We investigate the predictive performance of various classes of value-at-risk (VaR) models in several dimensions—unfiltered versus filtered VaR models, parametric versus nonparametric distributions, conventional versus extreme value distributions, and quantile regression versus inverting the conditional distribution function. By using the reality check test of White (2000), we compare the predictive power of alternative VaR models in terms of the empirical coverage probability and the predictive quantile loss for the stock markets of five Asian economies that suffered from the 1997–1998 financial crisis. The results based on these two criteria are largely compatible and indicate some empirical regularities of risk forecasts. The Riskmetrics model behaves reasonably well in tranquil periods, while some extreme value theory (EVT)-based models do better in the crisis period. Filtering often appears to be useful for some models, particularly for the EVT models, though it could be harmful for some other models. The CaViaR quantile regression models of Engle and Manganelli (2004) have shown some success in predicting the VaR risk measure for various periods, generally more stable than those that invert a distribution function. Overall, the forecasting performance of the VaR models considered varies over the three periods before, during and after the crisis. Copyright © 2006 John Wiley & Sons, Ltd.

/pdf/evaluating-predictive-performance-of-value-at-risk-models-in-3w90dq642u.pdf

Evaluating predictive performance of value‐at‐risk models in emerging markets: a reality check

https://epge.fgv.br/we/MFEE/GerenciamentodeRisco/2012?action=AttachFile&do=get&target=Artigo43.pdf

Using extreme value theory to measure value-at-risk for daily electricity spot prices

Extreme value theory is concerned with the study of the asymptotic distribution of extreme events, that is to say events which are rare in frequency and huge in magnitude with respect to the majority of observations. Statistical methods derived from it have been employed increasingly in finance, especially for risk measurement. This paper surveys some of those main applications, namely for testing different distributional assumptions for the data, for Value‐at‐Risk and Expected Shortfall calculations, for asset allocation under safety‐first type constraints, and for the study of contagion and dependence across markets under conditions of stress.

/pdf/extreme-value-theory-in-finance-a-survey-v1z0ix6pts.pdf

Extreme value theory in finance: a survey

The financial crisis of East Asia in 1997 was largely unanticipated and was characterized by sharp falls in asset prices and currency values in several countries simultaneously. Many empirical models have been developed to predict the occurrence of such crisis. However, the out-of-sample performance of these models is disappointing. Most theoretical explanations of the crisis emphasize the role of banking sector and revolve around models of moral hazard or self-fulfilling runs on liquidity. Empirical tests of the models are, however, rare. Much work remains to be done to explain the contagion, and the effects of equity capital flows.

https://www.anderson.ucla.edu/faculty/bhagwan.chowdhry/chowdhry-goyal.pdf

Understanding the financial crisis in Asia

This paper analyses several volatility models by examining their ability to forecast the Value-at-Risk (VaR) for two different time periods and two capitalization weighting schemes. Specifically, VaR is calculated for large and small capitalization stocks, based on Dow Jones (DJ) Euro Stoxx indices and is modeled for long and short trading positions by using non parametric, semi parametric and parametric methods. In order to choose one model among the various forecasting methods, a two-stage backtesting procedure is implemented. In the first stage the unconditional coverage test is used to examine the statistical accuracy of the models. In the second stage a loss function is applied to investigate whether the differences between the models, that calculated accurately the VaR, are statistically significant. Under this framework, the combination of a parametric model with the historical simulation produced robust results across the sample periods, market capitalization schemes, trading positions and confidence levels and therefore there is a risk measure that is reliable.

A Robust VaR Model under Different Time Periods and Weighting Schemes

Value-at-risk (VaR) measures are generated using extreme value theory by modelling the tails of the return distributions of six Asian financial markets during the recent volatile market conditions. The maxima and minima of these return series were found to be satisfactorily modelled within an extreme value framework and the value at risk measures generated within this structure were found to be different to those generated by variance–covariance and historical methods, particularly for markets characterised by high degrees of leptokurtosis such as Malaysia and Indonesia.

Value-at-risk: Applying the extreme value approach to Asian markets in the recent financial turmoil

Portfolio insurance strategies

A portfolio insurance strategy is a dynamic hedging process that provides the investor with the potential to limit downside risk while allowing participation on the upside so as to maximize the terminal value of a portfolio over a given investment horizon. First, this paper introduces the basic concepts and payoffs of a portfolio insurance strategy. Second, it describes the theory of alternative portfolio insurance strategies. Third, it empirically compares the performances of various portfolio insurance strategies during different markets and time periods. Fourth, it summaries the recent market developments of portfolio insurance strategies, especially in terms of the variations of features in CPPI investments. Finally, it addresses the impacts of these strategies on financial market stability.

Portfolio Insurance Strategies: Review of Theory and Empirical Studies

Portfolio selection models using variance, Value-at-Risk (VaR) and expected shortfall measures of risk are analysed, assuming differing underlying return distributions. The expected shortfall approach provides advantages relative to the VaR approach in terms of lower portfolio downside risks. Furthermore, using the extreme value distribution provides more insights for the investor relative to the empirical distribution. Analysing portfolio selection using these differing risk measures around the recent sub-prime mortgage problem period provides topical insights into the asset allocation process for the investor.

https://link.springer.com/content/pdf/10.1057%2Fjam.2008.15.pdf

Portfolio selection in an expected shortfall framework during the recent ‘credit crunch’ period

This paper compares traditional portfolio insurance strategies with modern risk-based dynamic asset allocation strategies within a currency portfolio context for reserve management. Given the objective of preserving reserve value, the evaluation of the hedging performances of various strategies focuses on four perspectives regarding, in particular, the return distribution of the hedged portfolio. In terms of the Sharpe Ratio, the constant proportional portfolio insurance is the best performer due to having the lowest volatility, while the Value at Risk strategy based upon the normal distribution is the worst due to its having the smallest return. From the perspective that the return distribution of the hedged portfolio is shifted to the right, the synthetic put performs the best, with the expected shortfall strategy the second best. In terms of the cumulative portfolio return across years, the expected shortfall strategy using the historical distribution ranks first, as a result of its participation in upward markets. Furthermore, the expected shortfall-based strategy results in a lower turnover within the investment horizon, thereby saving transaction costs.

An analysis of risk-based asset allocation and portfolio insurance strategies

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