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High-frequency trading

High-frequency trading is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand High-frequency trading rather than just read about it. In short: High-frequency trading (HFT) is a type of algorithmic automated trading system in finance characterized by high speeds, high turnover rates, and high order-to-trade ratios that leverages high-frequency financial data and electronic trading tools. While there is no single definition of HFT, among its key attributes are highly sophisticated algorithms, co-location, and very short-term investment horizons in trading se…

High-frequency trading — main illustration
High-frequency trading — illustration

Key takeaways

  • High-frequency trading belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect High-frequency trading to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of High-frequency trading from memory before moving on to harder problems.

Reference excerpt

High-frequency trading (HFT) is a type of algorithmic automated trading system in finance characterized by high speeds, high turnover rates, and high order-to-trade ratios that leverages high-frequency financial data and electronic trading tools. While there is no single definition of HFT, among its key attributes are highly sophisticated algorithms, co-location, and very short-term investment horizons in trading securities. HFT uses proprietary trading strategies carried out by computers to move in and out of positions in seconds or fractions of a second. In 2016, HFT on average initiated 10–40% of trading volume in equities, and 10–15% of volume in foreign exchange and commodities. High-frequency traders move in and out of short-term positions at high volumes and high speeds aiming to capture sometimes a fraction of a cent in profit on every trade. HFT firms do not consume significant amounts of capital, accumulate positions or hold their portfolios overnight. As a result, HFT has a potential Sharpe ratio (a measure of reward to risk) tens of times higher than traditional buy-and-hold strategies. High-frequency traders typically compete against other HFTs, rather than long-term investors. HFT firms compensate for low profit margins by executing extremely high volumes of trades, often numbering in the millions. A substantial body of research argues that HFT and electronic trading pose new types of challenges to the financial system. Algorithmic and high-frequency traders were both found to have contributed to volatility in the Flash Crash of May 6, 2010, when high-frequency liquidity providers rapidly withdrew from the market. Several European countries have proposed curtailing or banning HFT due to concerns about volatility. Other complaints against HFT include the argument that some HFT firms scrape profits from investors when index funds rebalance their portfolios.

History The rapid-fire computer-based HFT developed gradually since 1983 after NASDAQ introduced a purely electronic form of trading. At the turn of the 21st century, HFT trades had an execution time of several seconds, whereas by 2010 this had decreased to milli- and even microseconds. At that time, high-frequency trading was still a little-known topic outside the financial sector, with an article published by the New York Times in July 2009 being one of the first to bring the subject to the public's attention. On September 2, 2013, Italy became the world's first country to introduce a tax specifically targeted at HFT, charging a levy of 0.02% on equity transactions lasting less than 0.5 seconds.

Market growth In the early 2000s, high-frequency trading still accounted for fewer than 10% of equity orders, but this proportion was soon to begin rapid growth. According to data from the NYSE, trading volume grew by about 164% between 2005 and 2009 for which high-frequency trading might be accounted. As of the first quarter in 2009, total assets under management for hedge funds with high-frequency trading strategies were $141 billion, down about 21% from their peak before the worst of the 2008 financial crisis, although most of the largest HFTs are actually LLCs owned by a small number of investors. The high-frequency strategy was first made popular by Renaissance Technologies who use both HFT and quantitative aspects in their trading. Many high-frequency firms are market makers and provide liquidity to the market which lowers volatility and helps narrow bid–offer spreads, making trading and investing cheaper for other market participants.

Market share In the United States in 2009, high-frequency trading firms represented 2% of the approximately 20,000 firms operating today, but accounted for 73% of all equity order volume. The major U.S. high-frequency trading firms include Jane Street Capital , Hudson River Trading, Susquehanna International Group, XTX Markets, Virtu Financial, Tower Research Capital, IMC, Tradebot, Akuna Capital and Citadel LLC. The Bank of England estimates similar percentages for the 2010 UK market share, also suggesting that in Europe HFT accounts for about 40% of equity orders volume and for Asia about 5–10%, with potential for rapid growth. By value, HFT was estimated in 2010 by consultancy Tabb Group to make up 56% of equity trades in the US and 38% in Europe. As HFT strategies become more widely used, it can be more difficult to deploy them profitably. According to an estimate from Frederi Viens of Purdue University, profits from HFT in the U.S. has been declining from an estimated peak of $5bn in 2009, to about $1.25bn in 2012. Though the percentage of volume attributed to HFT has fallen in the equity markets, it has remained prevalent in the futures markets. According to a study in 2010 by Aite Group, about a quarter of major global futures volume came from professional high-frequency traders. In 2012, according to a study by the TABB Group, HFT accounted for more than 60 percent of all futures market volume in 2012 on U.S. exchanges.

Strategies High-frequency trading is quantitative trading that is characterized by short portfolio holding periods. All portfolio-allocation decisions are made by computerized quantitative models. The success of high-frequency trading strategies is largely driven by their ability to simultaneously process large volumes of information, something ordinary human traders cannot do. Specific algorithms are closely guarded by their owners. Many practical algorithms are in fact quite simple arbitrages which could previously have been performed at lower frequency—competition tends to occur through who can execute them the fastest rather than who can create new breakthrough algorithms. The common types of high-frequency trading include several types of market-making, event arbitrage, statistical arbitrage, and latency arbitrage. Most high-frequency trading strategies are not fraudulent, but instead exploit minute deviations from market equilibrium.

Market making

According to SEC:

… excerpt ends here. Continue reading the full article.

Illustrations

High-frequency trading illustration

Worked examples

Example 1 — a first encounter with High-frequency trading

Start with the simplest possible case. Write down what High-frequency trading claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to High-frequency trading before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about High-frequency trading ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of High-frequency trading

In research
High-frequency trading appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses High-frequency trading in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
High-frequency trading is common in secondary-school and first-year university syllabi. It links to neighbouring topics Algorithmic trading, Electronic trading systems, Financial markets, so understanding it makes those chapters shorter.
In everyday life
Look for High-frequency trading outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study High-frequency trading in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what High-frequency trading means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain High-frequency trading out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is High-frequency trading in simple terms?

High-frequency trading (HFT) is a type of algorithmic automated trading system in finance characterized by high speeds, high turnover rates, and high order-to-trade ratios that leverages high-frequency financial data and electronic trading tools. While there is no single definition of HFT, among it…

Why does High-frequency trading matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study High-frequency trading?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on High-frequency trading.

Tags

  • Algorithmic trading
  • Electronic trading systems
  • Financial markets
  • Mathematical finance
  • Share trading

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