Measuring Market Risk with Value at Risk (Wiley Series in Financial Engineering)

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Description

Figure 3 illustrates the calculation of B t and a deviation from a simple MA respectively. The B t in Figure 3 a is smoother than the deviation from the seven year MA in Figure 3b making it more stable for the calculation of regulatory capital. The deviation from the MA behaves procyclically as it neither detects nor avoids bubbles. The second unique element of the buVaR metric is the inflator, calculated using a boundary argument. A structural upper limit must also be determined: Wong suggests the inflator should also meet certain criteria to be deemed suitable.

A structural upper limit exists because of imposition of circuit breakers by regulators, and. Wong refers to the "avoidance of a one-size-fits-all" multiplier. The risk measure to calculate regulatory capital completes the buVaR model.

Measuring Market Risk with Value at Risk (Wiley Series in by Pietro Penza,Vipul K. Bansal PDF

Wong points out that ES is superior to conventional VaR because: In practice, the implementation and calculation of ES has been shown to be difficult Taylor, ES is estimated conditional on VaR, giving rise to the possibility that estimation and model risk for ES will be higher than for VaR, although the smoothing of the tails implies ES could be more stable than VaR. Risk forecasts which use For example, for a Student-t distribution , the The next section describes the data and methodology employed.

The data employed in the buVaR risk metric were daily closing prices for the following variables: The period of the data spans January to January This process is used to remove the exceedances outliers from the price series and Wong found an 8 per cent filter applied to a day rolling window to be appropriate. The day 4 years' worth of trading days window was found effective for US and Euro data as this period embraces at least one recent financial cycle. This may be adjusted accordingly depending on the data used as cycle lengths differ in markets and economies.

Wong does, however, warn that ideally only one crisis cycle-trough at a time should be present in a window period as large amounts of volatile data could distort the window period.

Wong sets the threshold for the rank filtering process at 8 per cent with the motivation that increasing it further would filter out too much information and subsequently flatten out bubbles and remove cyclical information. Reducing the bubble threshold would transform the method to a deviation from a simple MA which Wong showed to be ineffective. In this alternative history, calculated growth was sustainable, gradual and market bubbles and manias did not occur.

Wong labels this as the adaptive MA and asserts that it has the effect of being able to reduce the bubble indicator by reducing the window length m when it detects that rallies conform more to long-term growth L t than formation of assets bubbles. This is how the metric attempts not to penalise long-term growth but only the formation of assets bubbles.

This metric is intended to measure the degree of cyclical bubble formation and unlike a simple MA it meets the criteria mentioned in Section 2 for a suitable bubble indicator. This advantage compared to a simple MA is shown in Figure 4 illustrating the bubble indicator estimated using a simple MA and Wong's suggested adaptive MA.

B max is the largest absolute B n observed throughout the entire history of the asset. Figure 5 illustrates a stress testing analysis of w 2 in order to assess which level of w 2 would provide the smoothest day-to-day variation of buVaR.

The inflator acts as a multiplicative adjustment for every scenario, but only on the side of the return distribution of a day observation period in line with the month observation period for VaR as suggested by Basel II. As demonstrated in Section 3, the return distribution undergoes a transformation to the extent that if on day t: The buVaR metric, based on a historical approach evaluates a portfolio on shifted levels X i ' which are based on a set of scenarios.

To ensure that these shifted levels of the portfolio, asset or risk factor do not become negative they are calculated using log returns: In this univariate case a bank's portfolio is first evaluated using a product pricing function g. The next section details the results obtained from various indices, commodity prices and exchange rates.

BuVaR's two distinct features the bubble indicator, B t and the inflator, A t distinguish it from other market risk measurement tools. Wong suggests and conducts buVaR using a four year window period in the adaptive MA, arguing that the data should not include more than one crisis period. However, a four year window period is not necessarily optimal for all economies and markets.

Visual analysis, trend extraction and standard Fourier analysis are used in order to determine the most prominent cycle frequencies of the data used. While the HP filter establishes and extracts the trend and results in a smooth series, the appropriate window period to use in buVaR must still be calculated. This bubble's inception in saw several internet-based and related companies perform well, boosted by exceptional market confidence. However, the downturn caused several companies to close down as they had few tangible assets to absorb losses.

The trend extracted in Figure 8 through visual inspection looks to show a frequency of between six and eight years, however this is not conclusive. Standard Fourier analysis was used to extract cyclical market behaviour information and determine the relevant underlying frequency components. The frequency components for both time series indicate a principal frequency of approximately 6. The JSE has a secondary cycle of 4.

The frequency amplitudes in Figure 8 shows that a seven year window period may account for a more prominent market cycle, making the adaptive MA more accurate by accounting for an entire cycle.

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The seven year window will also only account for one crisis at a time avoiding the distortion of data as the last three major crises occurred approximately 10 years apart Wong, However, using a four year window period still has the possibility to yield noteworthy results as the frequency for this cycle length is still high and it makes it comparable to Wong's work.

