yt and Δyt denote inventories and change in inventories of High Frequency Traders for each second of a trading day; t = 0 corresponds to the opening of stock trading on the NYSE at 8:30:00 a.m. CT (9:30:00 ET) and t = 24, 300 denotes the close of Globex at 15:15:00 CT (4:15 p.m. ET); Δpt denotes the price change in index point units between the high-low midpoint of second t-1 and the high-low midpoint of second t. Regressing second-by-second changes in inventory levels of High Frequency Traders on the level of their inventories the previous second, the change in their inventory levels the previous second, the change in prices during the current second, and lagged price changes for each of the previous 20 previous seconds.)

for Passive and Aggressive inventory changes separately.

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Table above presents the regression results of the two components of change in holdings on lagged inventory, lagged change in holdings and lagged price changes over one second intervals. Panel A and Panel B report the results for May 3-5 and May 6, respectively. Each panel has four columns, reporting estimated coefficients where the dependent variables are net Aggressive volume (Aggressive buys minus Aggressive sells) by High Frequency Traders (∆AHFT), net Passive volume by High Frequency Traders (∆PHFT), net Aggressive volume by Market Makers (∆AMM), and net Passive volume by Market Makers (∆PMM).

We observe that for lagged inventories (NPHFTt−1), the estimated coefficients for Aggressive and Passive trades by High Frequency Traders are δAHFT = −0.005 (t = −9.55) and δPHFT = −0.001 (t = −3.13), respectively. These coefficient estimates have the interpretation that High Frequency Traders use Aggressive trades to liquidate inventories more intensively than passive trades. In contrast, the results for Market Makers are very different. For lagged inventories (NPMMt−1), the estimated coefficients for Aggressive and Passive volume by Market Makers are δAMM = −0.002 (t = −6.73) and δPMM = −0.002 (t = −5.26), respectively. The similarity of these coefficients estimates has the interpretation that Market Makers favor neither Aggressive trades nor Passive trades when liquidating inventories.

For contemporaneous price changes (in the current second) (∆Pt−1), the estimated coefficient Aggressive and Passive volume by High Frequency Traders are β0 = 57.78 (t = 31.94) and β0 = −25.69 (t = −28.61), respectively. For Market Makers, the estimated coefficients for Aggressive and Passive trades are β0 = 6.38 (t = 18.51) and β0 = −19.92 (t = −37.68). These estimated coefficients have the interpretation that in seconds in which prices move up one tick, High Frequency traders are net buyers of about 58 contracts with Aggressive trades and net sellers of about 26 contracts with Passive trades in that same second, while Market Makers are net buyers of about 6 contracts with Aggressive trades and net sellers of about 20 contracts with Passive trades. High Frequency Traders and Market Makers are similar in that they both use Aggressive trades to trade in the direction of price changes, and both use Passive trades to trade against the direction of price changes. High Frequency Traders and Market Makers are different in that Aggressive net purchases by High Frequency Traders are greater in magnitude than the Passive net purchases, while the reverse is true for Market Makers.

For lagged price changes, coefficient estimates for Aggressive trades by High Frequency Traders and Market Makers are positive and statistically significant at lags 1-4 and lags 1-10, respectively. These results have the interpretation that both High Frequency Traders’ and Market Makers’ trade on recent price momentum, but the trading is compressed into a shorter time frame for High Frequency Traders than for Market Makers.

For lagged price changes, coefficient estimates for Passive volume by High Frequency Traders and Market Makers are negative and statistically significant at lags 1 and lags 1-3, respectively. Panel B of Table presents results for May 6. Similar to May 3-5, High Frequency Traders tend to use Aggressive trades more intensely than Passive trades to liquidate inventories, while Market Makers do not show this pattern. Also similar to May 3-5, High Frequency Trades and Market makers use Aggressive trades to trade in the contemporaneous direction of price changes and use Passive trades to trade in the direction opposite price changes, with Aggressive trading greater than Passive trading for High Frequency Traders and the reverse for Market Makers. In comparison with May 3-5, the coefficients are smaller in magnitude on May 6, indicating reduced liquidity at each tick. For lagged price changes, the coefficients associated with Aggressive trading by High Frequency Traders change from positive to negative at lags 1-4, and the positive coefficients associated with Aggressive trading by Market Makers change from being positive and statistically significant at lags lags 1-10 to being positive and statistically significant only at lags 1-3. These results illustrate accelerated trading velocity in the volatile market conditions of May 6.

