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Evaluating Portfolio Risk Management: A New Evidence from DCC Models and Wavelet Approach

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Encyclopedia of Finance

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Abstract

We analyzed the volatility dynamics of three developed markets (the UK, USA, and Japan), during the period 2003–2011, by comparing the performance of several multivariate volatility models, namely, Constant Conditional Correlation (CCC), Dynamic Conditional Correlation (DCC), and consistent DCC (cDCC) models. To evaluate the performance of models, we used four statistical loss functions on the daily Value-at-Risk (VaR) estimates of a diversified portfolio in three stock indices: FTSE 100, S&P 500, and Nikkei 225. We based on one-day ahead conditional variance forecasts. To assess the performance of the abovementioned models and to measure risks over different timescales, we proposed a wavelet-based approach, which decomposes a given time series on different time horizons. Wavelet multiresolution analysis and multivariate conditional volatility models are combined for volatility forecasting to measure the co-movement between stock market returns and to estimate daily VaR in the time-frequency space. Empirical results show that the asymmetric cDCC model of (Aielli, G. P. Consistent estimation of large scale dynamic conditional correlations, working paper n.47, University of Messina, Department of Economics, Statistics, Mathematics and Sociology, 2008) is the most preferable according to statistical loss functions under raw data. The results also suggest that wavelet-based models increase predictive performance of financial forecasting in low scales according to number of violations and failure probabilities for VaR models.

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Notes

  1. 1.

    We decompose our time series up to scale 8 (scale J ≤ log2[(T − 1)/(L − 1) + 1], where T is the number of observations of stock market returns (T = 2112), and L is the length of the wavelet filter LA(8)). We used the wavelets R package for the MODWT.

  2. 2.

    The multivariate GARCH-based WVaR estimate for one-day ahead forecasts are defined as follows:

    \( {\mathrm{VaR}}_{t+m}^k(j)={\kappa}^{\prime }{d}_{t+m}+{z}_{\alpha }{\varsigma}_{t+m}(j) \)where zα denotes the normal quantile, κ′dt + m is the wavelet mean one-day ahead forecast estimate computed by forecasting VAR(1) based on wavelet components series. The wavelet weighted portfolio return is \( {d}_t^{Ptf}={\kappa}^{\prime }{d}_t:{d}_t={\left({d}_{UK,t},{d}_{US,t},{d}_{JP,t}\right)}^{\prime } \) denotes the vector of wavelet return components of FTSE 100 (dUK,t), S&P 500 (dUS,t), and NIKKEI 225 (dJP,t), κ′ = (κUK, κUS, κJP) is the vector of weights in the portfolio. ςt(j) = κ′Ht(j)κ, where Ht(j) is the wavelet conditional variance-covariance matrix defined in section “Model Specifications.” Briefly, the wavelet conditional mean and wavelet conditional variance-covariance estimates are calculated from forecasting the model defined in Eq. 21.

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Author information

Authors and Affiliations

  1. Laboratoire de recherche en Économie et Gestion: LR18ES27, Faculté des Sciences Economiques et de Gestion de Sfax, University of Sfax, Sfax, Tunisia

    Rabeh Khalfaoui

  2. Rajagiri Business School, Rajagiri Valley Campus, Kochi, India

    Aviral Kumar Tiwari

  3. South Ural State University, Chelyabinsk, Russian Federation

    Aviral Kumar Tiwari

  4. Institute of Business Research, University of Economics Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Aviral Kumar Tiwari & Xuan Vinh VO

Authors
  1. Rabeh Khalfaoui
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  2. Aviral Kumar Tiwari
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  3. Xuan Vinh VO
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Editors and Affiliations

  1. Rutgers School of Business, Rutgers, The State University of New Jer, Piscataway, NJ, USA

    Cheng-Few Lee

  2. Phoenix, AZ, USA

    Alice C. Lee

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Khalfaoui, R., Tiwari, A.K., VO, X.V. (2021). Evaluating Portfolio Risk Management: A New Evidence from DCC Models and Wavelet Approach. In: Lee, CF., Lee, A.C. (eds) Encyclopedia of Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-73443-5_108-1

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  • DOI: https://doi.org/10.1007/978-3-030-73443-5_108-1

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