The periodicity of market cycles and the amplitudes prominence of these cycles are affected in times of changing and volatile market conditions. The compression of market cycles is associated with increased serial correlation in the return series leading to volatility clustering Wong, In stressed conditions cycle compression causes cycle lengths to shorten and the amplitudes of these shorter cycles to increase.

The use of cycle compression in Figure 9 allows the analysis of cycle frequency amplitudes through different market conditions. Figure 9 illustrates that the seven year cycle remains the prominent cycle for most of the analysis. From approximately the amplitude of the seven year cycle increases severely due to the prolonged market euphoria preceding the financial crisis which began in Q3 However, the onset of the crisis sees both series rapidly changing direction and the four year cycle amplitude becoming the prominent cycle.

It is not unexpected for the shorter cycle length to increase in volatile, uncertain times. The cycle amplitudes converge again as stability returns to the market. Prior to January a seven year window period is used to apply the rank filtering process and subsequently create the alternative history where Wong suggests no market bubble or manias exist. Figure 10 shows how the ALSI doubles in the two years commencing January , however, buVaR and conventional ES move in opposite directions throughout this two year period.

BuVaR peaks approximately a year before the market does and this highlights the countercyclical capabilities of the metric.

The procyclical nature of conventional ES is illustrated in the periods from approximately January to January , and January and January , respectively. In the former period, the market increases gradually, but ES decreases due to the non-volatile favourable data being used to estimate ES. BuVaR through the bubble indicator and subsequent inflator increases significantly, in an attempt to avoid the formation of a market bubble.

In the latter period the market declines sharply with a significant increase in ES only followed three months later. The decline in buVaR after the financial crisis throughout the market rise is due to the metric avoiding the penalisation of long term growth. The decline of buVaR before the onset of the crisis could be argued to be an underestimation of risk, however, the effect of the significant regulatory capital estimation by buVaR prior to the crisis may dissolve or avoid bubble formation.

Wong asserts that due to buVaR leading crashes hindsight provides no benefit here. Statistical back-testing is not appropriate and hence visual testing has to be relied upon. BuVaR components for the seven year cycle estimations are shown in Figure The significant increase in the bubble indicator in Figure 11 used in the subsequent inflator illustrates how buVaR attempts to identify potential market bubbles for penalisation. The bubble indicator is estimated from the JSE alternative history time series which in turn is estimated through the rank filtering process.

The seven year MA of the original price series, which Wong asserts would not work as it does not conform to suitable characteristics for the estimation of the bubble indicator is also illustrated. The seven year cycle results are illustrated as estimations Fourier analysis, HP filter and cycle compression showing that the bubble indicator using this window period is more responsive.

This is due to the more prominent seven year market cycle being accounted for, ensuring that the full boom and bust of the cycle are taken into account while not over-distorting the data and modifying them enough to get reputable results. The results produced by the four year cycle window period are also not flawed as this cycle was prominent throughout periods of increased volatility.

However, for buVaR to be effective as a countercyclical risk measure it has to be consistently and continuously applied to a series in order to punish bubbles and prevent crises. Figure 12 resembles Figure 11 with regards to buVaR peaking approximately a year before the onset of the financial crisis.

BuVaR shows spikes throughout the market euphoria from to possibly attempting to curb excessive growth in countercyclical manner. BuVaR peaks as volatility increases in the market in the latter part of , however, the risk measure peaks again in the second half of and remains prominent for about three years. This may be due to the volatility of the market, but also the metric's countercyclical capability. This period in global finance is also highlighted by the sovereign credit crisis. Noteworthy is the significant increase in buVaR from late up until January , which may indicate the formation of a market bubble.

In addition, several economists suggested that would be a good year for the global economy reinforced by the weak international oil price and the strengthening US economy The World Bank, ; Mitchell, Applying buVaR to exchange rates may not only act as a warning signal to fluctuations, but may be used in conjunction with investments products affected by exchange rates.

Between January and midway through buVaR produces similar results as conventional ES for the weakening rand. However, for all the periods or just before these periods where the rand experiences sharp declines, buVaR is elevated above conventional ES. The crisis period from to initially shows a significantly elevated buVaR with ES again being late in the detection of the severe decrease in the exchange rate.

This reduction in the exchange rate may be due to investors divesting from emerging markets like South Africa. Also, in a challenging economic environment exports may drop possibly causing lower demand for the exchange rate as well. In Figure 14 buVaR diminishes as the price of oil increases gradually, however, when oil starts increasing significantly buVaR detects the bubble and changes direction whereas ES keeps decreasing. The spike in ES only occurs several months after the actual crash happens, thus emphasising the countercyclical ability of buVaR.

