Realized Volatility Indexes
Authors: Andrew Clark
Source: Journal of Indexes
Date: November/December 2011
In this article, the author first considers in turn the various hypotheses inherent to modern portfolio theory to see if they match the real market conditions. First of all, it is clear that investors invest at different time horizons. This is not without consequences on their investing objectives and the way they trade. This heterogeneity among investors has lead to the market being considered as fractal. This fractal characteristic relates to both the various investment horizons and time periods. Indeed, the market is made up of different groups of actors with different investment characteristics, and the interaction between this variety of characteristics is determinant for modelling the market as a whole. The second point is that investors have different views of risk (volatility). Olsen and Associates’ studies as well as that of Lynch and Zumbach (2003) have shown that this difference in risk is also fractal. It means that risk is analysed with a different frequency of observation and, as such, evaluated with different degrees of resolution. For example, some strategies expect to trade volatility over a few days, while portfolio managers consider volatility over at least one month. The third point concerns the views about stock price, which are also different according to the actors. Here again, the situation can be described as fractal. This phenomenon is explained by the fact that investors have different frequency of data observations (day, week, month), which cause volatility clusters, trend persistence, as well as time lags between interest rate changes and foreign exchange rate adjustments.
In order to deal with different investor time scales, the author proposes using a wavelet technique, with multiresolution analysis (MRA). The MRA serves to decompose a time series into its components. Using daily data, this mathematical technique allows the different time scales inherent to the market to be generated. Based on this technique, the author derived what he calls the Realized Volatility Index (RVI), an index based on the “no privileged time scale” argument. Clark compares this approach with some sophisticated Garch approaches, which have given impressive results according to him. Meanwhile, he believes that the RVI approach is better as it does not privilege any scale period in the computation, in contrast to GARCH approaches. The process to build an RVI index is the following. Firstly, different components of volatility are estimated with different scale periods. Secondly, all these components are aggregated using the multiresolution analysis, leading to the RVI index.
The author has investigated the accuracy of the RVI, compared with indices obtained with GARCH techniques (IGARCH, LM-ARCH). The test was performed over a four-year period starting in January 2007 and ending in December 2010. Based on three indicators, the root mean squared error (RMSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE), the RVI appears to be the best forecast method, as it exhibits the lowest error scores. He also compares the RVI with the VIX, and concludes on the superiority of the RVI. Meanwhile, for this latter result, he stresses that the VIX is not a forecast index, but an implied volatility index, so that this comparison must be taken cautiously.
The author concludes that the present results must encourage ETF providers to use RVI, all the more so in that such indices can be computed for all stocks and commodities with at least 10 years of data history, even if no options are available. Such indices appear to complement implied volatility indices which require option prices to be computed and which only exist for selected indices and securities.
Lynch, P. E., and Zumbach G. O. 2003. Market Heterogeneities and Causal Structure of Volatility. Quantitative Finance 3: 323-331.
Olsen and Associates, Publications: http://www.olsen.ch/publications/working_papers/