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A Snapshot on Marginal Risk Contributions

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Marginal Risk Contributions

Overview

This chapter focuses on marginal risk contributions, to portfolio loss volatility or to portfolio capital, and compares them with absolute risk contributions. Marginal risk contributions serve essentially for risk-based pricing with an ‘ex ante’ view of risk decisions, while absolute risk contributions are the basis for the capital allocation system.

Marginal risk contributions to capital are the correct references for risk-based pricing. Pricing based on marginal risk contributions charges to customers a mark-up equal to the risk contribution times the target return on capital.

The mark-up guarantees that the return on capital for the entire portfolio will remain in line with the target return when adding new facilities. However, prices based on marginal risk contributions are lower than prices based on absolute risk contributions.

This is a paradox, since the absolute risk contributions are the ones that sum to capital. In fact the new facility diversifies the risk of those existing facilities prior to the entrance of any new one. Therefore, adding a new facility results in a decline in all absolute risk contributions of existing facilities. Because of this decline, the overall return of the portfolio remains on target.

However, the ex-ante measure of risk-based performance, on the marginal contribution and the ex-post measure, on the absolute contribution, differ for the same facility.

The Marginal Risk Contributions

The marginal contributions of a facility, or a sub-portfolio, to the portfolio loss volatility or to capital are the differences of the portfolio loss volatility, or the portfolio capital, with and without the facility or sub-portfolio. We calculate below both marginal risk contributions (MRC) to loss volatility and to capital. All calculations use the example of a two-obligor (A and B)

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