Tag Archives: Finance

What is the optimal trading frequency in financial markets?

Trading speeds in financial markets have increased dramatically over the last decade. In markets for equities, futures and foreign exchange, transactions take place in milliseconds to microseconds (or even nanoseconds). Markets for fixed-income securities like corporate bonds and over-the-counter derivatives like interest rate swaps and CDS are also catching up quickly by adopting electronic trading.

The dramatic speed-up of financial transactions can perhaps only be matched by the intensity of the events and debates surrounding it, especially in the context of high-frequency trading. To many, the Flash Crash of May 2010 was a wakeup call for reevaluating market structure. A series of technology glitches proved to be highly costly for some brokers, proprietary firms and marketplaces in terms of profits and reputation. The SEC launched investigations into HFT firms and their strategies. The French regulators introduced financial transaction tax. Michael Lewis wrote “Flash Boys.” The list goes on.

With these events and controversy come important economic questions: What are the costs and benefits to investors for speeding up trading? Is there an “optimal” trading frequency at which the financial market should operate? And does a faster market affect one group of investors more than another?

In a recent research paper, Welfare and Optimal Trading Frequency in Dynamic Double Auctions, my coauthor Prof. Songzi Du (Simon Fraser University) and I attempt to answer these questions.

Our starting point is very simple. Trading frequency can be measured by how often investors transact through market. A higher-frequency market allows investors to access the market more often per unit of clock time. When investors meet each other in the market, they trade. Trading can be motivated by new information about future asset value and idiosyncratic trading incentives such as tax or inventory considerations.

A fundamental function of financial market is to reallocate assets from investors who value them less to investors who value the assets more, at the right price. The better this function is fulfilled, the more efficient the market is in reallocating the asset. We say that the market “improve welfare”—that is, make all investors better off—if it makes the reallocation of assets more efficient.

The bright side and dark side of a higher-frequency market

A higher trading frequency is double-edged sword. The optimal trading frequency depends on how the benefit and cost balance each other.

On the bright side, a higher-frequency market is more responsive to new information. Investors benefit from being able to react immediately to news. For example, following earnings announcements or merger-acquisition news, an investor may find his previous allocation on a stock no longer desirable. The sooner investors react to this information by trading, the better off they are. This effect favors a high-frequency market.

On the dark side, a higher-frequency market reduces the aggressiveness of investors’ trades. Investors are said to be more aggressive if they are willing to tolerate a greater market impact to achieve their target asset position. For example, aggressive execution means trading larger quantities more quickly. By contrast, unaggressive execution means splitting a large order into many small pieces and trading them gradually over time. The more frequently the market allows investors to transact, the stronger is their incentive to split orders over time to avoid price impact; hence, it takes longer to reach desired asset positions, and this is inefficient. If, however, a market opens infrequently, it encourages investors to trade aggressively now—failing to trade now means waiting for longer for the next opportunity to trade; this in turn leads to a faster convergence to efficient allocations. In this sense, somewhat counter intuitively, a lower-frequency market enhances allocation efficiency.

Scheduled versus stochastic news

We show that the optimal trading frequency depends on the nature of information arrivals, which determines the tradeoff between the benefit and cost of a higher trading frequency.

For scheduled arrivals of information, such as earnings announcements and macroeconomic data releases, we find that the optimal trading frequency should be equal to or lower than the frequency of information arrivals. For example, if news only arrives once per day, it is never optimal for investors to trade more than once a day. Moreover, if the market is competitive enough, the optimal trading frequency is equal to the information frequency.

For stochastic arrivals of information, such as surprise news of mergers and acquisitions, we show that the optimal trading frequency can be much higher. Moreover, if the market is competitive enough, continuous trading (the highest-frequency market) turns out to be optimal.

What does this tell us about optimal trading frequency in reality? Assets such as large-cap stocks or Treasuries that have frequent, unpredictable news shocks should be traded close to continuously. Small, illiquid stocks or bonds that have scarce news may best trade in a low-frequency market that only opens a few times a day; concentrating trading interests at specific time creates a deeper market. Therefore, there is no “one size fits all” optimal trading frequency for all securities.

For more details of this research, see “Welfare and Optimal Trading Frequency in Dynamic Double Auctions”, by Songzi Du and Haoxiang Zhu, http://ssrn.com/abstract=2040609.

Haoxiang Zhu is an Assistant Professor of Finance at MIT Sloan School of Management.

A New Measure of Financial Intermediary Constraints

Hui Chen teaches 15.433 Investments at MIT Sloan

The ability to measure the degree of financial intermediary constraint is of crucial importance for regulators and investors. Standard measures of intermediary constraint often focus directly on the riskiness of the financial institutions themselves, such as their level of credit risk, volatility, or leverage ratio. One such example is the TED spread, which is the difference between LIBOR, a short-term interest rate for uncollateralized interbank loans, and the yield for Treasury bills. Large TED spreads indicate that banks, and hence uncollateralized interbank lending, are risky, which is the case during the financial crisis of 2008-09 (see in the picture below). However, safe banks are not the same as unconstrained banks. In fact, a period of low TED spreads could be precisely because of the tight constraints that limit the banks’ ability to take on risky investment.