We further examine how high frequency trading activity is related to market prices. Figure below illustrates how prices change after HFT trading activity in a given second. The upper-left panel presents results for buy trades for May 3-5, the upper right panel presents results for buy trades on May 6, and the lower-left and lower-right present corresponding results for sell trades. For an “event” second in which High Frequency Traders are net buyers, net Aggressive Buyers, and net Passive Buyers value-weighted average prices paid by the High Frequency Traders in that second are subtracted from the value-weighted average prices for all trades in the same second and each of the following 20 seconds. The results are averaged across event seconds, weighted by the magnitude of High Frequency Traders’ net position change in the event second. The upper-left panel presents results for May 3-5, the upper-right panel presents results for May 6, and the lower two panels present results for sell trades calculated analogously. Price differences on the vertical axis are scaled so that one unit equals one tick ($12.50 per contract).

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When High Frequency Traders are net buyers on May 3-5, prices rise by 17% of a tick in the next second. When HFTs execute Aggressively or Passively, prices rise by 20% and 2% of a tick in the next second, respectively. In subsequent seconds, prices in all cases trend downward by about 5% of a tick over the subsequent 19 seconds. For May 3-5, the results are almost symmetric for selling.

When High Frequency Traders are buying on May 6, prices increase by 7% of a tick in the next second. When they are aggressive buyers or passive buyers, prices increase by increase 25% of a tick or decrease by 5% of a tick in the next second, respectively. In subsequent seconds, prices generally tend to drift downwards. The downward drift is especially pronounced after Passive buying, consistent with the interpretation that High Frequency Traders were “run over” when their resting limit buy orders were “run over” in the down phase of the Flash Crash. When High Frequency Traders are net sellers, the results after one second are analogous to buying. After aggressive selling, prices continue to drift down for 20 seconds, consistent with the interpretation that High Frequency Traders made profits from Aggressive sales during the down phase of the Flash Crash.

Testing Hypothesis H3. Both HFTs and Market Makers scratch trades; HFTs scratch more. A textbook market maker will try to buy at the bid price, sell at the offer price, and capture the bid-ask spread as a profit. Sometimes, after buying at the bid price, market prices begin to fall before the market maker can make a one tick profit by selling his inventory at the best offer price. To avoid taking losses in this situation, one component of a traditional market making strategy is to “scratch trades in the presence of changing market conditions by quickly liquidating a position at the same price at which it was acquired. These scratched trades represent inventory management trades designed to lower the cost of adverse selection. Since many competing market makers may try to scratch trades at the same time, traders with the lowest latency will tend to be more successful in their attempts to scratch trades and thus more successful in their ability to avoid losses when market conditions change.

To examine whether and to what extent traders engage in trade scratching, we sequence each trader’s trades for the day using audit trail sequence numbers which not only sort trades by second but also sort trades chronologically within each second. We define an “immediately scratched trade” as a trade with the properties that the next trade in the sorted sequence (1) occurred in the same second, (2) was executed at the same price, (3) was in the opposite direction, i.e., buy followed by sell or sell followed by buy. For each of the trading accounts in our sample, we calculate the number of immediately scratched trades, then compare the number of scratched trades across the six trader categories.

The results of this analysis are presented in the table below. Panel A provides results for May 3-5 and panel B for May 6. In each panel, there are five rows of data, one for each trader category. The first three columns report the total number of trades, the total number of immediately scratched trades, and the percentage of trades that are immediately scratched by traders in five categories. For May 3-6, the reported numbers are from the pooled data.

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This table presents statistics for immediate trade scratching which measures how many times a trader changes his/her direction of trading in a second aggregated over a day. We define a trade direction change as a buy trade right after a sell trade or vice versa at the same price level in the same second.

