Optimisation of trading portfolios under regulatory capital constraints

Brice Benaben and Andrew Green

Like a rational economic agent, investment banks aim to maximise their expected profits. Their profits are derived from providing financial services and products to corporate and institutional clients. This is the main source of risk rather than taking market views as the Volcker Rule prohibits banks from proprietary trading. The important feature in the trading portfolios construction is the risk allocation, which is the topic of this chapter.

However, investment banks‘ risk frameworks have a regulatory dimension. While servicing their clients, banks take market risks, which are managed within their trading portfolios. Due to the important role of banks within the financial system, banks are regulated, and regulatory rules ensure that they have enough capital to cover these market risks.

We will review the regulatory rules, and focus first on the methodology to compute the market risk capital for the trading books. The new regulatory rules (Fundamental Review of the Trading Book, FRTB) encourage banks to cover a wide spectrum of market risks using modern risk management concepts.

Our second focus is on capital value adjustment (KVA). Investment banks have large positions in

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