This section uses a simple example to calculate various loss statistics including risk contributions. The example uses a pure default model, building up on the example of the two-obligor portfolio with 10% default correlation identical to that of Chapter 46. We do not replicate all detailed calculations.
This section provides the theoretical formulas of portfolio loss variance and volatility and their decomposition in absolute risk contributions, and shows how to derive the capital allocation. This is the basic capital allocation model. The next section illustrates these theoretical formulas and provides a fully detailed numerical example using the above two-obligor portfolio example.
The marginal contributions of a facility, or a subportfolio, 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 subportfolio. We calculate below both marginal risk contributions (MRC) to loss volatility and to capital.
Marginal risk contributions are relevant for such decisions as adding or removing a subportfolio, or pricing a new transaction according to its incremental risk. As with absolute risk contributions, marginal risk contributions refer either to capital or to loss volatility.
The goal of risk-based pricing is to ensure a minimum target return on capital, in line with shareholders requirements. A hurdle rate serves as a benchmark for risk-based pricing and for calculating creation or destruction of value with Shareholders Value Added (SVA).
The implication of what precedes is that we need both risk contributions, but for different purposes. Absolute risk contributions are ex post measures. They measure risk contributions for a given set of facilities. Therefore, absolute risk contributions serve to allocate capital for an existing portfolio. Marginal risk contributions are ex ante measures and serve for […]
Classical profitability measures include the Return On Equity (ROE) and the Return On Assets (ROA). Risk-based profitability measures embed risk adjustment combining expected loss and economic capital.
The revenues include the interest margin plus fees. The operating costs allocated to a transaction or portfolios include direct costs and overheads. In addition revenues, costs and risk should relate to the same perimeter. If risk is client-based, there is a case for consolidating all revenues and costs over the client portfolios.
The definition of a minimum required return for shareholders is a well-known topic with well-known solutions, as mentioned above when referring to the CAPM and APT models of required returns on equity given risk. We focus more here on its implications, first with respect to terms of pricing and second with respect to the capital […]
According to the CAPM, the required return on capital results from the market price of systematic risk of the stock. The APT model would provide similar benchmarks. Hence, it is possible to define a cost of equity depending on the risk of the banks stock required return in the equity market.
