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Trying to understand what risk controls are used for algorithms that are classified as

a) execution algos such as twap, vwap

b) market making algos such as auto pricing, inventory management, auto hedging algos

I know there is a ton of guidance online about risk controls such as order notionals, message throttles, etc. however is there anything out there which is a bit more specific?

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There's 2 different types of risk controls that you're referring to.

The first class (for execution algos) is at a regulatory level and has to do with broker dealer requirements mandated by rules such as 15c3-5 and MiFID II. These are generally a series of exposure, margin and credit controls that need to be carried out on a pre-order basis. The regulation is not very specific, so the guidelines are better understood by guidance letters and enforcement actions such as this one.

The second class has to do with risk management at a strategy-level. This often includes statistical quantities like VaR, maximum drawdown, leverage ratio etc., but also shares overlap with those mandated at a regulatory level. The exact set of risk controls varies by firm.

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