Variance Risk Premium on EURO STOXX 50
Abstract
The variance risk premium is implied variance minus subsequent realised variance. On the EURO STOXX 50 the implied leg is VSTOXX, the volatility index Euronext's derivatives complex is built around. A positive premium is the compensation sellers of variance have historically received for being short crash convexity.
Yahoo Finance does not list a EURO STOXX variance future in a form this study can hold. The page therefore does two things that can be measured from the index and from VSTOXX, and it labels the second one as a proxy. First, it records the premium itself. Second, it asks whether the sign of last month's premium lines up with next month's EURO STOXX 50 return. Being long the equity index when the premium is positive is the equity leg of a vol-selling story. It is not the variance swap.
Premium and the regression
VSTOXX is the official STOXX daily history (h_v2tx.txt). Yahoo Finance does not serve that series. EURO STOXX 50 prices are Yahoo adjusted closes. Implied variance is . Realised variance is the mean of squared daily index returns over 21 sessions, multiplied by 252.
The forecast regression is ordinary least squares of next month's index return on this month's VRP, with an intercept. The slope's t-statistic uses the usual OLS standard error. Separately, a Newey–West test is reported on the mean of the premium scaled by , so the units are a monthly variance rather than a percent return.
The timed wealth path earns the index total return in a month when the previous month's premium was positive, and earns zero otherwise. There is no option premium collected. If the chart beats buy-and-hold, it did so by sitting out months, not by selling variance.
Empirical results
The bar chart is the average premium by calendar year, in annualised variance units. The wealth chart compares the sign rule with buying and holding the EURO STOXX 50. Both should be read next to the slope test: a wealth gap without a detectable slope is a small-sample path.
VSTOXX, from the official STOXX history, squared into variance units, minus 21-day realized variance of ^STOXX50E. Mean premium 0.010. The slope of next-month ^STOXX50E return on that premium is 0.047 (t=0.27). The timed book is long the equity index only when last month's premium is positive. It is not a variance swap.
Growth of 1. Dates are thinned when the path is daily.
| Test | Estimate | t | p | Reading |
|---|---|---|---|---|
| Mean variance risk premium | 0.001 | 6.27 | <0.001 | Premium is annualized implied variance minus annualized realized variance. The tested series is that gap divided by 12 so the mean is a monthly variance unit. |
| Next-month index return on VRP | 0.047 | 0.27 | 0.788 | OLS slope. Estimate is in return per unit of annualized variance, not a percent. |
Calendar-year returns
| Year | Strategy | Benchmark |
|---|---|---|
| 2012 | -0.9% | 4.6% |
| 2013 | 16.2% | 18.0% |
| 2014 | 4.8% | 1.1% |
| 2015 | -4.9% | 4.8% |
| 2016 | -1.8% | 0.1% |
| 2017 | 6.5% | 6.5% |
| 2018 | -14.8% | -14.8% |
| 2019 | 20.2% | 25.5% |
| 2020 | -14.1% | -4.7% |
| 2021 | 20.6% | 20.6% |
| 2022 | -6.7% | -11.9% |
| 2023 | 17.1% | 19.2% |
| 2024 | 6.8% | 7.7% |
| 2025 | 15.8% | 19.0% |
| 2026 | 7.3% | 10.4% |
Series that entered the sample
| Ticker | Name | First | Last | Days |
|---|---|---|---|---|
| ^STOXX50E | EURO STOXX 50 | 2012-01-03 | 2026-11-12 | 3726 |
| V2TX | VSTOXX | 1999-01-04 | 2026-11-12 | 7133 |
Sharpe ratios use a zero risk-free rate. Costs, where charged, are a flat one-way bps haircut on weight turnover. Source: Yahoo Finance. Assignment seed 20261113.
What this does not show
VSTOXX is a model-free implied volatility of a 30-day variance strip. Subtracting a 21-day realised variance matches the horizon only roughly. A clean premium uses the variance that was implied for the same window that then realised.
The sign rule has no short-vol payoff, no delta hedge, and no crash loss beyond the index loss in the months it stays invested. It is the wrong object for sizing a short-variance book.
Yahoo Finance adjusted closes are not a point-in-time index membership file. The constituent lists are a liquid large-cap panel, fixed in the repository, not the official index as it stood on each rebalance date.
The risk-free rate is set to zero in every Sharpe ratio. A local bill rate would lower the ratios and would not, by itself, change a long-short spread.
Costs are a flat one-way haircut on weight turnover. They do not include borrow fees, lot-size rules, auction imbalance, stamp duty, or the Shanghai and Hong Kong short-sale bans that bind a live short book.
This is a research record. It is not a recommendation to trade the sleeve.