Category: Research

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.

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

Stimulus or austerity: an economist’s search for answers

New finance faculty member Jonathan Parker examines the effects of 2008 stimulus payments

Professor Jonathan Parker

In February 2008, Congress passed a $100 billion stimulus bill aimed at shoring up an an economy on the edge of freefall.

The stimulus awarded a tax rebate of up to $600 per person or $1,200 per couple in hopes that recipients would spend the money and prop up the sagging economy.

Jonathan Parker, one of MIT Sloan’s newest professors, said he believes the 2008 Economic Stimulus Act offers a promising opportunity to study a vexing question: Is household stimulus effective and good public policy?

“My research suggests that the stimulus payments did increase spending, and the extent to which they did informs us about the effects of similar policies on the economy.” Parker said. “We now have a reasonable idea about the spending responses to hitting the Fiscal Cliff or to a proposed tax change.”

“Whether the stimulus bill was good public policy, some will say ’yes,’ others will say ’no,’” he said. “That’s one of the things I’m studying.”

Parker joins MIT Sloan from Northwestern’s Kellogg School of Management, where he wrote several papers examining the impact of stimulus spending. He says at MIT he expects to continue to study stimulus spending versus austerity.

“My view is there is not a great case for either,” Parker said. “A convincing quantitative picture is still murky. A requisite for clarifying that picture is a better understanding of how firms and households behave. That’s what I’m continuously chasing.”

Parker’s path

This fall, Parker returns to MIT, where he received his doctorate in 1996. He joins an impressive roster of finance faculty at MIT Sloan, which is home to Nobel laureate Robert Merton and 2012 Time 100 honoree Andrew Lo.

“It’s a great institution with fantastic colleagues, from the grad students to the most senior faculty member,” Parker said. “It’s an exciting place to be.”

It is also a personal homecoming for Parker, who was born in Portland, Ore., but raised in the Boston suburb of Newton.

As a child, Parker couldn’t avoid being influenced by the academic life. Both parents worked at Boston University—his mother was an administrator, his father a professor of ancient Near Eastern languages and religion specializing in the ancient language Ugaritic.

While he didn’t choose economics until college, Parker’s studies began at the kitchen table.

“My mother was continuously coming up with mechanisms to make sure things were reasonably fairly divided between me and my brother,” he said. For instance, one brother sliced a piece of cake and the other brother got to pick which slice he got. “There’s something about that in economics, determining allocations in reasonable ways, understanding incentives, and thinking about how to make mechanisms that efficiently allocate resources,” said Parker.

His parents sent him to the rigorous Roxbury Latin School in the West Roxbury neighborhood of Boston. Parker went on to earn a bachelor’s in economics and mathematics from Yale University in 1988, and later a PhD in economics from MIT. The longtime headmaster at Roxbury Latin, F. Washington “Tony” Jarvis, an Episcopal priest who oversaw the school from 1974 to 2004, left a lasting impression.

“He was an inspirational figure for thinking about living for more than a house in the suburbs and the 2.5 kids and a minivan,” Parker said. “It was about doing something bigger, better, and beneficial to other people rather than measuring success in life by income.”

Work and public service

Parker studies household economics and asset pricing—the big economic questions that touch on people’s everyday lives.

After posts at the University of Michigan and the University of Wisconsin, Parker taught at Princeton University.

In 2009, while at Northwestern, Parker was tapped to join a team of economists charged with devising a way to attach values to the assets in the government’s Troubled Asset Relief Program (TARP) portfolio. It was critical to find ways to help the government pin values to assets to protect taxpayers. There were many challenges, Parker said.

“How do we value claims the government holds against AIG, Citigroup, and most of the smaller banks in the U.S.?” Parker asked. “Many of the claims on these institutions held by the U.S. government—and so taxpayers—were not traded in the marketplace, so how do you figure out their worth? Given that some may not pay the government back, and the government controls policies that influence whether they will be able to, how do you price the risk in these banks?”

Parker’s work studying the efficacy of stimulus spending started at Princeton with the tax rebates of 2001, and continued at Northwestern. There he set out in several studies to measure exactly what households did with their stimulus checks, and why, with an eye toward influencing future policy.

In 2012, Parker wrote “The Economic Stimulus Payments of 2008 and the Aggregate Demand for Consumption,” with Christian Broda of Duquesne Capital Management. The pair used consumer purchase scans to see how the tax rebates were spent.

What they learned was that after rebates arrived, households raised spending 10 percent in the first week and 4 percent in the following seven weeks, then the spending trailed away. Almost all consumer spending was by households with incomes of $35,000 or less and with two months or less of liquid assets.

Parker said it is tough to sell stimulus programs if households believe they don’t work and are costly because they add to the nation’s long-term debt.

“The $64,000 question is, ’What do we do now—with the US debt to GDP as high as it is and a perceived need to increase spending for demand?’” Parker said. “There’s a tough trade-off because household spending reflects not just cash flow, but also future concerns about who’s going to pay, and will there be a default crisis?”

His research so far doesn’t give a clear answer—stimulus or austerity. But then again, no one has the answer yet.

“Economists who get on TV and say ’I’m sure we should do more stimulus’ or claim that the only way forward is austerity, they are not getting there from the academic evidence they’ve read,” Parker said. “They’re getting there from somewhere else.”

“I’m always humbled by how little we know,” Parker said. “The world is infinitely more complex than our economic models. So we’re continuously learning. Some of the biggest questions in economics are still up for grabs.”