Advertisement

Economic and financial risk factors, copula dependence and risk sensitivity of large multi-asset class portfolios

  • Catherine BruneauEmail author
  • Alexis Flageollet
  • Zhun Peng
Original Research

Abstract

In this paper we propose a flexible tool to estimate the risk sensitivity of financial assets when exposed to any sort of risks, including extreme ones, from the financial markets and the real economy. This tool works with observations and a priori views. Our contribution is threefold. First, we combine copulas and factorial structures which allow us to capture the whole dependencies between the returns of a large number of assets of multiple classes. We build what we call a Cvine Risk Factors (CVRF) model, which can disentangle financial and explicitely economic like activity, inflation, emerging, etc, and more generally speaking real sphere related risks. Second, this model provides the way to extend the well known linear multibeta relationship in a non-linear version and to assess the exposures of any asset to several factorial risk directions in the cases where the risks are extreme. The exposure measures are relevant Cross Conditional Values at Risk (Cross-CVaR). Third, as an application of the methodology, we solve an optimization program to find portfolios that are the most diversified in capital while being immunized to extreme shocks to a given risk factorial direction. Varying the immunization constraint, we recover the portfolio strategies which are the most widely used today. For example, adopting the ERC (Equal Risk Contribution) rule insures optimal capital based diversification and immunization against inflation risk. Accordingly, we propose a unified view and a rationalization ex post of several current portfolio strategies that appear different at a first glance.

Keywords

Complex dependence Regular vine copula Factors Non-linear multibeta relationship Portfolio management Risk management Risk parity Extreme risks Stress testing 

