What is quantitative finance?

The short answer

A quant takes a claim about markets, such as “stocks that fell sharply this week tend to bounce next week”, and refuses to believe it until the data agrees. The claim becomes a precise rule. The rule is run over years of past prices. The result is checked against data the rule never saw while it was being built. Only then does anyone consider trading it, and even then the size of each trade is set by how much could be lost.

That habit, from idea to rule to test to measured risk, is the whole field in miniature. Everything else is the tools that make each step reliable.

Where quants work

Quants work in four kinds of places, and the work differs a lot between them.

• Banks, often called the sell side. Banks sell products such as options and structured notes to clients. Their quants build the models that put a fair price on those products and measure how much risk the bank carries from selling them.
• Hedge funds and asset managers, the buy side. Their quants look for patterns in prices and other data that predict returns, then build portfolios that try to profit from them.
• Proprietary trading firms and market makers. These firms trade their own money, often thousands of times a second. Their quants work on short-term prediction, order placement and the speed of their systems.
• Risk, regulation and financial technology. Insurers, regulators, exchanges and data companies all employ people who build, check or supply the models the others use.

The work, step by step

Most quantitative work, whatever the employer, follows the same loop.

1. State the idea precisely. “Momentum works” is not testable. “Buy the tenth of stocks with the best twelve-month return, skipping the latest month, and hold for one month” is.
2. Get clean data. Prices need adjusting for splits and dividends, and the list of stocks must include the companies that later went bust, or the test will look better than reality.
3. Test it on the past. This is called a backtest. It includes trading costs, because a strategy that trades often can lose its whole edge to costs.
4. Check it out of sample. The rule is run on a stretch of data that played no part in designing it. Many strategies that look excellent in step 3 fail here.
5. Size the risk. Before trading, the quant decides how much to put on each position so that a bad run is survivable.
6. Trade it and watch it. Live results are compared with what the test promised. When they drift apart, the model is questioned before more money is risked.

The maths, without the fear

Four areas of mathematics do most of the work.

• Probability and statistics. Market returns are random, so every result is an estimate with an error around it. Statistics says how far that error goes. A strategy that made money over two years may simply have been lucky, and statistics is how you tell.
• Calculus and optimisation. Used to find the best portfolio for a given level of risk, and to see how a price changes when its inputs change.
• Linear algebra. A portfolio of five hundred stocks is a vector, and the way those stocks move together is a matrix. Factor models and risk models are linear algebra at heart.
• Stochastic calculus. The maths of quantities that move randomly through time. It is essential for pricing options and other derivatives, and much less used on the buy side.

One fact matters early: real returns have fatter tails than the bell curve. Large losses happen far more often than a normal distribution predicts. Any model that assumes otherwise will understate risk exactly when it matters most.

The code

Quants test ideas by writing programs. Python, with libraries such as pandas and NumPy, is the everyday tool for loading data, running tests and drawing results. SQL is how the data gets out of a database in the first place. C++ appears where speed counts, in pricing libraries and in trading systems that react in microseconds.

You do not need to be a software engineer to start. You do need to reach the point where you can load ten years of prices, compute something from them and trust the answer.

Three common misunderstandings

“Quants predict the market.” Mostly they do not. A good quantitative strategy is often right only slightly more than half the time. It makes money because it is applied many times, with costs controlled and losses limited.

“A great backtest proves a strategy works.” A backtest is easy to fool. Try enough variations and one will look brilliant by chance. This is why out-of-sample checks, and a record of how many ideas were tried, matter more than any single result.

“It is all about speed.” Speed matters for a small group of high-frequency firms. Most quantitative work runs on daily or weekly data, and the hard part is thinking clearly about evidence.

Where to go next

If the loop above interests you, the next questions are what the jobs look like and how people get them. Read about quant careers, then the step-by-step route to becoming a quant. Or start with the Institute’s free course, which covers this ground in six hours.