Classifications and Key Concepts of Credit Risk (II)
“Behold, the fool saith, "Put not all thine eggs in the one basket" - which is but a matter of saying, "Scatter your money and your attention"; but the wise man saith, "Pull all your eggs in the one basket and - WATCH THAT BASKET." Mark Twain, Pudd'nhead Wilson's Calendar
In the first part of this article, we finished by looking to the relationship between value-at-risk (VaR), expected loss (EL) and unexpected loss (UL). VaR and other traditional measures are useful but do not account for concentration risk, a subject discussed in this article. We finish the article by presenting the concept of RARORAC.
Concentration Risk
Concentration risk arises when borrowers are exposed to common risk factors which could simultaneously affect their willingness and ability to repay their obligations. Examples of common risk factor are interest rates or exchange rates.
Concentration was traditionally mitigated by minimising exposure to a single borrower, minimizing risk through higher granularity and portfolio diversification. a standard metric used is the Herfindahl–Hirschman Index (HHI).
Portfolio credit risk models specifically factor in a borrower’s risk contribution to concentration and allow for segmentation of the portfolio risk with a more holistic perspective. Examples of credit risk models used for economic capital purposes are CreditMetrics, KMV Portfolio Manager, CreditRisk+ or CreditPortolioView. The selection of the most appropriate model depend on a multitude of factors as all of these models have advantages/disadvantages.
Default co-dependency’s can be modelled with
- Asset value correlations: which look at the influence of external events on asset values
- Default correlations: which look at historical correlations among homogenous borrower groups.
From a portfolio perspective, it is also important to measure how an individual exposure, or the addition of a new exposure, contributes to overall portfolio risk. One such measure is marginal VaR, which calculates the incremental portfolio risk from an individual exposure. The marginal contribution can be calculated as:
Where:
ULCi = marginal contribution of the ith loan portfolio unexpected loss
ULportfolio = portfolio unexpected loss
wi = weight of the ith loan in the overall portfolio
The same measure can be expressed under the Markowitz mean-variance framework as:
Where:
pi,portfolio = default correlation between the i th loan and the overall portfolio
RARORAC
The risk-adjusted return on capital (RAROC) and the risk-adjusted return on risk-adjusted capital (RARORAC) are popular among banks in measuring risk-adjusted performance. Both are used by the business to assess whether returns generated exceed the market risk premium required by capital or not.
RARORAC should incorporate funding cost, EL, allocated economic capital and excess return required by shareholders:
Transactions create value if RARORAC exceeds a minimum target, e.g., return on equity (ROE):
And the economic value added (EVA) that measure the firm’s economic profit can be determined as:
where Ke is the cost of shareholder capital.
The goal of this type analysis is to get a global perspective of profitability, costs, revenues, and risks by segmenting customers to identify profitable vs unprofitable relationships. Capital currently set aside for unprofitable or marginally profitable customers/transactions could then be reallocated to more profitable opportunities/transactions.
Sources:
Giacomo De Laurentis, Renato Maino, and Luca Molteni, Developing and Using Internal Ratings (West Sussex, UK: John Wiley & Sons, 2010). Chapter 2