Variance Risk Premium
The variance risk premium (VRP) is the persistent spread by which implied variance — the variance level priced into options markets — exceeds subsequently realized variance, representing compensation that option sellers extract from buyers who are willing to pay a premium to hedge against volatility uncertainty.
The variance risk premium is one of the most extensively documented and debated phenomena in financial economics. Across decades of data on S&P 500 options, implied volatility measured by instruments such as the CBOE VIX has on average exceeded the realized volatility subsequently observed in the market by several percentage points. Because variance is the square of volatility, the gap in variance terms is even more pronounced: implied variance consistently exceeds realized variance, meaning sellers of variance through instruments such as variance swaps collect a premium on average over time.
Several explanations have been proposed for this premium. The most widely accepted view is that the VRP is a genuine risk premium compensating volatility sellers for bearing left-tail equity risk during periods when volatility spikes and equity prices fall simultaneously. Because volatility is high precisely when investors most need their equity portfolios to perform — or at minimum, when they cannot afford to absorb losses — sellers of volatility protection must be compensated for accepting this concentrated risk. The VRP is therefore analogous to the equity risk premium, the term premium in bonds, or the credit spread premium in corporate debt.
An alternative explanation focuses on investor preferences and behavioral factors: investors are loss-averse and have disproportionate fear of tail events, causing them to overpay for downside protection. Options market makers, by contrast, are sophisticated risk managers who understand that the probability of extreme outcomes is lower than fearful investors believe, and they extract a premium for providing that protection.
In practice, the VRP drives entire hedge fund strategies. Short-volatility funds systematically sell options on the S&P 500, collect premium, and delta-hedge the directional exposure, attempting to harvest the average VRP while managing drawdown risk. The largest risks to these strategies are regime changes — periods such as the 2008 financial crisis or March 2020 COVID shock — when realized volatility massively overshoots implied volatility before the next options sale, creating sudden and large losses that can overwhelm months of accumulated premium income.
The VIX minus subsequent 30-day realized volatility of the S&P 500 is the most common simple measure of the VRP. Academic papers by Carr and Wu, Bollerslev and Todorov, and others provide rigorous decompositions of the VRP into diffusive and jump components, with jump risk compensation accounting for a disproportionate share of the total premium.