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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.

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  • $\begingroup$ 2 quick refs to get you started: Chen, Equity Mkt Vol and Expected Risk Premium research.stlouisfed.org/wp/2006/2006-007.pdf Kim, Is There a Positive Relationship between Stock Market Volatility and the Equity Premium? muse.jhu.edu/article/170205 $\endgroup$ – noob2 Mar 6 '17 at 15:26
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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:

  1. 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

  2. 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.

  3. Take the difference between the annualized square root of the ARCH model and implied volatility.

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