Volatility Risk Premium: Fear, Insurance and the Price of Convexity

Instrument check · 8 October 2026

Cboe’s current product description separates the VIX index, its futures and options, and explains the historical tendency for implied index volatility to exceed subsequent realised volatility. That tendency does not establish today’s expected profit after execution, financing and crash risk. Cboe primary product reference.

This edition retains historical charts and hypothetical examples with their dates and labels. It does not convert an intraday VIX observation into a forward realised-volatility forecast. A current trade would require a consistent option strip, maturity, executable prices and a documented forecast distribution. The useful public article is the insurance-pricing framework and its failure modes, not a standing instruction to sell volatility.

Volatility can be both an input to a risk model and the exposure an investor chooses to hold. The distinction explains why a portfolio owner may willingly pay for an option that has a negative standalone expected return, while an option seller may earn a positive average premium and still carry an unattractive risk of ruin.

This reference report brings together the introductory volatility readings, a historical implied-versus-realised chart and the collection’s market-risk case studies. Its central purpose is to distinguish the price of insurance from a guaranteed trading edge. Historical source claims are retained with their original status; they are not updated market estimates or audited investment results.

Three quantities that often share the same label

Three volatility quantities with different meanings

They answer different questions and can differ for legitimate reasons.

Implied volatility includes more than a consensus prediction of future movement. It can reflect compensation for bearing unpleasant states, hedging demand, supply constraints, market frictions and the instrument’s payoff. A buyer purchasing protection against a loss that threatens the rest of the portfolio may accept a premium above an unbiased forecast of average future variance.

A realised-volatility number is also an estimate rather than an unqualified fact. Daily closing returns, intraday squared returns and a gap-aware OHLC estimator need not give the same number. A comparison becomes meaningful only after the observation window, annualisation and definition of realised risk are aligned.

Figure 01 · Conceptual framework

A tradable premium signal uses an entry-time forecast

How the parts connect

1. AImplied measure at entrymarket pricingEx-ante comparison
2. BForecast available at entryforward-looking estimateEx-ante comparison
3. CImplied measure at entryoriginal referenceEx-post assessment
4. DRealised future intervallater observationEx-post assessment

Ex ante signal versus ex post premium

Suppose $IV_t$ is today’s implied volatility for a selected horizon and $RV_{t,t+h}$ is the volatility subsequently realised over that horizon. The ex post difference is:

$$VRP^{\mathrm{vol}}_{t,h}=IV_t-RV_{t,t+h}.$$

It is available only after the future interval has ended. A live trading signal must instead compare today’s implied level with a forecast available today, such as $\widehat{RV}_{t,h}$. Substituting the subsequently realised number into an entry rule creates look-ahead bias.

For variance-linked payoffs, the economically relevant comparison is often in variance units:

$$VRP^{\mathrm{var}}_{t,h}=IV_t^2-RV_{t,t+h}^2.$$

The two spreads are related but not interchangeable. An identical three-point volatility spread has different variance implications at 10% versus 7% than at 30% versus 27%. The level matters, and a payoff proportional to variance should be analysed in variance units.

A dated chart in the research material compares three-month implied volatility with a 60-day historical measure over a 2010–2012 observation window. It usefully illustrates that the two series and their spread vary through regimes. It does not by itself estimate an ex post, horizon-matched risk premium: the maturities differ, and the historical measure looks backward rather than forward from each quoted option date.

Why investors pay for convexity

An option changes the shape of outcomes. A protective put can make a severe downside scenario less damaging while leaving much of the upside intact. That asymmetry can be valuable even when the protection usually expires unused. Its value to an investor depends on the rest of the balance sheet, liquidity needs and tolerance for bad states.

Supply is not unlimited. Selling convexity often requires margin, access to hedging instruments, operational resources and the willingness to absorb losses when capital is scarce. A premium may persist because those costs rise at the very moment insurance is most valuable.

This is why a high average win rate cannot settle the question. A sequence of small gains can coexist with rare losses that dominate cumulative wealth. The investor needs the whole payoff distribution, including financing needs during a loss, rather than only the frequency with which implied volatility exceeds subsequent realised volatility.

The introductory source claims that implied volatility can exceed realised volatility by roughly two to three points on average. A later reading reports a 3.2-point average and positive outcomes in 78% of months for a specific 2020–2025 sample. These remain distinct source-reported claims with different apparent samples and definitions. They should not be combined into one current estimate or treated as verified evidence that a specific strategy will make money.

Delta-hedged option profit depends on variance and path

For a small interval under a simplified continuous-path setting, the profit of a delta-hedged long option can be approximated by:

$$d\Pi\approx\tfrac12\Gamma S^2 (\sigma_{\mathrm{real}}^2-\sigma_{\mathrm{implied}}^2)dt.$$

In words: The approximate hedged gain combines the difference in squared volatilities with half the curvature, the squared underlying level and elapsed time.

Here $\Gamma$ is the long option’s gamma, $S$ the underlying level and $dt$ the time increment. The expression suppresses funding, execution, jumps and model effects. For the corresponding short option, the sign reverses when gamma is expressed as the long option’s positive gamma.