BuVaR again swings upwards around and stays significantly elevated as the price of the commodity increases rapidly. The depreciating ZAR is prominent in Figure 15 , while constant increase in the price of oil from onwards is portrayed in Figure In Figure 15 , the price of crude oil in USD fluctuates, but on average remains flat for the same period. Figure 15 reflects similar results to those in Figure 14 , with buVaR decreasing as the price of oil gradually increases. This aligns with the goal of buVaR not to punish growth, only bubbles. Again, buVaR increases as it detects the bubble whereas ES declines, only to increase sharply months after the severe decline in the oil price.

Relaxing the assumptions of i. The BuVaR metric was demonstrated by Wong to be more accurate rather than more precise than VaR, providing a 'best guess' of losses. These values are situated somewhere between the VaR measured by traditional methods and a reasonable capped value. BuVaR does not generate a single solution for potential losses, but rather a practical value that may be effectively employed for determining risk capital.

This value will be higher than a conventionally calculated VaR number, leading to a higher capital buffer, but compensates for the complex, fat-tailed loss distribution. The financial crisis of emphasised the severe effects of behaviour, markets and risk metrics being procyclical in nature. This significantly underestimated phenomenon contributed to both the market euphoria and subsequent turmoil in global finance in the first decade of the 21 st century.

The replacement of VaR by ES although an improvement on risk measurement, has not provided a solution in terms procyclicality. However, the system wide implementation of countercyclical capital buffer may not be a straight forward process as all bank specific effects are still unidentified. For instance, banks in smaller or illiquid economies may struggle to implement minimum countercyclical regulatory requirements. Furthermore, what if one bank is an outlier in an economy and has to retain capital when it is in a downward slump or vice versa?

BuVaR provides a forward looking alternative to VaR attempting to account for procyclicality while incorporating the benefits of ES. Determining the appropriate length of market cycles is crucial in buVaR in order to calculate an effective alternative history. Fourier analysis and cycle compression provide adequate analysis of data in order to determine the length and prominence of market cycles. The analysis in Section 5 illustrates that buVaR detects bubbles and significantly increases required regulatory capital before ES does.

This confirms the metric's countercyclical abilities to calculate regulatory capital in a forward looking manner. Future research opportunities include the application of buVaR to considerably more portfolios, indices and commodities with different cycle characteristics.

By observing output from many disparate sources, fat-tail loss patterns may be evaluated and connections established. The VaR measured under various market cycles i. Comparing these against buVaR estimates may provide some insight into the subtle interplay between market dynamics and portfolio or single asset losses. Alternative histories may also be derived using different metrics, including the HP filter. The buVaR technique and the HP filter for example could be applied to relevant data and alternative histories constructed.

The results obtained could be compared to establish differences and similarities and, with the benefit of hindsight, could lead research to the superior technique since backtesting could easily establish which method produced the most accurate VaR estimates. A natural coherent alternative to value at risk. Economic notes, 31 2: Coherent measures of risk.

Mathematical Finance, 9 3: Properties of distortion risk measures. Methodology and Computing in Applied Probability, 11 3: The case for a better functioning securitisation market in the European Union. Amendment to the capital accord to incorporate market risks. Revisions to the Basel II market risk framework updated 31 Dec Guidance for national authorities operating the countercyclical capital buffer. A global regulatory framework for more resilient banks and banking systems. Messages from the academic literature on risk measurement for the trading book.

週間記事閲覧ランキング

Fundamental review of the trading book: A revised market risk framework updated 31 Dec How accurate are value-at-risk models at commercial banks? The Journal of Finance, 57 3: Market liquidity and its incorporation into risk management, Banque de France. Financial Stability Review, 8 May: Modelling the business cycle of South Africa: Coherence versus elicitability in measures of market risk. International Advances in Economic Research, 20 3: An introduction to value-at-risk. Backtesting general spectral risk measures with application to expected shortfall, working paper.

A new concept or extreme risk and fund allocation. Journal of Alternative Investments, 13 3: Extreme spectral risk measures: An application to futures clearing house margin requirements. On time-scaling of risk and the square-root-of-time rule. The case for value-at-risk. The new market risk regulations. Converting 1-Day volatility to h-Day volatility: Published in condensed form as scale models. Liquidity-adjusted intraday value at risk modelling and risk management: Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses or returns , and yields a number of useful conclusions.

Heath, , Coherent measures of risk, Mathematical Finance, 9, Schachter, , Estimating Value at Risk with a precision measure by combining kernel estimation with historical simulation, Review of Derivatives Research, 1, Tang, , Nonparametric inference of value at risk for dependent financial returns, Journal of Financial Econometrics, 3, Dowd, , Extreme quantile-based risk measures: Chichester and New York Evans, M.

Peacock, , Statistical Distributions, 3rd edition. Chichester and New York Frey, R.

McNeil, , VaR and expected shortfall in portfolios of dependent credit risks: Tunaru, , Coherent risk measures under filtered historical simulation, Journal of Banking and Finance, 29, Liu, , Sensitivity analysis of distortion risk measures, mimeo, University of Toronto. Laurent, , Sensitivity analysis of values at risk, Journal of Empirical Finance, 7,

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