Are combination forecasts of S&P 500 volatility statistically superior?

of information that is reflected in the combination (and some of the individ-
ual) model based volatility forecasts. These findings extend those of Becker,
Clements and White (2006). There it was established that the VIX did not
contain any information superior to that in the combination of all MBF. This
research goes further and it can now be claimed that the VIX, not only contains
no additional information, but also does not fully incorporate the information
contained in MBF. The VIX can, therefore, not be seen as the best possible
combination of all MBF.

Two interpretations can be attached to this finding. First, it could be argued
that the options market is not informationally efficient in the sense that it does
not incorporate all information available from MBF of volatility. While this
paper finds statistical evidence to support this statement, a more robust check
would be to establish whether the use of the statistically superior volatility
forecast would deliver significant excess profits in an appropriate trading strat-
egy. Second, it is possible that a time-varying volatility risk premium breaks
the link between IV and actual realised volatility¹⁰. Making allowance for this
possibility is beyond the scope of this paper.

5 Conclusion

Issues relating to forecasting volatility have attracted a great deal of attention in
recent years. There have been many studies into the relative merits of implied
and model based volatility forecasts. It has often been found that implied
volatility offers a superior volatility forecast when compared against individual
¹⁰There is some evidence for time variation in the volatility risk premium (e.g. Bollerslev
et al., 2006).

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