LO 2.4: Identify advantages and disadvantages o f non-parametric estimation

LO 2.4: Identify advantages and disadvantages o f non-parametric estimation methods. *
Any risk manager should be prepared to use non-parametric estimation techniques. There are some clear advantages to non-parametric methods, but there is some danger as well. Therefore, it is incumbent to understand the advantages, the disadvantages, and the appropriateness of the methodology for analysis.
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Topic 2 Cross Reference to GARP Assigned Reading – Dowd, Chapter 4
Advantages of non-parametric methods include the following:
Intuitive and often computationally simple (even on a spreadsheet).
Not hindered by parametric violations of skewness, fat-tails, et cetera. Avoids complex variance-covariance matrices and dimension problems. Data is often readily available and does not require adjustments (e.g., financial
statements adjustments).
Can accommodate more complex analysis (e.g., by incorporating age-weighting with
volatility-weigh ting).
Disadvantages of non-parametric methods include the following:
Analysis depends critically on historical data. Volatile data periods lead to VaR and ES estimates that are too high. Quiet data periods lead to VaR and ES estimates that are too low. Difficult to detect structural shifts/regime changes in the data. Cannot accommodate plausible large impact events if they did not occur within the
sample period.
Difficult to estimate losses significantly larger than the maximum loss within the data set
(historical simulation cannot; volatility-weigh ting can, to some degree).
Need sufficient data, which may not be possible for new instruments or markets.
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Topic 2 Cross Reference to GARP Assigned Reading – Dowd, Chapter 4
K e y C o n c e p t s
LO 2.1
Bootstrapping involves resampling a subset of the original data set with replacement. Each draw (subsample) yields a coherent risk measure (VaR or ES). The average of the risk measures across all samples is then the best estimate.
LO 2.2
The discreteness of historical data reduces the number of possible VaR estimates since historical simulation cannot adjust for significance levels between ordered observations. However, non-parametric density estimation allows the original histogram to be modified to fill in these gaps. The process connects the midpoints between successive columns in the histogram. The area is then removed from the upper bar and placed in the lower bar, which creates a smooth function between the original data points.
LO 2.3
One important limitation to the historical simulation method is the equal-weight assumed for all data in the estimation period, and zero weight otherwise. This arbitrary methodology can be improved by using age-weighted simulation, volatility-weighted simulation, correlation-weighted simulation, and filtered historical simulation.
The age-weighted simulation method adjusts the most recent (distant) observations to be more (less) heavily weighted.
The volatility-weighting procedure incorporates the possibility that volatility may change over the estimation period, which may understate or overstate current risk by including stale data. The procedure replaces historic returns with volatility-adjusted returns; however, the actual procedure of estimating VaR is unchanged (i.e., only the data inputs change).
Cor relation-weigh ted simulation updates the variance-covariance matrix between the assets in the portfolio. The off-diagonal elements represent the covariance pairs while the diagonal elements update the individual variance estimates. Therefore, the correlation-weighted methodology is more general than the volatility-weighting procedure by incorporating both variance and covariance adjustments.
Filtered historical simulation is the most complex estimation method. The procedure relies on bootstrapping of standardized returns based on volatility forecasts. The volatility forecasts arise from GARCH or similar models and are able to capture conditional volatility, volatility clustering, and/or asymmetry.
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Topic 2 Cross Reference to GARP Assigned Reading – Dowd, Chapter 4
LO 2.4
Advantages of non-parametric models include: data can be skewed or have fat tails; they are conceptually straightforward; there is readily available data; and they can accommodate more complex analysis. Disadvantages focus mainly on the use of historical data, which limits the VaR forecast to (approximately) the maximum loss in the data set; they are slow to respond to changing market conditions; they are affected by volatile (quiet) data periods; and they cannot accommodate plausible large losses if not in the data set.
