Credit Risk
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Subject
Emmanuel Noblet
Credit risk
diversification benefit, Allocation key to portfolio components.
economic
capital:
Measure,
Attribution
portfolio
Recent years have witnessed significant advances in the design, calibration and implementation of credit risk portfolio models. ING currently uses Moodys KMV (Kealhofer, McQuown and Vasicek) Portfolio Manager ([PM]).
Models enrich managements ability to make informed decisions to identify concentrations of risk and opportunities for diversification within a disciplined and objective framework, and thus offer a more sophisticated, less arbitrary alternative to traditional lending limit controls.
It is thus essential to make sure models are in line with managements goals and vice versa to make sure management takes some perspective to understand how the central measure it returns, namely credit risk economic capital ([EC]), is constructed and what it means.
This memo aims at explaining:
A) how credit risk is measured;
B) what the implications of attributing or not portfolio diversification effects are; C) how this portfolio measure is then allocated back to the portfolio components.
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Allocation key to portfolio components. 2/11 Date
13 June 2006
A – How is credit risk measured?
Back to basics, a credit risk portfolio model is a function that maps a set of facility-level characteristics and market-level parameters to a distribution of potential portfolio credit losses.
This definition is better known as Value-at-Risk ([VaR]). The concept of VaR has become the standard risk measure used to evaluate exposure to risk. In general terms, the VaR is the amount of capital required to ensure, with a given degree of certainty α, that the firm does not become technically insolvent, over a given time horizon tH.
There are two very important notions in this definition:
1. The time horizon tH;
2. The degree of certainty α.
The risk management time horizon tH should reflect the time a financial institution is committed to holding its portfolio. In other words, the time horizon should in principle reflect the length of time ING Bank is exposed to credit risk, and cannot substantially reduce this risk and / or increase capital. This time is affected by contractual and legal constraints on the one hand and by liquidity considerations on the other.
Illiquid markets1 pose a problem for the interpretation of VaR numbers. This was first brought to the attention of professional risk managers by Lawrence and Robinson in Liquid measures. Risk, 8 July, PP52-55, 1995. To quote from their paper:
“If we ask the question: “Can we be 98% confident that no more than l would be lost in liquidating the position?” the answer must be “no”. To see why, consider what this measure of VaR implies about the risk management process and the nature of financial markets. In the liquidation scenario we are considering the following sequence of events is implied: at time t it is decided to liquidate the position; during the next 24 hours nothing is done []; after 24 hours of inaction the position is liquidated at prices which are drawn from a [prespecified] distribution unaffected by the process of liquidation. This scenario is hardly credible. [] In particular, the act of liquidating itself would have the effect of moving the price against the trader disposing of a long position or closing out a
1 A market for a security is termed liquid if investors can buy or sell large amounts of the security in short time without dramatically affecting its price. Conversely, a market in which the attempt to trade has a large impact on price since there is no counterparty willing to take the other side of the trade, is termed illiquid.
Allocation key to portfolio components. 3/11 Date
13 June 2006
They conclude that “any useful measures of VaR must take into account the costs of liquidation on the prospective loss.” The events surrounding the near-bankruptcy of the hedge fund LTCM in summer 1998 clearly showed that the concerns of Lawrence and Robinson are more than justified. In fact, illiquidity of markets is regarded by many as the single most important source of risk. Ideally, we should therefore embed the effects of market illiquidity into our models. However, this turns out to be difficult for a number of reasons: first, the price impact of trading a particular amount of a security at a given point in time is hard to measure; it depends on such elusive factors as market mood or the distribution of economic information among agents; second, in illiquid markets, agents are forced to close their position gradually over time to minimize the price impact of their transactions, this in turn would lead to different time horizons tH for different positions, rendering impossible the aggregation of risk measures across portfolios. As a result, this market liquidity factor is most often ignored when computing VaR numbers or related risk measures. In principle, INGs retained time horizon is one year. One could nevertheless imagine that EC is computed at different time horizons for different asset classes to identify “hotspots”.
The degree of certainty α is arbitrary chosen, as there is no right or wrong position, as long as this choice is aligned with managements goals.
INGs current choice (99.95%, i.e., given the chosen time horizon of one year, going bankrupt once in 2000 years) reflects INGs willingness to provide comfort to policyholders and regulators in case of extreme losses, as well as to keep cost of debt to