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Interpreting VIX–S&P 500 Realized Beta Conventions

Article Quant Q&A · Author: Trajan
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Summary

The document reports a stated convention for calculating a three-month realized beta between VIX and the S&P 500. It describes blending first-, second-, and third-month VIX futures to form a three-month volatility measure, using changes in futures levels for that leg and log returns for the S&P 500 leg. It presents the beta as a ratio of the resulting VIX and S&P 500 volatility measures.

The author asks how shorter-dated futures can represent a three-month horizon, why the two assets use different return measures, and why the numerator is not multiplied by the VIX futures level. The document supplies no worked calculation, derivation, or answer to these questions; its evidence is limited to a report of the convention in a cited market document. As a result, it serves as a prompt to investigate measurement choices rather than a complete method for reproducing or interpreting the statistic. In particular, the precise futures weighting, return scaling, and meaning of the ratio are not established in the text.

Key ideas

  • The reported three-month VIX measure blends first-, second-, and third-month VIX futures.
  • The cited convention uses VIX futures level changes and S&P 500 log returns.
  • The document states the realized beta as a ratio of the two volatility measures.
  • The author questions the horizon construction, differing return conventions, and scaling of the numerator.
  • No derivation or worked example is provided to settle those methodological questions.

Tags

VolatilityFuturesStatistics
Full text
# VIX/SPX Realized Beta Calculation


# VIX/SPX Realized Beta Calculation












In https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that

3M VIX/SPX realized Beta calculation:

- Use a blend of 1st, 2nd and 3 month VIX futures to calculate VIX 3M RVOL

- Use level change instead of log return for VIX futures RVOL calculation

- Use log returns for SPX 3M RVOL calculation

- 3M VIX/SPX realized Beta = VIX 3M RVOL (based on level change)/SPX 3M IVOL (based on log return)

1) I dont see how the 1st and 2 month futures can be used to calculate 3M realised volatility?

2) Why use level change instead of log return?

3) Why use log returns to SPX though?

4) Why has we not times the numerator by VIX futures in my other question (linked)?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.