Category: Faculty

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.

Bridging the knowledge gap on governments as financial institutions

Ask most finance experts about the “world’s largest financial institutions,” and you’ll hear names like Citigroup, ICBC (China’s largest bank) and HSBC. However, governments top the list of large financial institutions, with investment and insurance operations that dwarf those of any private enterprise. For instance, last year the U.S. federal government made almost all student loans and backed over 97% of newly originated mortgages. Add to that Uncle Sam’s lending activities for agriculture, small business, energy and trade, plus its provision of insurance for private pensions and deposits, and you’ll discover it’s an $18-trillion financial institution. By comparison, JP Morgan Chase, the largest U.S. bank, had assets totaling about $2.4 trillion.

While government practices differ across countries, the basic story is much the same everywhere. As the world’s largest and most interconnected financial institutions — and through their activities as rule-makers and regulators — governments have an enormous influence on the allocation of capital and risk in society. And as financial actors they are confronted with the same critical issues as their private-sector peers: How should a government assess its cost of capital? How should its financial activities be accounted for? What are the systemic and macroeconomic effects? Are the institutions well-managed? Are its financial products well-designed?

Surprisingly, little research has focused on governments as financial institutions in their own right, and on finding solutions to the challenges they face. While private-sector financial theory and practice have benefited from decades of transformational innovations, public-sector financial thinking and education have not kept pace.

To help to bridge this knowledge gap, MIT is launching the Center for Finance and Policy (CFP) under the aegis of MIT Sloan’s Finance Group. A primary goal of the CFP is to be a catalyst for innovative, cross-disciplinary, and non-partisan research and educational initiatives. Its activities will address the unique challenges facing governments in their role as financial institutions, and also as regulators of private financial institutions. The aim is to provide much-needed support for policymakers and practitioners that will ultimately lead to improved decision-making, greater transparency, and better financial policies.

A quick look at recent headlines shows just how much is at stake and some of the significant decisions that need to be made. There’s the announcement by the BRICs about the formation of the New Development Bank, which will serve as a channel for large government-backed investments in those countries. In the U.S. there’s been heated debate over whether the Export-Import Bank should be reauthorized and whether the federal student loan programs are adequately serving students. There’s also the question of if, how and when the U.S. mortgage market will be reprivatized.

Research supported by the CFP is organized around three main tracks: the evaluation and management of government financial institutions, the regulation of financial markets and institutions, and the measurement and control of systemic risk. A critical focus of the CFP is the dissemination of knowledge to turn theory and data analysis into practice. That will be accomplished through policy briefs, conferences, the website, a visiting scholars program, and other initiatives.

We’re also focusing on education. The aim is to provide greater access to the tools of modern financial analysis to current and future regulators, policymakers and other stakeholders in the public sector. People working in the public sector have traditionally faced barriers to obtaining high-level financial education due to the cost and lack of a developed curriculum. We’re planning to use MIT edX to develop and offer material that will reach a broad audience free of charge. We also plan to offer special executive education programs and short courses at Sloan. To support those efforts, the CFP is investing in curriculum development in the application of financial concepts to public policy contexts.

The CFP will be officially announced in conjunction with our inaugural conference, which will take place Sept. 12-13. The conference will highlight new research related to its three main research areas. It features six paper sessions, three panel discussions, and a keynote address. Over 100 participants are expected to attend including policymakers, practitioners, and academics. The event will be available afterwards online.

I believe that the CFP’s research and educational initiatives will significantly move the needle on how policymakers think about their role as financial decision-makers and regulators, and ultimately have transformative effects on the quality and conduct of financial policy.

Deborah Lucas is the Sloan Distinguished Professor of Finance at MIT Sloan and Director of the MIT Center for Finance and Policy

Designing More Efficient CDS Auctions

Professor Haoxiang Zhu

Credit default swaps (CDS) are an important derivative class. According to the Bank for International Settlements, as of June 2013, CDS contracts have $24 trillion notional amount outstanding and $725 billion market value globally.