In a recent research paper with Professor Scott Joslin at the University of Southern California and Sophie Ni at the Hong Kong University of Science and Technology, we propose a different approach to measure the tightness of intermediary constraint by observing how financial intermediaries manage their tail risk exposures. Specifically, we focus on financial intermediaries’ trading activities in the market of deep out-of-the-money put options on the S&P 500 index.

Our measure is motivated by theory. I will sketch out the main ingredients of the model here. We consider a general equilibrium setting where two types of agents, public investors and financial intermediaries, have different beliefs about the chances of major market crashes. Such disagreements lead to trading in the crash insurance market, with the more optimistic financial intermediaries selling crash insurance to the public investors during normal times. The assumption of financial intermediaries being more optimistic about tail risks is a shortcut to capture their superior ability to manage tail risks, or agency problems such as government guarantees and compensation schemes that encourage financial institutions to take on tail risks.

As in practice, financial intermediaries in our model face risk constraints, which limit the amount of tail risks they can take on relative to their net worth. If the intermediary risk constraint starts to tighten, which could be due to higher levels of tail risks in the economy or trading losses that reduce the net worth, the financial intermediaries will effectively become more risk averse, and their ability to provide risk sharing with the public investors will be reduced. As a result, the amount of crash insurance sold by the financial intermediaries becomes lower and can even turn negative (as the financial intermediaries become net buyers of crash insurance). In addition, the tighter constraint and reduced risk sharing will also make crash insurance more expensive and lead public investors to demand a higher risk premium for the aggregate stock market.

The deep out-of-the-money put options on the S&P 500 index (DOTM SPX puts) are effectively insurances against major market crashes and are well suited to test our theory. The figure below plots the net amount of DOTM SPX puts that public investors acquire each month (henceforth referred to as PNBO). This also reflects the net amount of the same options that broker-dealers and market-makers (financial intermediaries) sell in that month. The net public purchase of DOTM index puts was positive for the majority of the months prior to the recent financial crisis in 2008, suggesting that the financial intermediaries (public investors) were mainly net sellers (buyers) of crash insurance. A few exceptions include the Asian financial crisis (December 1997), the Russian default, the financial crisis in Latin America (November 1998 to January 1999), and the Iraq War (April 2003). However, starting in 2007, PNBO became significantly more volatile. It turned negative during the quant crisis in August 2007, and then rose significantly and peaked in October 2008, following the bankruptcy of Lehman Brothers. Afterwards, PNBO plunged rapidly and turned significantly negative in the following months. Following a series of government actions, PNBO first bottomed in April 2009, rebounded briefly, and then dropped again in December 2009 as the European sovereign debt crisis escalated.We find that PNBO is negatively related to the expensiveness of the DOTM SPX puts relative to the at-the-money options. This result is the opposite of the prediction of the demand pressure theory for option pricing, whereby exogenous demand shocks push up both the amount of options public investors buy and the price of the options, thus inducing a positive correlation between the public demand for an option and its expensiveness. Instead, the result is consistent with time variation in the tightness of intermediary constraints driving the pricing of the options and the endogenous public demand simultaneously.

Moreover, we find that PNBO significantly predicts future market excess returns. During the period from 1991 to 2012, a one-standard deviation decrease in PNBO is associated with a 3.4% increase in the subsequent 3-month market excess return. The R-square of the return-forecasting regression is 17.4%. The return predictability of PNBO is, again, consistent with the prediction of a tightened intermediary constraint driving up aggregate market risk premium.

Two alternative explanations of our predictability results are: (1) PNBO is merely a proxy for standard macro or financial factors that drive the aggregate risk premium; (2) the predictability captures the direct impact of intermediaries’ constraints on the aggregate risk premium. Consistent with the second view, we find that the predictive power of PNBO is unaffected by the inclusion of a long list of return predictors in the literature, including price-earnings ratio, dividend yield, net payout yield, consumption-wealth ratio, variance risk premium, default spread, term spread, and various tail risk measures.

In addition, we also compare PNBO with a list of funding constraint measures (including the VIX index, the growth rate of broker-dealer leverage, and liquidity measures in the Treasury market). We find that financial intermediaries tend to reduce their supply of market crash insurances when these measures of funding constraints tighten. When regressing market excess returns on lagged PNBO and other funding constraint measures jointly, only the coefficient on PNBO remains significant, which suggests that PNBO contains unique information about the aggregate risk premium relative to the other measures of funding constraints.

