The effectiveness of the combined use of VIX and Support Vector Machines on the prediction of S&P 500

Abstract

The aim of this research is to analyse the effectiveness of the Chicago Board Options Exchange Market Volatility Index (VIX) when used with Support Vector Machines (SVMs) in order to forecast the weekly change in the S&P 500 index. The data provided cover the period between 3 January 2000 and 30 December 2011. A trading simulation is implemented so that statistical efficiency is complemented by measures of economic performance. The inputs retained are traditional technical trading rules commonly used in the analysis of equity markets such as Relative Strength Index, Moving Average Convergence Divergence, VIX and the daily return of the S&P 500. The SVM identifies the best situations in which to buy or sell in the market. The two outputs of the SVM are the movement of the market and the degree of set membership. The obtained results show that SVM using VIX produce better results than the Buy and Hold strategy or SVM without VIX. The influence of VIX in the trading system is particularly significant when bearish periods appear. Moreover, the SVM allows the reduction in the Maximum Drawdown and the annualised standard deviation.

Appendix

Annualised return:

$$R^{\text{A}} = 250*\frac{1}{n}\sum\limits_{i = 1}^{n} {r_{i} }$$

(12)

Standard deviation:

$$\sigma^{\text{A}} = \sqrt {250} \sqrt {\frac{1}{n - 1}\sum\limits_{i = 1}^{n} {\left( {r_{i} - \overline{r} } \right)^{2} } }$$

(13)

Sharpe ratio:

$${\text{SR}} = \frac{{R^{\text{A}} }}{{\sigma^{\text{A}} }}$$

(14)

Maximum Drawdown calculated in S&P 500 points:

$${\text{MDD}} = \mathop {\hbox{min} }\limits_{t = 1, \ldots ,n} \left( {F_{t} - \mathop {\hbox{max} }\limits_{\tau = 1, \ldots ,t} (F_{\tau } )} \right)$$

(15)

where F _t is the accumulated fund with each different strategy.