Application of GARCH-Copula Model in Portfolio Optimization

Aleš Kresta


Although the cornerstone of modern portfolio theory was set by Markowitz in 1952, the portfolio optimization problem is a never-ending research topic for both academics and practitioners. In this problem the future prediction of time series evolution plays an important role. However, it is rarely addressed in research. In the paper we analyze the applicability of the GARCH-copula model. To be more concrete we assume the investor maximizing Sharpe ratio while the future evolution of the time series is simulated by means of the AR(1)-GARCH(1,1) model using the copula modelling approach. The bootstrapping technique is applied as a benchmark. From the empirical results we found out that the GARCH-copula model provides better forecasts of future financial time series evolution than the bootstrapping method. Assuming the investor is maximizing the Sharpe ratio, both the final wealth increases and maximum drawdown decreases when we apply the GARCH-copula model compared to the application of bootstrapping technique.


portfolio optimization, Sharpe ratio, GARCH, copula function

Full Text:


Show references Hide references

Biglova, A. et al. (2004). Different approaches to risk estimation in portfolio theory. The Journal of Portfolio Management, 31(1), pp. 103-112.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), pp. 307-327.

Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1(2), pp. 223-236.

Elton, E. J. et al. (2014). Modern Portfolio Theory and Investment Analysis. 9th Ed. Hoboken: Wiley.

Engle, R. F. (1982). Auto-regressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), pp. 987-1007.

Farinelli, S. et al. (2008). Beyond Sharpe ratio: Optimal asset allocation using different performance ratios. Journal of Banking & Finance, 32(10), pp. 2057-2063.

Huang, J. J. et al. (2009). Estimating value at risk of portfolio by conditional copula-GARCH method. Insurance: Mathematics and Economics, 45(3), pp. 315-324.

Cherubini, U. et al. (2004). Copula Methods in Finance. Chichester: Wiley.

Cherubini, U. et al. (2011). Dynamic Copula Methods in Finance. Chichester: Wiley.

Konno, H. and Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5), pp. 519-531.

Kresta, A. (2015). Financial Engineering in Matlab: Selected Approaches and Algorithms, SAEI, vol. 33. Ostrava: VSB-TU Ostrava.

Lundblad, C. (2007). The risk return tradeoff in the long run: 1836–2003. Journal of Financial Economics, 85(1), pp. 123-150.

Mandelbrot, B. (1963). The Variation of Certain Speculative Prices. The Journal of Business, 36(4), pp. 394-419.

Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), pp. 77-91.

Nelsen, R. B. (1997). Dependence and order in families of Archimedean copulas. Journal of Multivariate Analysis, 60(1), pp. 111-122.

Rank, J. (2006). Copulas: From Theory to Application in Finance. London: Risk Books.

Shalit, H. and Yitzhaki, S. (1984). Mean‐Gini, Portfolio Theory, and the Pricing of Risky Assets. The journal of Finance, 39(5), pp. 1449-1468.

Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), pp. 119-138.

Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), pp. 49-58.

Sklar, A. (1959). Fonctions de repartition à n dimensions et leurs marges. Publications de l'Institut de statistique de l'Université de Paris, 8, pp. 229-231.

Wang, Z.-R. et al. (2010). Estimating risk of foreign exchange portfolio: Using VaR and CVaR based on GARCH–EVT-Copula model. Physica A: Statistical Mechanics and its Applications, 389(21), pp. 4918-4928.

Young, M. R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44(5), pp. 673-683.


  • There are currently no refbacks.

Crossref Cited-by (4)

The listed references are provided by Cited-by (Crossref service) and thus do not represent the full list of sources citing the article.

1. Conditional mean-variance and mean-semivariance models in portfolio optimization
Hanene Ben Salah, Ali Gannoun, Mathieu Ribatet
Journal of Statistics and Management Systems  first page: 1,  year: 2020

2. Application of Performance Ratios in Portfolio Optimization
Aleš Kresta
Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis  vol: 63,  issue: 6,  first page: 1969,  year: 2015

3. Application of Performance Ratios in Portfolio Optimization
Aleš Kresta
Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis  vol: 63,  issue: 6,  first page: 1969,  year: 2015

4. Evaluation of multivariate GARCH models in an optimal asset allocation framework
Nor Syahilla Abdul Aziz, Spyridon Vrontos, Haslifah M. Hasim
The North American Journal of Economics and Finance  vol: 47,  first page: 568,  year: 2019