In HFT, are strategies (e.g. optimal execution, market making) purely mathematical or do they mainly rely on the technology (e.g. speed, collocation)? originally appeared on Quora: the place to gain and share knowledge, empowering people to learn from others and better understand the world.

Answer by Christian Daniel Griset, Former quant and theoretical physicist, on Quora:

From my experience, high-frequency trading strategies require speed, mathematical modeling and a lot of gaming.

The Speed Game:

In HFT, technology is key, almost by definition. When you're playing a speed game you need 1) proximity, 2) hardware and 3) highly efficient algorithms.

Proximity matters because, as you can imagine, the closer you are to the exchange, the faster you see and react to its activity. This is due to the speed of light being finite.

Hardware matters a lot, and tends to be a highly intricate problem facing HFTs. FPGAs have caught fire, as well as "microwave towers". FPGAs are a type of hardware with the trade off that you need to encode simple logic, but it can execute on that logic very quickly. With respect to microwave towers, they've grown in importance especially for international trading. Rather than sending signals through underground fiber cables, the signals are sent from tower to tower, and packets travel faster through air than fiber (most of the time). It also matters that operational speed is a function of raw machine temperature, among other things.

The efficiency of algorithms is a deep problem. Big O analysis isn't enough here, you need to know the exact processing speed of simple operations like multiplication and addition (divisions are extremely expensive and should be avoided at all costs). Further, each operation adds up, which means you want your models to be extremely simple. A model using 500 features will very often underperform one using only 3 features even if the model is "more predictive". This is because predicability doesn't mean anything if you can't successfully act on those predictions.

The Math Game:

There's a ton of math in HFT. Note that the complex math very often involves research and creating a strategy. While the algorithms need to be simple, the research needn't be.

At the most basic level, there's classical stats. You'll need to be able to thoroughly vet any hypothesis. Financial data is extremely noisy, and validation requires extreme care in preparing and running any analysis.

There's also "machine learning". Often, machine learning in HFT means running intricate statical fits on linear models. SVMs and neural networks are usually more difficult to apply, in large part because of market noise. Outside of in/out sample methodology, there's a lot of interesting work around the kind of targets and "objective functions" you use. With respect to targets, you have to have an idea of what you're trying to predict. Do you choose to fit on the midpoint five minutes into the future? The thirty second EMA ten minutes from now? Next trade, or ten trades? End of day auction trade price? All of these will likely lead to qualitatively different fits. Objective functions are the functions used for optimization. In classical OLS, the objective function is simply:

Objective functions are highly nontrivial in how they fit, select, over and under fit. Lasso's are nice because they pick out only a handful of features from your feature set, so if you fit on 500 features, perhaps only five return nonzero (this is because absolute values aren't differentiable at zero). However there are significant difficulties around how to handle outliers and highly correlated variables.

Another interesting mathematical component involves risk management. Risk management can often be decomposed as a linear algebra problem. Your goal as a trader/quant isn't only to maximize PNL, but also make sure on any given day your portfolio doesn't blow up. One useful strategy is hedging your portfolio with broad market indices. You can use PCA, for example supplied by Barra for equities, to identify precisely where portfolio risk lies and optimizing how to hedge, taking into account "hedging costs".

The Game:

The market isn't full of innocent players trading on what they honest to god think is a great price. Many players aim to manipulate markets using a large variety of techniques. For example, some sophisticated players might recognize when markets are "too flimsy" so buy some shares, see the market overreact, shooting to a much higher price, then sell at the higher price. More intricate gamesmanship involve exotic order types offered by exchanges and gaming the quirks of exchange microstructure.

All in all:

HFT strategies incorporate to some level speed, mathematical modeling and market gaming. Some strategies are highly focused speed trades, while others take advantage of market quirks, but in general successful HFT shops are highly versed in each of these facets.

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