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Risk management is an important and helpful process for investors, hedge funds, traders and market makers. One of its key points is the appropriate estimation of risk measures which can improve the...

In this paper, we analyse the recent principal volatility components analysis procedure. The procedure overcomes several difficulties in modelling and forecasting the conditional covariance matrix in large dimensions arising from the curse of dimensionality. We show that outliers have a devastating effect on the construction of the principal volatility components and on the forecast of the conditional covariance matrix and consequently in economic and financial applications based on this forecast. We propose a robust procedure and analyse its finite sample properties by means of Monte Carlo experiments and also illustrate it using empirical data. The robust procedure outperforms the classical method in simulated and empirical data.

Based on a General Dynamic Factor Model with infinite-dimensional factor space and MGARCH volatility models, we develop new estimation and forecasting procedures for conditional covariance matrices in high-dimensional time series. The finite-sample performance of our approach is evaluated via Monte Carlo experiments and outperforms most alternative methods. This new approach is also used to construct minimum one-step-ahead variance portfolios for a high-dimensional panel of assets. The results are shown to match the results of recent proposals by Engle et al. (2019) and De Nard et al. (2021) and achieve better out-of-sample portfolio performance than alternative procedures proposed in the literature.

Several procedures to estimate daily risk measures in cryptocurrency markets have been recently proposed in the literature. Among them, procedures taking into account the presence of extreme observations, as well as procedures that include more than a single regime, have performed substantially better than standard methods in terms of volatility and Value-at-Risk forecasting. Three of those procedures are revisited in this paper, and their Value-at-Risk forecasting performance is evaluated using recent cryptocurrency data that includes periods of turbulence. Those procedures are also extended to estimate the Expected Shortfall, and a comprehensive backtesting exercise based on both calibration tests and scoring functions is performed. In order to mitigate the influence of model misspecification and enhance the forecasting performance obtained by individual models, we evaluate the use of forecast combinations strategies. In our empirical application, procedures that are robust to outliers performed slightly better than regime-switching models. We found some evidence that combining strategies can improve the forecasting of Value-at-Risk and Expected Shortfall, particularly for the 1% risk levels, making them an interesting alternative to be used by practitioners.

Beyond their importance from the regulatory policy point of view, Value-at-Risk (VaR) and Expected Shortfall (ES) play an important role in risk management, portfolio allocation, capital level requirements, trading systems, and hedging strategies. Unfortunately, due to the curse of dimensionality, their accurate estimation and forecast in large portfolios is quite a challenge. To tackle this problem, two procedures are proposed, being one of them based on a filtered historical simulation method in which high-dimensional conditional covariance matrices are estimated via a general dynamic factor model with infinite-dimensional factor space and conditionally heteroscedastic factors, and the other one based on a residual-based bootstrap scheme. The procedures are applied to a panel with concentration ratio close to one. Backtesting and scoring results indicate that both VaR and ES are accurately estimated under our methods, which outperforms alternative approaches available in the literature.

Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of f...

Bootstrap procedures are useful to obtain forecast densities for both returns and volatilities in the context of generalized autoregressive conditional heteroscedasticity models. In this paper, we analyse the effect of additive outliers on the finite sample properties of these bootstrap densities and show that, when obtained using maximum likelihood estimates of the parameters and standard filters for the volatilities, they are badly affected with dramatic consequences on the estimation of Value-at-Risk. We propose constructing bootstrap densities for returns and volatilities using a robust parameter estimator based on variance targeting implemented together with an adequate modification of the volatility filter. We show that the performance of the proposed procedure is adequate when compared with available robust alternatives. The results are illustrated with both simulated and real data.

This package provides a robust bootstrap procedure to obtain forecast densities for both return and volatilities in a GARCH context. The forecast densities are useful to obtain forecast intervals as well as to estimate risk measures such as Value-at-Risk (VaR). Additionally, we also provide the robust GARCH estimator of Boudt et al. (2013) with the modification introduced by Trucios et at. (2017). This procedure showed good finite sample properties in both Monte Carlo experiments and empirical data. For a recent implementation of this procedure see Trucios (2019).

