Realized vs Implied Vol: Reading the Volatility Risk Premium

Summary. Implied volatility on equity indices has on average exceeded the volatility that subsequently materialized. The gap is the variance (or volatility) risk premium. This article defines the premium precisely, summarizes the empirical evidence, explains why it exists, uses a simulation to show why a positive average premium coexists with occasional large losses for sellers, and describes how to measure the premium in practice.

1. Definitions

Let $R{V}_{t,t+\tau }$ be realized variance over the next $\tau$ days, computed from daily returns $r$:

The market's price for that variance is the variance swap rate, which can be replicated from a strip of out-of-the-money options [1]. The VIX is constructed on the same principle: its square is a model-free estimate of 30-day risk-neutral expected variance for the S&P 500 [2, 3]. Carr and Wu define the variance risk premium as the difference between expected realized variance under the physical measure $\mathbb{P}$ and its price under the risk-neutral measure $\mathbb{Q}$ [4]:

With this sign convention the premium is negative on average for the S&P 500: buyers of variance pay more than they receive. Practitioners often quote the same idea in volatility points as implied volatility minus subsequent realized volatility, which is positive on average.

2. Evidence

• Carr and Wu find large, negative average variance risk premiums for the S&P 500 and other indices, and show that they are not explained by the classical market-beta channel alone [4].
• Bakshi and Kapadia show that delta-hedged index option portfolios earn negative average returns, consistent with a negative market volatility risk premium [5].
• Coval and Shumway report that zero-beta at-the-money straddles on the S&P 500 lose about 3% per week on average [6].
• Bollerslev, Tauchen and Zhou show that the difference between implied and realized variance predicts equity returns at horizons of a few months [7].

2.1 The premium in recent data

The same pattern is visible in the last decade of data. Figure 1 compares the VIX on each day with the S&P 500's realized volatility over the following 21 trading days, from October 2016 to September 2026 [8, 9]. Over 2,490 trading days, the VIX averaged 18.7 and subsequent realized volatility averaged 15.0. The spread averaged 3.7 volatility points (median 4.7) and was positive on 84% of days.

The distribution of the spread (Figure 2) shows the other side of the trade. Most days sit a few points above zero, but the left tail is long: the spread was below −6.8 points on 5% of days and below −10 points on 3.3%. The most negative value, −72 points, came on 20 February 2020, when the VIX was still low and the following month contained the COVID-19 crash.

3. Why the premium exists

• Hedging demand. Investors buy index puts as portfolio insurance. Dealers who absorb that demand bear inventory risk and charge for it; Gârleanu, Pedersen and Poteshman show that end-user demand pressure raises option prices, especially for index puts [10].
• Volatility rises in bad times. Volatility tends to increase when the market falls. A long-variance position therefore pays off when wealth is low, which makes it valuable insurance and justifies a negative expected return.
• Jump risk. Index option prices include compensation for rare large declines. In most months no such decline occurs, so realized variance falls short of the price; in the months when it occurs, realized variance is far above it [11].

4. Positive on average, dangerous in the tail

Figure 3 illustrates why sellers of volatility usually win and occasionally lose heavily. It simulates daily index returns with a GARCH(1,1) process whose parameters are in the range commonly estimated for daily equity index returns (long-run volatility 17%, $\alpha =0.09$, $\beta =0.89$) and computes realized volatility over non-overlapping 21-day windows.

The simulated distribution is right-skewed: its median (about 14.8%) is below its mean (about 16.1%). If implied volatility is priced three points above the mean, at about 19.1%, realized volatility comes in below implied in about 76% of months. The remaining months include the tail: the 95th percentile is about 28% and the 99th about 38%.

The payoff profile turns that tail into large losses. A short variance swap with vega notional $N_{\text{vega}}$ and strike $K$ pays

which is concave in realized volatility ${\sigma }_R$. Figure 4 compares it with a short volatility swap. With a strike of 18 and $100,000 vega notional, the short variance position earns at most $900,000 if realized volatility is zero but loses about $3.5 million if it is 40 and about $9.1 million if it is 60.

5. Measuring the premium in practice

1. Choose a horizon, usually 30 calendar days, and use a matching implied measure: the VIX for the S&P 500 or the 30-day at-the-money implied volatility for a single name.
2. Compute trailing realized volatility over the same horizon as a proxy for expected realized volatility. Trailing realized volatility is a backward-looking estimate; forecasting models such as GARCH or HAR give better proxies.
3. Track the spread over time rather than reading a single value. A spread that is unusually wide relative to its own history indicates expensive options; a negative spread indicates that realized volatility is running above what options price.

A wide premium on its own does not make short volatility safe. It is widest after shocks, when realized volatility can still rise further. The same caution applies to regimes defined by dealer positioning: in a short-gamma regime realized volatility is more likely to exceed implied.

6. Instruments

7. Sizing

Because the payoff is concave and the distribution is right-skewed, the relevant risk is the tail, not the average month. Short-volatility positions should be sized so that a realized volatility several times the strike is survivable, and combined with defined-risk structures where possible. DataFirst reports realized and implied volatility side by side so the spread can be tracked over time.

For educational and informational purposes only. Not financial advice. Options trading involves substantial risk of loss. The simulation is illustrative and not a forecast; real return distributions have fatter tails than a GARCH model with normal shocks.

References

1. Demeterfi, K., Derman, E., Kamal, M., & Zou, J. (1999). More than you ever wanted to know about volatility swaps. Goldman Sachs Quantitative Strategies Research Notes.
2. Cboe Global Markets. Cboe Volatility Index (VIX) methodology. White paper. cdn.cboe.com/api/global/us_indices/governance/VIX_Methodology.pdf
3. Whaley, R. E. (2009). Understanding the VIX. Journal of Portfolio Management, 35(3), 98–105. doi.org/10.3905/JPM.2009.35.3.098
4. Carr, P., & Wu, L. (2009). Variance risk premiums. Review of Financial Studies, 22(3), 1311–1341. doi.org/10.1093/rfs/hhn038
5. Bakshi, G., & Kapadia, N. (2003). Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies, 16(2), 527–566. doi.org/10.1093/rfs/hhg002
6. Coval, J. D., & Shumway, T. (2001). Expected option returns. Journal of Finance, 56(3), 983–1009. doi.org/10.1111/0022-1082.00352
7. Bollerslev, T., Tauchen, G., & Zhou, H. (2009). Expected stock returns and variance risk premia. Review of Financial Studies, 22(11), 4463–4492. doi.org/10.1093/rfs/hhp008
8. S&P Dow Jones Indices LLC. S&P 500 [SP500]. Retrieved from FRED, Federal Reserve Bank of St. Louis, 9 October 2026. fred.stlouisfed.org/series/SP500
9. Cboe Global Markets. Cboe Volatility Index: VIX [VIXCLS]. Retrieved from FRED, Federal Reserve Bank of St. Louis, 9 October 2026. fred.stlouisfed.org/series/VIXCLS
10. Gârleanu, N., Pedersen, L. H., & Poteshman, A. M. (2009). Demand-based option pricing. Review of Financial Studies, 22(10), 4259–4299. doi.org/10.1093/rfs/hhp005
11. Bates, D. S. (2000). Post-'87 crash fears in the S&P 500 futures option market. Journal of Econometrics, 94(1–2), 181–238. doi.org/10.1016/S0304-4076(99)00021-4