Integrating Regulatory Risk Across Different Horizons

Summary

The document addresses how market, credit, and operational risks can contribute to a common regulatory capital measure despite being assessed over different time horizons. Its answer frames this as a risk integration problem: estimate loss distributions for the relevant risk factors at planning horizons informed by their liquidity horizons, model dependencies between those risks, and specify how positions are treated as time passes.

For a liquid trading portfolio, the answer illustrates that a longer planning period can be represented as successive shorter periods, with the portfolio rolled over between them. This makes clear that capital aggregation is not simply the addition of headline risk figures calculated at incompatible horizons; it depends on horizon alignment, correlation assumptions, and rollover conventions. The response is a high-level outline rather than a regulatory formula or worked calculation. It does not specify a particular framework, calibration method, or treatment for every risk category, so implementation requires further guidance and modeling choices.

Key ideas

• Risk integration estimates loss distributions on planning horizons related to the risks’ liquidity horizons.
• Combining risk measures requires modeling dependence between the relevant risk factors.
• Long planning periods can be divided into shorter intervals for liquid portfolios, with rollover assumptions.
• The answer outlines the issues but does not give a specific capital formula or calibration procedure.

Tags

# Calculation of Regulatory Capital


# Calculation of Regulatory Capital












As per my understanding, the `Regulatory capital` for a Financial institution is calculated as sum of `Market risk, Credit risk, and Ops risk`.

However, in most cases, the Market risk is calculated as 10 days horizon and Credit risk for 1 year horizon.

Then how can these 2 measures be additive to come up with a single measure for capital?

I appreciate your insight.

## Answer by Sharad (score 1)

https://quant.stackexchange.com/a/59845

There is a significant amount of literature on this topic ("risk integration") and a number of different approaches have been proposed. A relatively accessible introduction to this topic (See Chapter 7 in particular) can be found here: Stress Testing and Risk Integration in Banks. At a high level, adding the risk measures involves estimating the loss distributions of the different risk factors at their planning horizons (which are a function of their individual liquidity horizons), modeling their correlations, and making some assumption as to how the more liquid portfolios are rolled over at the end of each planning period. For example, a one-year planning period might be split up into 12 months for a very liquid trading book.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.