One Premium in Four Disguises: Volatility Arbitrage, Implied Correlation and the (Apparent) Decay of the Dispersion Premium, 2006–2026

Abstract

Four strategies commonly sold as distinct forms of “volatility arbitrage” are an implied-versus-realised volatility trade, a Cboe Volatility Index (VIX) term-structure calendar, a correlation-gated dispersion proxy, and a skew-gated short-volatility trade. We test whether any of them earns a premium beyond the plain variance risk premium (VRP). We rebuild 1- and 5-month constant-maturity VIX futures returns from public exchange settlement data for January 2006 to September 2026. Each strategy has a daily return correlation of 0.71–0.95 with passive short VIX futures, and index put-writing has 0.66. In spanning regressions on passive short volatility and the market, the largest Newey–West alpha t-statistic is 2.16. It belongs to the calendar spread, which is a fixed combination of two VRP positions. That result fails a Holm correction (p = 0.09), and its t-statistic drops to 1.37 when exchange-traded products (ETPs) replace futures. No strategy clears a Bonferroni hurdle over an 81-configuration parameter grid. The Cboe S&P 500 Dispersion Index (DSPX) predicts realised dispersion among large-cap stocks (rank information coefficient, IC, 0.48; t = 5.9 after controlling for VIX and trailing dispersion; out-of-sample R² gain of 12%). It does not, however, predict dispersion among sector exchange-traded funds (ETFs), and implied correlation (the Cboe 1-month implied correlation index, COR1M) subsumes it in a horse race. The Cboe SKEW index (SKEW) is neither a premium nor a reliable warning. We also rebuild a 20-year implied-correlation premium. With an equal-weighted realised correlation, the premium was large before 2015 and significantly negative after 2020 (t = −2.7). That sign reversal comes from a mismatch between a capitalisation-weighted index and an equal-weighted basket, and the mismatch grows with market concentration. Under the realised measure that matches the construction of COR1M, the premium falls from 3.7 to 0.6 correlation points per month. The decline is not statistically significant, and the post-2020 premium is close to zero rather than negative. A DSPX-struck variance-dispersion swap is equally stable through 2020. Of three published short-volatility enhancements, only VIX-proportional sizing survives out of sample (Sharpe ratio 0.57 to 0.79), and it is still spanned by the plain premium after a multiple-testing correction. Declaration of generative AI use: All research questions, hypotheses, study designs and conclusions are the author’s own, including the decision to re-audit the author’s earlier exploratory results, which identified data errors in them. Under the author’s direction, generative AI tools (Claude Code, Anthropic) wrote most of the analysis code and ran it, and assisted with drafting, editing and formatting the text, and with typesetting. The author reviewed all code, results and text and takes full responsibility for the content of this paper.