This table shows that High Frequency Traders scratched 2.84 % of trades on May 3-5 and 4.26 % on May 6; Market Makers scratched 2.49 % of trades on May 3-5 and 5.53 % of trades on May 6. While the percentages of immediately scratched trades by Market Makers is slightly higher than that for High Frequency Traders on May 6, the percentages for both groups are very similar. The fourth, fifth, and sixth columns of the Table report the mean, standard deviation, and median of the number of scratched trades for the traders in each category.

Although the percentages of scratched trades are similar, the mean number of immediately scratched trades by High Frequency Traders is much greater than for Market Makers: 540.56 per day on May 3-5 and 1610.75 on May 6 for High Frequency Traders versus 13.35 and 72.92 for Market Makers. The differences between High Frequency Traders and Market Makers reflect differences in volume traded. The Table shows that High Frequency Traders and Market Makers scratch a significantly larger percentage of their trades than other trader categories.

Manifold(s) of Deleuzean/De Landian Intensity(ies): The Liquid Flowing Chaos of Complexity

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The potential for emergence is pregnant with that which emerges from it, even if as pure potential, lest emergence would be just a gobbledygook of abstraction and obscurity. Some aspects of emergence harness more potential or even more intensity in emergence. What would intensity mean here? Emergence in its most abstract form is described by differentiation, which is the perseverance of differing by extending itself into the world. Thus intensity or potentiality would be proportional to intensity/quality, and degree/quantity of differentiation. The obvious question is the origin of this differentiation. This comes through what has already been actualized, thus putting forth a twist. The twist is in potential being not just abstract, but also relative. Abstract, because potential can come to mean anything other than what it has a potential for, and relative, since, it is dependent upon intertwining within which it can unfold. So, even if intensity for the potential of emergence is proportional to differentiation, an added dimension of meta-differentiation is introduced that not only deals with the intensity of the potential emergence it actualizes, but also in turn the potential, which, its actualization gives rise to. This complexification of emergence is termed complexity.

Complexity is that by which emergence intertwines itself with intensity, thus laden with potentiality itself. This, in a way, could mean that complexity is a sort of meta-emergence, in that, it contains potential for the emergence of greater intensity of emergence. This implies that complexity and emergence require each other’s presence to co-exist and co-evolve. If emergence is, by which, complexity manifests itself in actuality in the world, then complexity is, by which, emergence surfaces as potential through intertwining. Where would Deleuze and Guattari fit in here? This is crucial, since complexity for the said thinkers is different from the way it has been analyzed above. And let us note where the difference rests. To have to better cope with the ideas of Deleuze and Guattari, it is mandated to invite Manuel De Landa with his intense reading of the thinkers in question. The point is proved in these words of John Protevi,

According to Manuel DeLanda, in the late 60s, Gilles Deleuze began to formulate some of the philosophical significance of what is now sometimes referred to as “chaos/complexity theory,” the study of “open” matter/energy systems which move from simple to complex patterning and from complex to simple patterning. Though not a term used by contemporary scientists in everyday work (“non-linear dynamics” is preferred), it can be a useful term for a collection of studies of phenomena whose complexity is such that Laplacean determinism no longer holds beyond a limited time and space scale. Thus the formula of chaos/complexity might be “short-term predictability, long-term unpredictability.

Here, potentiality is seen as creative for philosophy within materialism. An expansion on the notion of unity through assemblages of multiple singularities is on the cards, that facilitate the dislodging of anthropocentric view points, since such views are at best limited, with over-insistence on the rationale of world as a stable and solid structure. The solidity of structures is to be rethought in terms that open vistas for potential creation. The only way out to accomplish this is in terms of liquid structures that are always vulnerable to chaos and disorder considered a sine qua non for this creative potential to emerge. In this liquidity, De Landa witnesses the power to self-organize and further, the ability to form an ethics of sorts, one untouched by human static control, and which allows an existence at the edge of creative, flowing chaos. Such a position is tangible in history as a confluence of infinite variations, a rationale that doesn’t exist when processes are dynamic, thus wanting history to be rooted in materialism of a revived form. Such a history is one of flowing articulations not determined by linear and static constructions, but by infinite bifurcations, of the liquid unfolding, thus exposing a collective identity from a myriad of points and perspectives. This is complexity for Deleuze and Guattari, which enables a re-look at material systems through their powers of immanent autopoiesis or self-organization.