General dynamic factor models have demonstrated their capacity to circumvent the curse of dimensionality in the analysis of high-dimensional time series and have been successfully considered in many economic and financial applications. As second-order models, however, they are sensitive to the presence of outliers—an issue that has not been analyzed so far in the general case of dynamic factors with possibly infinite-dimensional factor spaces (Forni et al. 2000, 2015, 2017). In this paper, we consider this robustness issue and study the impact of additive outliers on the identification, estimation, and forecasting performance of general dynamic factor models. Based on our findings, we propose robust versions of identification, estimation, and forecasting procedures. The finite-sample performance of our methods is evaluated via Monte Carlo experiments and successfully applied to a classical data set of 115 US macroeconomic and financial time series.

In this supplementary material we discuss the results corresponding to the case without short-selling constraints of the empirical application in the paper of Trucios et al. (2019). These results are given in Tables 9-16.

Risk management is an important and helpful process for investors, hedge funds, traders and market makers. One of its key points is the appropriate estimation of risk measures which can improve the investment decisions and trading strategies. The high volatility of cryptocurrencies turns them a really risky investment and consequently, appropriate risk measures estimation is extremely necessary. In this paper, we deal with the estimation of two widely-used risk measures such as Value-at-Risk and Expected Shortfall in a cryptocurrency context. To face the presence of outliers and the correlation between cryptocurrencies, we propose a methodology based on vine copulas and robust volatility models. Our procedure is illustrated in a seven-dimensional equal-weight cryptocurrency portfolio and displays good performance.

Over the last few years, Bitcoin and other cryptocurrencies have attracted the interest of many investors, practitioners and researchers. However, little attention has been paid to the predictability of their risk measures. This paper compares the predictability of the one-step-ahead volatility and Value-at-Risk of Bitcoin using several volatility models. We also include procedures that take into account the presence of outliers and estimate the volatility and Value-at-Risk in a robust fashion. Our results show that robust procedures outperform non-robust ones when forecasting the volatility and estimating the Value-at-Risk. These results suggest that the presence of outliers plays an important role in the modelling and forecasting of Bitcoin risk measures.

The (M)GARCH models are probably the most widely used to estimate and predict volatility. Estimation and prediction of volatility are very important in many financial applications. One important issue in the application of (M)GARCH models is the frequent presence of outliers in financial time series and their effects in all stages of model application. We present some issues involved in making inference in (M)GARCH models in the presence of additive outliers. Specifically, we present the effects of outliers on specification, estimation of models, and their volatility and volatility prediction. We also present some robust methods to estimate the model and to predict volatility. We emphasize the presentation of robust methods for volatility forecast density.

Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of financial returns. Although the decisions are based on forecasts covariance matrix little is known about effects of outliers on the uncertainty associated with these forecasts. In this paper we analyse these effects on the context of dynamic conditional correlation (DCC) models when the uncertainty is measured using bootstrap methods. We also propose a bootstrap procedure to obtain forecast densities for return, volatilities, conditional correlation and VaR that is robust to outliers. The results are illustrated with simulated and real data.

Many financial decisions, such as portfolio allocation, risk management, option pricing and hedge strategies, are based on forecasts of the conditional variances, covariances and correlations of financial returns. The paper shows an empirical comparison of several methods to predict one-step-ahead conditional covariance matrices. These matrices are used as inputs to obtain out-of-sample minimum variance portfolios based on stocks belonging to the S&amp, P500 index from 2000 to 2017 and sub-periods. The analysis is done through several metrics, including standard deviation, turnover, net average return, information ratio and Sortino&rsquo, s ratio. We find that no method is the best in all scenarios and the performance depends on the criterion, the period of analysis and the rebalancing strategy.