## BLOCK III: CAPITAL ALLOCATION AND RISK CONTRIBUTIONS

Category: Risk Management in Banking

The risk contribution of a facility to a reference portfolio is the risk of the facility not diversified away by the portfolio diversification. It is much lower than the standalone risk of the facility. Risk contributions serve several purposes:

• Measuring the risk not diversified away by diversification.

• Allocating capital to existing facilities or segments of the reference portfolio, and defining limits in capital.

• Allocating capital to new facilities or portfolios for decision-making purposes.

• Comparing risk-adjusted performances, for the existing portfolio, or defining risk-based pricing, for new transactions, using Risk-adjusted Return on Capital (RaRoC) measures.

There are different risk contributions:

• Absolute risk contributions sum to the portfolio loss volatility or the portfolio capital.

• Marginal contributions are the incremental risk of a facility or a portfolio segment to the reference portfolio. They are the difference of risks with and without the facility or the subset of facilities selected.

Models derive absolute risk contributions from the formula giving the variance of the portfolio losses as a function of individual facility value variances and covariances. Marginal risk contributions require a with and without calculation of the portfolio risk.

KMV Portfolio Manager calculates the absolute risk contributions, and Credit Metrics provides the marginal risk contributions. Otherwise, end-users can calculate absolute risk contributions to the portfolio loss variance (volatility) using the analytical formula giving the portfolio loss variance (volatility) as a function of pair covariances. Running with and without calculations provides marginal risk contributions.

In Chapters 51 and 52, we show that absolute risk contributions serve for capital allocation within an existing portfolio and that marginal risk contributions serve for risk-based pricing of new facilities.

BLOCK IV: RISK-RETURN VIEW

Once income and risk for a portfolio are available, it becomes possible to alter the risk-return profile of the portfolio by changing the structure of the portfolio. The rationale follows the classical portfolio optimization theory: minimize risk given return or maximize revenues given risk, or maximize the Sharpe ratio (expected return/volatility) of the portfolio.

Within this familiar theoretical framework, it is relatively straightforward to optimize mathematically the portfolio, without integrating any business constraint. Only KMV Portfolio Manager offers a risk-return optimization function, but it ignores such constraints as limits on industries or countries for instance.

In addition, portfolio models serve as what if tools for determining how portfolio management alters the risk-return profile of the portfolio. It becomes possible to find the effect of a securitization or of credit derivatives and insurance on the overall risk-return profile. What if simulations help us to find which portfolio structures are better than others in terms of both risk and return. As such, portfolio models fully address the economics of portfolio management.