Abstract
A set of regional and country’s equity indices have been evaluated and analysed in their Value at Risk (VaR) and Conditional Value at Risk (CVaR) in this paper, using computational methods based on the Johnson systems. Comparing the main statistics and the values of the two cited measures of financial risk obtained using a roll-over mechanism in the period January 2008–July 2012, the impact of the crisis on equity market risk can be shown. It seems that for all regions and countries the patterns are very similar: there is a peak of all the risk measures adopted at the beginning of the crisis (September 2008–February 2009) and another turbulent period in 2011 (from July to December). In other terms, the global patterns of the main financially relevant countries and their regional aggregations demonstrate that “One Financial system”, and just one, is already at work, in theory and in practice. On the other hand, the scale of the risk measures differs from one country to another: e.g., with a probability of 1 %, the potential daily loss on an equity position in Latin America in the worst period arrives to about 25 %, the Emerging Markets as a whole show values around 20 % and Asia arrives to 15 %, while the US and European corresponding values are below 14 %. This is true whatever the risk measure and whatever the confidence interval (which, again, influences strongly the scale of the risk values). Looking in detail to the last period (April 2012–July 2012), a general improvement could be appreciated: the risk measures are all around 4 % if not on one hand Italy and Spain (around 6 %), Greece (around 10 %) and on the other hand the “virtuous” Chile (around 1.5 %), again with reference to a probability of 1 %. Nevertheless, indices of performance (expected return over risk measure) have been evaluated and compared. They give sometimes different answers to the risk measures themselves.
Similar content being viewed by others
Notes
The symbol “←” in the definition of VaR has just the meaning of generalized inverse of the considered function; if the function F admits an inverse, the symbol “←” becomes “−1”.
Yahoo!®Finance (http://finance.yahoo.com/) supplies historical data on the indices used in this work; close prices adjusted for dividends and splits have been considered.
References
Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Fin 9(3):203–228
Favre L, Galeano JA (2002) Mean-modified value at risk optimization with hedge funds. J Altern Invest Fall:5
Griffiths-Hill Archive (1976) Algorithms 99 and 100. Appl Stat 25: 180 and 190, (http://lib.stat.cmu.edu/griffiths-hill/99 and http://lib.stat.cmu.edu/griffiths-hill/100)
Hill ID, Hill R, Holder RL (1976) Algorithms AS 99. Fitting Johnson curves by moments. Appl Stat 25:180–189
Johnson NL (1949) Systems of frequency curves generated by methods of translation. Biometrika 36:149–176
Johnson NL (1965) Tables to facilitate fitting su frequency curves. Biometrika 52:547–558
Li XM, Rose LC (2009) The tail risk of emerging stock markets. Emerg Mark Rev 10:242–256
Rachev S (ed) (2003) Handbook of heavy tailed distributions in finance. Elsevier, Amsterdam
Shapiro SS, Slifker JF (1980) The Johnson system: selection and parameter estimation. Technometrics 22(2):239–246
Sharpe WF (1994) The Sharpe ratio. J Portfolio Manag Fall:45–58
Simonato JG (2011) The performance of Johnson distributions for computing value at risk and expected shortfall. J Deriv 19(1):7–24
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Stucchi, P., Dominese, G. Evolution of Equity Market Risk During the Crisis: Europe, Americas and Asia. Transit Stud Rev 19, 163–178 (2012). https://doi.org/10.1007/s11300-012-0238-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11300-012-0238-2
Keywords
- Country equity conditional value at risk
- Financial crisis
- Risk measures
- Expected shortfall
- Skewness
- Kurtosis