JEL Classification

G11 G17 G32 

Notes

Supplementary material

References

  1. Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44(2), 182–198.Google Scholar
  2. Acharya, V., Engle, R., & Richardson, M. (2012). Capital shortfall: A new approach to ranking and regulating systemic risks. American Economic Review, 102, 59–64.CrossRefGoogle Scholar
  3. Alexander, C., & Sheedy, E. (2008). Developing a stress testing framework based on market risk models. Journal of Banking and Finance, 32, 2220–2236.CrossRefGoogle Scholar
  4. Ang, A., Chen, J., & Xing, Y. (2006). Downside risk. Review of Financial Studies, 19(4), 1191–1239.CrossRefGoogle Scholar
  5. Bedford, T., & Cooke, R. M. (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32(1–4), 245–268.CrossRefGoogle Scholar
  6. Bedford, T., & Cooke, R. M. (2002). Vines-a new graphical model for dependent random variables. Annals of Statistics, 30(4), 1031–1068.CrossRefGoogle Scholar
  7. Bender, J., Briand, R., & Nielsen, F. (2010). Portfolio of risk premia: A new approach to diversification. Journal of Portfolio Management, 36(2), 17–25.CrossRefGoogle Scholar
  8. Brechmann, E. C., & Czado, C. (2013). Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Statistics & Risk Modeling, 30(4), 307–342.CrossRefGoogle Scholar
  9. Brechmann, E. C., Hendrich, K., & Czado, C. (2013). Conditional copula simulation for systemic risk stress testing. Insurance: Mathematics and Economics, 53, 722–732.Google Scholar
  10. Brechmann, E.C., & Schepsmeier, U. (2013). Modeling dependence with C- and D-Vine Copulas: The R Package CDVine. Journal of Statistical Software, 52(3), 1–27. http://www.jstatsoft.org/v52/i03/.
  11. Bruder,B., & Roncalli, T. (2013). Managing risk exposures using the risk parity approach, Working Paper, LYXOR Resarch.Google Scholar
  12. Campbell, J. Y., & Cochrane, J. H. (1999). By force of habit: A consumption-based explanation of aggregate stock market behaviour. Journal of Political Economy, 107, 205–251.CrossRefGoogle Scholar
  13. Campbell, J. Y., Viceira, L. M., & Sunderam, A. (2013). Inflation bets or deflation hedges? The changing risks of nominal bonds. Critical Finance Review, 6, 263–301.CrossRefGoogle Scholar
  14. Chamberlain, G., & Rothschild, M. (1983). Arbitrage, factor structure, and mean-variance analysis on large asset markets. Econometrica, 51(5), 1281–1304.CrossRefGoogle Scholar
  15. Cherubini, U., Gobbi, F., Mulinacci, S., & Romagnoli, S. (2012). Dynamic copula methods in finance. England: Wiley.Google Scholar
  16. Choueifaty, Y., Froidure, T., & Reynier, J. (2013). Properties of the most diversified portfolio. Journal of Investment Strategies, 2(2), 49–70.CrossRefGoogle Scholar
  17. Clarke, R. G., de Silva, H., & Murdock, R. (2005). A factor approach to asset allocation. The Journal of Portfolio Management, 32(1), 10–21.CrossRefGoogle Scholar
  18. Cochrane, J. H. (2011). Discount rates. The Journal of Finance, 66(4), 1047–1109.CrossRefGoogle Scholar
  19. Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating Time varying risk premia in the term structure: The arch-M model. Econometrica, 55(2), 391–407. 1987.CrossRefGoogle Scholar
  20. Engle, R. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339–350.CrossRefGoogle Scholar
  21. Engle, R., Jondeau, E., & Rockinger, M. (2012). Systemic Risk in Europ. Review of Finance, 19(1), 145–190.CrossRefGoogle Scholar
  22. Fama, E. F., & French, K. R. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25, 23–49.CrossRefGoogle Scholar
  23. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56.CrossRefGoogle Scholar
  24. Genest, C., Rémillard, B., & Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44(2), 199–213.Google Scholar
  25. Giot, P., & Laurent, S. (2003). Value-at-risk for long and short trading positions. Journal of Applied Econometrics, 18(6), 641–663.CrossRefGoogle Scholar
  26. Heinen, A., & Valdesogo, A. (2009). Asymmetric CAPM dependence for large dimensions: The Canonical Vine Autoregressive Model. CORE Discussion Papers 2009069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).Google Scholar
  27. Ilmanen, A. (2011). Expected returns: An investor’s guide to harvesting market rewards (1st ed.). New York: Wiley.CrossRefGoogle Scholar
  28. Jin, X, & Lehnert, T, (2009). Large Portfolio Risk Management and Optimal Portfolio Allocation with Dynamic Copulas. LSF Research Working Paper, 11-10.Google Scholar
  29. Kurowicka, D., & Cooke, R. M. (2007). Sampling algorithms for generating joint uniform distributions using the vine-copula method. Computational Statistics & Data Analysis, 51(6), 2889–2906.CrossRefGoogle Scholar
  30. Lee, B. S. (2009). Stock returns and inflation revisited. Working paper, available at SSRN: http://ssrn.com/abstract=1326501.
  31. Lehnert, T. & Jin, X., (2009). Large portfolio risk management and optimal portfolio allocation with dynamic copulas. LSF Research Working Paper, 11-10.Google Scholar
  32. Maillard, S., Roncalli, T., & Teiletche, J. (2010). The properties of equally weighted risk contribution portfolios. The Journal of Portfolio Management, 36(4), 60–70.CrossRefGoogle Scholar
  33. Mausser, H. (2003). Calculating quantile-based risk analytics with L-estimators. Journal of Risk Finance, 4(3), 61–74.CrossRefGoogle Scholar
  34. Meucci, A. (2006). Beyond Black–Litterman in practice: A five-step recipe to input views on non-normal markets. Available at SSRN: http://ssrn.com/abstract=872577.
  35. Meucci, A. (2007). Risk contributions from Generic User-defined Factors. symmys.com.Google Scholar
  36. Meucci, A. (2010). The Black–Litterman approach: Original model and extensions. The encyclopedia of quantitative finance. New York: Wiley.CrossRefGoogle Scholar
  37. Meucci, A., Santangelo, A., & Deguest, R., (2014). Measuring portfolio diversification based on optimized uncorrelated factors. Available at SSRN: http://ssrn.com/abstract=2276632.
  38. Page, S., & Taborsky, M. (2011). The myth of diversification: Risk factors vs. asset classes. The Journal of Portfolio Management, 37(4), 1–2.CrossRefGoogle Scholar
  39. Ross, S. (1976). The arbitrage theory of capital pricing. Journal of Economic Theory, 13, 341–360.CrossRefGoogle Scholar
  40. Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris, 8, 229–231.Google Scholar
  41. Tumminello, F. L., & Mantegna, R. N. (2007). Hierarchically nested factor model from multivariate data. EPL (Europhysics Letters), 78, 30006.CrossRefGoogle Scholar
  42. Weiss, G. (2013). Copula-GARCH versus dynamic conditional correlation: An empirical study on VaR and ES forecasting accuracy. Review of Quantitative Finance and Accounting, 41(2), 179–202.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Catherine Bruneau
    • 1
    Email author
  • Alexis Flageollet
    • 2
  • Zhun Peng
    • 3
  1. 1.Centre d’Economie de la SorboneUniversity Paris I Panthéon-SorbonneParisFrance
  2. 2.ParisFrance
  3. 3.University of Evry and EPEE, Batiment IDFEvryFrance

Personalised recommendations