Our study sheds new light on a specific channel, the crash insurance market, through which intermediary constraints affect aggregate risk sharing and asset prices. Our measure of financial intermediary constraint has several advantages compared to the existing measures. Compared to the accounting-based measures such as the leverage for financial institutions, our measure has the advantage of being forward-looking and available at higher (daily) frequency. Unlike price-based measures such as the TED spread, our measure moves the focus away from whether the financial institutions themselves are risky and instead onto whether they behave as constrained in the financial markets.

For details of this research, see Hui Chen, Scott Joslin, and Sophie Ni, “Demand for Crash Insurance, Intermediary Constraints, and Stock Return Predictability.”

Early Peek Advantage?

From 2007 to June 2013, a small group of fee-paying, high-speed traders received the bi-monthly results of the Michigan Index of Consumer Sentiment (ICS) from Thomson Reuters at 9:54:58, two seconds before the broader release at 9:55:00. This arrangement was initially reported on April 5, 2013 by Financial Times regarding a complaint by a former Thomson Reuters employee for his dismissal after telling US federal agent about this arrangement of tiered distribution of information. Wider media coverage followed in June and July as well as a review by the office of New York Attorney General (see, for example, “Thomson Reuters Gives Elite Traders Early Advantage” by CNBC and “Traders Pay for an Early Peek at Key Data” by Wall Street Journal on June 12, “Seconds Out” by Economists on July 13, 2013). In July 2013, Thomson Reuters decided to suspend the program.

Despite the negative “optics” projected by this practice of tiered information release, a series of questions were raised: To what extent does it give an advantage to those with early information? Does it hurt general investors and hence damage the integrity of the financial market? How does it affect the efficiency of the price discovery process in the market? More careful analysis is needed in order to answer these questions.

In a recent research paper with Professor Xing Hu at University of Hong Kong and Professor Jun Pan at MIT, we have examined in detail the price dynamics and trading activity in E-mini S&P 500 futures around ICS releases during this episode. We focus on S&P 500 futures because ICS, reflecting consumer opinions of the overall economy, is likely to move the entire market instead of individual stocks. Being highly liquid and unaffected by short-sale constraints, E-mini S&P 500 futures is an ideal instrument to trade on both positive and negative market-wide information.

During the period when Thomson Reuters offers early peek advantage, we find abnormally high trading activity in E-mini S&P 500 futures at 9:54:58 on ICS announcement days. On average, the trading volume jumps to 1,473 contracts per second at 9:54:58, well above the sample average of 124 contracts per second, which reflects the trading volume of general investors. One second later at 9:54:59, the abnormal volume drops to 261 contracts, still well above the sample average but sharply down from the trading volume at 9:54:58. The volume pattern makes two points: First, early peek by high-frequency traders does generate high volume of trading, but mostly among themselves. (There is no reason be believe that general investors will choose to trade more at the time when they have an information disadvantage.) Second, the first second at 9:54:58 is disproportionally more meaningful to them.

More detailed study of price dynamics after the early peek reveals a clearer picture: We find that the prices are fully adjusted to the ICS news after the first 10% of the trades during 9:54:58, which lasts about 14 to 16 milliseconds. There is no evidence of further price drift after the initial price discovery. This implies that most of the transactions during 9:54:58 and all the transactions afterwards, including the public announcement at 9:55:00, are traded at the fully adjusted market prices. The scope of the early peek advantage is therefore narrowly contained and limited to high-speed traders trading amongst themselves. Outside of this narrow time window, general investors, as well as high-speed traders, trade at fully adjusted prices and are not disadvantaged by the early peek of a few.

The initiation and later suspension of the early peek program by Thomson Reuters also provides a natural experiment for us to examine how different mechanisms of information release might impact the speed of price discovery. Associated with the early peek program is highly concentrated trading amongst those fee-paying, high-speed traders over a span of two seconds. As a result of this intense and coordinated trading, we see a superfast price discovery in the order of 14 to 16 milliseconds. After the suspension of the early peek program, however, we do not see the same level of trading intensity and we find that the price discovery takes much longer. From this perspective, one might argue that, as a mechanism of information release, the tiered program provides a venue to facilitate concentrated and coordinated trading among informed high-speed traders and therefore makes price discovery more efficient.

How information actually transmits and impounds into market prices remain a central question in our understanding of how the financial market functions. Empirical investigations aimed at tackling this question are always hindered by the fact that most information is private in nature and hence unobservable to researchers, even ex post. The multi-tiered process adapted by data vendors in feeding market-moving information to their different clients, as in the case of Thomson Reuters when releasing CSI data, offers a rare instance where we know precisely what information is transmitted, when and to what subset of market participants. This situation allows us to examine with more clarity how information, private to some traders, drives their trading behavior and influences the market. It may also help us to better design and regulate the information dissemination process in the market.

For details of this research, see Grace Xing Hu, Jun Pan and Jiang Wang, “Early Peek Advantage?”