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Volatility-dependent correlations: further evidence of when, where and how

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Abstract

This paper expands on the usefulness of conditioning correlations on market volatility to generate forecasts of the covariance matrix in two contexts: within a single market and between several international markets. The dynamic conditional correlation family provides an illustration of the relationship between volatility and correlation. We use a portfolio allocation problem to compare covariance forecasts over a range of portfolio sizes and sub-samples of high and low market volatility. Findings confirm recent results for these models in comparable examples and extend these results through the two comprehensive out-of-sample analyses including large dimensional and international settings. This study furthers our understanding of the linkage between volatility and correlations and provides guidance for exploiting correlation’s dependence on volatility, emphasising its importance for differing market states and portfolio characteristics.

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Notes

  1. The suitability of dynamic conditional correlation (DCC) models for large dimensions further motivates this choice.

  2. Recently, caution has been advised when using the DECO model, with suggestions out-of-sample results may be sample specific in some cases (see, for example, Christoffersen et al. 2014).

  3. Bauwens and Otranto (2016) use data up to 2012 for portfolios of 3 and 30 US equities.

  4. Studies of international correlations, for example Christoffersen et al. (2014), tend to use weekly returns to avoid issues with market trading across time zones.

  5. The paper makes reference to both Bauwens and Otranto (2013) and the recently published Bauwens and Otranto (2016). The specification of the VDCC framework used here is based more closely on that found in the earlier 2013 version and readers will benefit from reading both.

  6. Bauwens and Otranto (2013) also allow the parameter b to be time varying, however find it to be constant. This was also confirmed to be the case in preliminary experiments here.

  7. Bauwens and Otranto (2016) use VIX / 100 in their experiment, however in preliminary exercises conducted for this paper the logarithm is preferred.

  8. The evaluation methodology applied here is similar to that used in Clements et al. (2015).

  9. There are several alternative loss functions to choose from, including QLIKE, MSE and MAE. To enable the focus of the paper to remain predominantly on economic benefit of volatility dependence and portfolio management, the global minimum variance portfolio is used here.

  10. Prices were downloaded from the Thomson Reuters Tick History database, via SIRCA.

  11. The in-sample period is 2000 observations, leaving \(T=2269\) out-of-sample forecasts and forecast horizon is one day. The correlation parameters are re-estimated over an expanding window every 5 observations (the equivalent of one trading week).

  12. The length of sub-periods in this paper (805 observations and 751 observations for Low 1 and Low 2, respectively) allow inferences to be drawn unburdened by drastically unequal lengths of sub-period, unlike other forecasting studies undertaken in this manner (Christoffersen et al. 2014; Bauwens and Otranto 2016; Clements et al. 2015).

  13. This level of risk aversion is considered to be an appropriate choice, as Ghysels et al. (2005) have previously found the coefficient to be 2.6. Fleming et al. (2001, 2003) used coefficients of 1 and 10 to represent investors with relatively low and high risk aversion, respectively. Expected returns of 6% and 10%, as well as a risk coefficient of \(\lambda =5\), were also used, however, did not lead to any qualitative difference in the results.

  14. Prices were downloaded from the Thomson Reuters Tick History database, via SIRCA.

  15. The literature provides some guidance for the assumption of US dominance in terms of the VIX. For example, Beber et al. (2009) use both the VIX and VSTOXX as perceived market security risk of the European bond market and find each give similar results. Changes in the VIX had significant predictive ability for daily European returns during the recent crisis (Sarwar 2014). Providing analysis in an international context, using the regional volatility index as well as the US-based index, is therefore appropriate.

  16. The initial in-sample period for both analyses is 2000 observations, leaving \(T=1457\) (VSTOXX) and \(T=1919\) (VIX) forecasts. The forecast horizon is one day and correlation parameters are re-estimated over an expanding window every 5 observations (the equivalent of one trading week).

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Authors and Affiliations

  1. Auckland University of Technology, Private Bag 92006, Auckland, 1142, New Zealand

    Ayesha Scott

  2. Queensland University of Technology, GPO Box 2434, Brisbane, QLD, 4001, Australia

    Adam Clements & Annastiina Silvennoinen

Authors
  1. Adam Clements
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  2. Ayesha Scott
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  3. Annastiina Silvennoinen
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Corresponding author

Correspondence to Ayesha Scott.

Additional information

An earlier version of the paper was presented at the NZESG 2015 meeting in Brisbane and the feedback of participants, especially Robert Reed, is gratefully acknowledged. We would also like to thank Jonathan Dark and George Milunovich, and two anonymous referees for helpful comments.

A Appendix

A Appendix

See Tables 12, 13, 14, 15.

Table 12 List of 14 European indices and VSTOXX summary statistics, entire period spans 7 January 1999 to 31 December 2014
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Table 13 List of 14 European indices and VIX summary statistics, entire period spans 4 June 1996 to 31 December 2014
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Table 14 List of stocks included in each portfolio for US equities dataset
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Table 15 Details of the 100 US equities included in the full dataset and VIX summary statistics, entire period spans 3 January 1996 to 31 December 2014
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Clements, A., Scott, A. & Silvennoinen, A. Volatility-dependent correlations: further evidence of when, where and how. Empir Econ 57, 505–540 (2019). https://doi.org/10.1007/s00181-018-1473-0

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