Implied Versus Realized Volatility as an Equity Return Signal
Summary
The note discusses whether volatility helps explain or forecast the equity premium, focusing on the gap between implied volatility and estimated realized volatility. It suggests estimating variance from OHLC data, smoothing it with an ARCH-family model, and comparing the resulting annualized volatility estimate with implied volatility. The relative size of this gap is presented as a possible indicator of short-term market risk pricing and next-day index returns.
The author reports that the return relationship appeared statistically significant in their research but was too weak to overcome day-trading fees and slippage. They also describe VIX futures term structure as a more promising application: steep contango or backwardation is linked to futures roll returns. These are personal research claims rather than a systematic evidence review; the excerpt is truncated during its discussion of the backwardation trade and supplies no full methodology, sample details, or independent validation. The proposed signals should therefore be treated as hypotheses with implementation and market-regime limits.
Key ideas
- Compare implied volatility with a historical realized-volatility estimate to study volatility risk pricing.
- OHLC-based variance estimates can be smoothed with ARCH-family models.
- The author reports a short-lived association between the volatility gap and next-day index returns.
- The reported equity signal was not strong enough to cover intraday trading costs.
- VIX futures term structure is proposed as a way to study roll returns.
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Full text
# relationship between volatility and equity premium # relationship between volatility and equity premium I am working on the equity premium. Does anybody know one or two authors who address the relationship between volatility and equity premium? I.e. how does vola influence the equity premium? In addition, I am looking for a paper which summarizes the stylized facts on equity premium such as the reactions to vola changes or fluctuations in returns. Is there an author addressing this topic? Thanks in advance. ## Answer by David Addison (score 2) https://quant.stackexchange.com/a/32860 In general, if you're looking for papers on the topics involving statistical anomalies, such as this, I highly recommend Quantpedia.com's section on the implied volatility premium. I think access to the full site is well worth the price tag. Anyway, I wrote a paper on this a few years back based on my own research. The volatility risk premium papers with which I familiar deal mostly with the options premia, and not specifically with regards to the equity indices themselves. In my experience, you basically to want to compare the implied volatilty (IV) (i.e., VIX for the indices) with the best possible estimate of the historical realized standard deviation (RV). The delta is slightly indicative of next-day equity returns. This appears to be a day-trading signal that collapses quickly. A relatively positive delta -- where IV less RV exceeds historical norms -- indicates the presence of positive premium (i.e., the market is risk-averse) in which rising equity prices are more likely. A relatively narrow delta indicates, on the other hand, that a sentiment has gotten over-confident and that a downside correction is likely. The delta relative to historical norms can be measured using various standardization methods and over various time-frames while retaining a statistically significant ability to forecast next-day index returns. However, it wasn't a strong enough correlation to overcome fees and slippage within a day-trading context. However, it did become sufficiently attractive to trade VIX Futures when I applied the risk premium concept to the the term structure of VIX Futures. The term structure is historically indicative of the VIX Futures roll-returns. Shorting VIX Futures on a steep futures contango contango is consistently profitable. Going long the VIX Futures on steeply backwardated term structure hi One simple method for distilling the IV equity premium may proceed as follows: - The first step is to determine instantaneous market variance. Yhang and Zhang give an efficient method for estimating variance using freely available OHLC data: http://ftp.ams.sunysb.edu/papers/2000/susb00_25.pdf - Combine the instantaneous estimate of variance with one of the ARCH (i.e. G-ARCH, E-ARCH) models for combining exponential time weighting with mean reversion. - Take the difference between the annualized square root of the ARCH model and implied volatility.
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