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Topic 2 Cross Reference to GARP Assigned Reading – Dowd, Chapter 4
C o n c e p t C h e c k e r s
Johanna Roberto has collected a data set of 1,000 daily observations on equity returns. She is concerned about the appropriateness of using parametric techniques as the data appears skewed. Ultimately, she decides to use historical simulation and bootstrapping to estimate the 5% VaR. Which of the following steps is most likely to be part of the estimation procedure? A. Filter the data to remove the obvious outliers. B. Repeated sampling with replacement. C. Identify the tail region from reordering the original data. D. Apply a weighting procedure to reduce the impact of older data.
All of the following approaches improve the traditional historical simulation approach for estimating VaR except the: A. volatility-weighted historical simulation. B. age-weighted historical simulation. C. market-weighted historical simulation. D. correlation-weighted historical simulation.
Which of the following statements about age-weighting is most accurate? A. The age-weighting procedure incorporates estimates from GARCH models. B.
If the decay factor in the model is close to 1, there is persistence within the data set.
C. When using this approach, the weight assigned on day i is equal to:
w(i) = Xi_1 x (1 X )/(1 X ) .
D. The number of observations should at least exceed 230.
Which of the following statements about volatility-weighting is true? A. Historic returns are adjusted, and the VaR calculation is more complicated. B. Historic returns are adjusted, and the VaR calculation procedure is the same. C. Current period returns are adjusted, and the VaR calculation is more
D. Current period returns are adjusted, and the VaR calculation is the same.
All of the following items are generally considered advantages of non-parametric estimation methods except: A. ability to accommodate skewed data. B. availability of data. C. use of historical data. D. little or no reliance on covariance matrices.
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Topic 2 Cross Reference to GARP Assigned Reading – Dowd, Chapter 4
C o n c e p t C h e c k e r An s w e r s
1. B Bootstrapping from historical simulation involves repeated sampling with replacement. The
5% VaR is recorded from each sample draw. The average of the VaRs from all the draws is the VaR estimate. The bootstrapping procedure does not involve filtering the data or weighting observations. Note that the VaR from the original data set is not used in the analysis.
2. C Market-weighted historical simulation is not discussed in this topic. Age-weighted historical simulation weights observations higher when they appear closer to the event date. Volatility- weighted historical simulation adjusts for changing volatility levels in the data. Correlation- weighted historical simulation incorporates anticipated changes in correlation between assets in the portfolio.
3. B
If the intensity parameter (i.e., decay factor) is close to 1, there will be persistence (i.e., slow decay) in the estimate. The expression for the weight on day i has i in the exponent when it should be n. While a large sample size is generally preferred, some of the data may no longer be representative in a large sample.
4. B The volatility-weighting method adjusts historic returns for current volatility. Specifically, return at time t is multiplied by (current volatility estimate / volatility estimate at time t). However, the actual procedure for calculating VaR using a historical simulation method is unchanged; it is only the inputted data that changes.
5. C The use of historical data in non-parametric analysis is a disadvantage, not an advantage. If the estimation period was quiet (volatile) then the estimated risk measures may understate (overstate) the current risk level. Generally, the largest VaR cannot exceed the largest loss in the historical period. On the other hand, the remaining choices are all considered advantages of non-parametric methods. For instance, the non-parametric nature of the analysis can accommodate skewed data, data points are readily available, and there is no requirement for estimates of covariance matrices.
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The following is a review of the Market Risk Measurement and Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Ba c k t e s t i n g VaR
Topic 3
E x a m F o c u s
We use value at risk (VaR) methodologies to model risk. With VaR models, we seek to approximate the changes in value that our portfolio would experience in response to changes in the underlying risk factors. Model validation incorporates several methods that we use in order to determine how close our approximations are to actual changes in value. Through model validation, we are able to determine what confidence to place in our models, and we have the opportunity to improve their accuracy. For the exam, be prepared to validate approaches that measure how close VaR model approximations are to actual changes in value. Also, understand how the log-likelihood ratio (LR) is used to test the validity of VaR models for Type I and Type II errors for both unconditional and conditional tests. Finally, be familiar with Basel Committee outcomes that require banks to backtest their internal VaR models and penalize banks by enforcing higher capital requirements for excessive exceptions.
B a c k t e s t i n g V a R M o d e l s