A CDS contract is a default insurance contract written on a firm, loan or sovereign country. Buyers of protection (CDS buyers) pay periodic premiums on a notional amount of debt to sellers of protection (CDS sellers), until the contract expires or default occurs, whichever is earlier. For example, if a bond investor wishes to insure against the default of $100 million corporate bonds, and a five-year CDS contract on that bond is quoted at 500 basis points (5%) per year, then the CDS buyer pays $5 million per year to the CDS seller for five years. If the bond defaults within five years, the CDS seller pays the CDS buyer the loss given default. The question is: What are the recovery value and default compensation?

The market uses CDS auctions to determine the recovery value of a defaulted bond. For example, the auction-determined recovery rate of Greece debt is 21.5 cents per euro. So, CDS sellers pay CDS buyers 78.5 (=100-21.5) cents per euro of debt insured. In addition to settling CDS contracts, CDS auctions also give investors an opportunity to trade defaulted bonds at zero bid-ask spread. Given the sheer size of CDS markets and high-profile defaults in the recent recession, it is important that CDS auctions deliver unbiased prices and efficient allocations. But do they?

In a recent research paper with Professor Songzi Du of Simon Fraser University, we find that the current design of CDS auctions leads to systematically biased prices and inefficient allocations.

To understand why the auction design is biased and inefficient, we need to understand the auction procedure itself. A CDS auction consists of two stages. In the first stage, investors who have CDS positions submit market orders (called “physical requests”) to buy or sell the defaulted bonds. An investor’s market order on the bond must be in the opposite direction of his CDS position, and no larger in magnitude. The sum of these market orders, called “open interest,” is sold in the second stage, which is a uniform-price auction. Importantly, only one-sided limit orders are allowed in the second stage. If the open interest is to buy, only limit sell orders are allowed; if the open interest is to sell, only limit buy orders are allowed. The market-clearing price in the second stage is the “official” recovery rate of the defaulted bond for settling CDS.

From 2006 to November 2013, this auction procedure has settled more than 140 defaults, including those of Lehman Brothers, Fannie Mae, General Motors, and Greece, among others.

Through a formal auction model, we show that the biased design comes from the restrictions imposed on the two stages of CDS auctions. To get the intuition, consider a CDS buyer. A CDS buyer naturally wishes to sell the defaulted bonds to minimize the uncertainty in the auction final price; he can eliminate this price risk by selling an amount equal to his CDS position. If this CDS buyer also has a low value for owning the bonds (for information or hedging motives), he would want to sell more. But the auction procedure forbids him from selling these additional quantities. A supply to sell is therefore suppressed in the first stage. In the second stage, this supply is suppressed again if the open interest is to sell (as only buy limit orders are allowed). Information from a suppressed demand cannot come into the price. Therefore, price is systematically biased, and allocations of bonds are inefficient.

This is not the end of the story. In an earlier version of the same research paper, we show that, if CDS traders are large, they also have a strong incentive to manipulate the final price auction price—to get favorable settlement payments on their CDS positions. Manipulation also leads to price biases.

The administrators of CDS auctions are aware of the biased prices; as a remedy, they impose a price cap or a price floor, depending on dealers’ quotes and the direction of the open interests. But this measure is imperfect and can backfire. We find that although a price cap or floor can correct price biases, it can also make bond allocations even less efficient.

What is a better solution then? We show that a simple, unconstrained double auction delivers better price discovery and allocative efficiency. A double auction for settling CDS is similar to the open and close auctions on stock exchanges. Since double auctions have done well in equity markets, why not consider it for CDS auctions?

For details of this research, see Songzi Du and Haoxiang Zhu, “Are CDS Auctions Biased and Inefficient?”. An earlier version of this paper is summarized by FT Alphaville (part 1, part 2).

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