LO 53.2: Explain how model risk and variability can arise through the

LO 53.2: Explain how model risk and variability can arise through the implementation of VaR models and the mapping of risk factors to portfolio positions. * 1
Risk management is typically implemented via computer systems that help to automate gathering data, making computations, and generating reports. These systems can be made available commercially, and are typically used by smaller firms, while larger firms tend to use their own in-house systems, often in combination with commercial models. The implementation process for computing risk is usually referred to as the firms VaR m od el, although the general computation process can apply to any risk measure other than VaR.
Data preparation is crucial in risk measurement systems. There are three types of data involved: 1. M ark et data is time series data (usually asset prices) that is used in forecasting the
distribution of future portfolio returns. Market data involves obtaining the time series data, removing erroneous data points, and establishing processes for missing data. All of these steps can be costly but necessary.
2. S ecurity m aster data is descriptive data on securities, including maturity dates,
currency, and number of units. Building and maintaining data for certain securities, including equities and debt, can be challenging; however, it is critical from a credit risk management perspective.
3. P osition data matches the firms books and records but presents challenges as data must
be collected from a variety of trading systems and across different locations.
Once the data is collected, software is used to compute the risk measures using specific formulas, which are then combined with the data. Results are then published in documents for reporting by managers. All of these steps can be performed in numerous ways and can lead to several issues within the risk measurement system. We focus on two of these issues: the variability of the resulting measures and the appropriate use of data.
Variability in risk measures, including VaR, is both a benefit and a problem. Managers have significant discretion and flexibility in computing VaR, and parameters can be freely used in
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many different ways. This freedom in measuring VaR leads to two significant problems in practice: 1. Lack o f standardization o f VaR param eters. Given the variability in VaR measurements and managers discretion, parameters including confidence intervals and time horizons can vary considerably, leading to different measurements of VaR.
2. D ifferen ces in VaR m easurem ents. Even if VaR parameters were standardized, differences
in measuring VaR could lead to different results. These include differences in the length of the time series used, techniques for estimating moments, mapping techniques (discussed in the next section) and the choice of risk factors, decay factors in using exponentially weighted moving average (EWMA) calculations, and the number of simulations in Monte Carlo analysis.
Varying parameters can lead to materially different VaR results. For example, one study using different combinations of parameters, all within standard practice, of portfolios consisting of Treasury bonds and S&P 500 index options indicated that VaR results differed considerably by a factor of six or seven times. A simple read of the different VaR models published in the annual reports of some of the larger banks can give an indication of the variability in their measurements.
R i s k F a c t o r M a p p i n g f o r Va R C a l c u l a t i o n s
Mapping refers to the assignment of risk factors to positions. Mapping choices can also impact VaR results. These could include practical choices among alternatives where each alternative has its benefits and disadvantages. For example, managers have a choice between cash flow mapping and duration-convexity mapping for fixed income securities. Cash flo w m a p p in g leads to greater accuracy (each cash flow is mapped to a fixed income security with an approximately equal discount factor); however, du ration -convex ity m a p p in g requires fewer and less complex computations, reducing costs and potential data errors as well as model risks.
It may also be difficult to locate data that addresses specific risk factors. One example is the previously widespread practice of mapping residential mortgage-backed securities (RMBS) or other securitized products to corporate credit spreads of the same rating. Because data on securitization spreads is typically not widely available, using a proxy risk factor of generic corporate bond spreads can be misleading, especially since previously lower spreads on securitizations widened considerably more during the recent financial crisis than did corporate spreads. This is an example of model risk and the inefficiency of VaR estimates in modeling large movements in market prices.
Incorrect mapping to risk factors can create risks such as liquidity risk and basis risk. Liquidity risk arises from divergences in model and market prices. For example, convertible bonds can be mapped to risk factors including implied volatilities, interest rates, and credit spreads based on the theoretical (model) price of the convertible bond using a replicating portfolio. However, significant divergences in model and market prices are difficult to capture with market data, and as a result, VaR estimates based on the replicating portfolio can considerably understate risk, creating liquidity risk.
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Basis risk is the risk that a hedge does not provide the required or expected protection. Basis risk arises when a position or its hedge is mapped to the same set of risk factors, which can be done when it is difficult to distinguish between two closely related positions. While this results in a measured VaR of zero, the positions have significant basis risk. Basis risk is also present in the risk modeling of securitization exposures where securitizations are hedged with corporate credit default swap (CDS) indices of similar ratings.
Other strategies can also lead to misleading VaR estimates. For example, event-driven strategies have outcomes that are close to binary and depend on a specific event occurring, including mergers or acquisitions, bankruptcy, or lawsuits. For these trades, the range of results cannot be measured based on historical return data. Dynamic strategies are another example, where risk is generated over time rather than at a specific point in time.
C r e d i t M a r k e t i n E a r l y 2005