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Hybrid forecasting models for S&P 500 index returns

Akihiro Fukushima (Information Services International Dentsu, Inc., Tokyo, Japan)

Journal of Risk Finance

ISSN: 1526-5943

Article publication date: 16 August 2011




The purpose of this paper is to propose two hybrid forecasting models which integrate available ones. A hybrid contaminated normal distribution (CND) model accurately reflects the non‐normal features of monthly S&P 500 index returns, and a hybrid GARCH model captures a serial correlation with respect to volatility. The hybrid GARCH model potentially enables financial institutions to evaluate long‐term investment risks in the S&P 500 index more accurately than current models.


The probability distribution of an expected investment outcome is generated with a Monte Carlo simulation. A taller peak and fatter tails (kurtosis), which the probability distribution of monthly S&P 500 index returns contains, is produced by integrating a CND model and a bootstrapping model. The serial correlation of volatilities is simulated by applying a GARCH model.


The hybrid CND model can simulate the non‐normality of monthly S&P 500 index returns, while avoiding the influence of discrete observations. The hybrid GARCH model, by contrast, can simulate the serial correlation of S&P 500 index volatilities, while generating fatter tails. Long‐term investment risks in the S&P 500 index are affected by the serial correlation of volatilities, not the non‐normality of returns.

Research limitations/implications

The hybrid models are applied only to the S&P 500 index. Cross‐sectional correlations among different asset groups are not examined.


The proposed hybrid models are unique because they combine available ones with a decision tree algorithm. In addition, the paper clearly explains the strengths and weaknesses of existing forecasting models.



Fukushima, A. (2011), "Hybrid forecasting models for S&P 500 index returns", Journal of Risk Finance, Vol. 12 No. 4, pp. 315-328.



Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited

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