The formula helps explain the insurance premium, but it does not make total option profit equal to a simple difference of two volatility percentages. Gamma varies with spot and time, so the path and timing of realised movement matter. Two periods with the same overall realised volatility can generate different hedged-option results if movement occurs when the option has different convexity exposure.

Without dynamic hedging, directional exposure adds another major component. A short put, an iron condor and a short variance swap can all be described as selling volatility while carrying different distributions of spot, tail and path risk. Their returns should not be substituted for one another.

Figure 02 · Conceptual framework

Why the price of convexity rises when capital is scarce

How the parts connect

1. AAdverse market stateinsurance demand can increaseDemand for protection
2. BAdverse market statecapacity can contractProtection supply
3. CDemand for protectiondemand sideConvexity price
4. DProtection supplysupply sideConvexity price
5. EConvexity pricecompensation for bearing riskSeller exposure

Regimes change both the opportunity and the risk

A calm period can produce a low realised estimate and a positive implied-minus-forecast spread. That may reflect a premium, but it may also reflect information about a scheduled event absent from the historical estimator. An election, policy decision or earnings announcement can change the forward distribution before daily realised volatility responds.

After a shock, the reverse can occur. Realised volatility remains high because the shock is still in the lookback window, while option prices reflect a possible reduction in future uncertainty. A negative implied-minus-past-realised spread is therefore not automatically evidence that options are cheap.

The source uses illustrative annualised volatility-index bands below 12, 12–18, 18–25 and above 25 to discuss calm, ordinary, elevated and stressed environments. It also uses entry and exit thresholds of 20, 22 or 25 in different strategies. These are examples of rule design, not one consistent historical policy. Merging them into a single “official” threshold would change the original research.

A better report records the strategy-specific rule, its economic rationale and its test period. An absolute threshold is also sensitive to structural changes in the market’s baseline volatility. A percentile may adjust for recent history, but it introduces its own lookback and regime assumptions.

Historical case studies need the right denominator

Public-history cases and the denominators that matter

All three cases concern asymmetric payoff denominators. Premium, collateral, notional and total portfolio capital are different bases. A dramatic percentage becomes informative only when the report identifies which base is being used.

Figure 03 · Qualitative comparison

A spectacular hedge return needs the right denominator

A spectacular hedge return needs the right denominator

Reported result	Correct denominator or unit	What it does not establish
Hedge premium multiple	Correct denominator or unitPremium paid for the specified protection	What it does not establishReturn on the investor’s entire portfolio
Whole-book return	Correct denominator or unitTotal portfolio capital with all hedge costs and losses	What it does not establishPerformance of the hedge in isolation
Volatility spread	Correct denominator or unitConsistent volatility or variance units and horizon	What it does not establishExecutable strategy profit after costs and funding

Low volatility is not automatically low risk

A recent calm interval can support low estimates of standard deviation while leverage accumulates or liquidity becomes fragile. A strategy that scales exposure mechanically upward as measured volatility falls may increase the loss from a sudden gap. Risk therefore includes the possibility that the observation regime changes before the model can respond.

Conversely, high volatility is not automatically an argument to sell insurance. A high option price may be appropriate if realised movement will be even greater, the smile is reflecting a discontinuity or the investor cannot finance the possible interim loss. Mean reversion in a long historical series does not guarantee the survival of a position entered at the first apparent extreme.

The useful distinction is between an estimated premium and the capacity to bear the associated downside. A position can have a positive expected value in a model while being unsuitable at a size that risks insolvency or forced liquidation. The risk budget and financing horizon must therefore be part of the thesis rather than an afterthought.

What a credible premium study should report

A research study should state the implied measure, option horizon, realised estimator and whether it compares future or past realisation. It should show the average and distribution of the spread, the share of negative observations and the severity of the worst intervals. Overlapping horizons should be recognised because they create dependent observations.

If the study claims investment performance, it needs an actual tradable expression. Show entry quotes, leg quantities, hedge assumptions, transaction costs, collateral treatment, position sizing and exits. A theoretical premium series is not a strategy equity curve. The difference is especially large when the payoff has jumps, daily resets or a changing hedge requirement.

Report gross and net performance separately. Identify whether risk reduction comes from better forecasting, lower average exposure, a volatility filter, a purchased hedge or a favourable sample. These can all be useful, but they are different sources of return and should not be credited to one unexplained “edge.”

Avoid turning survivor selection into a premium estimate

A study of volatility sellers that includes only strategies still operating at the end of the period can overstate the reward for selling insurance. Strategies that suffered a terminal loss, closed after a liquidity event or stopped reporting belong to the economic history too. The same concern applies to rolling products whose design changed or whose earlier share units were repeatedly consolidated.

The observation unit also matters. A month-by-month premium series with overlapping horizons contains repeated exposure to some of the same daily shocks. Treating every overlapping observation as independent makes an average appear more precisely estimated than it is. A fair statistical analysis should preserve or account for that dependence.

Finally, a decision to buy protection should be evaluated alongside the exposure it is meant to protect. A hedge can have negative average standalone return while improving the probability that a leveraged or cash-constrained portfolio survives a stress. Conversely, an insurance seller can report attractive average premium while placing the rest of its capital at risk in exactly the same bad states. The sign of the isolated strategy’s average return is therefore not a complete assessment of its economic role.

These considerations do not invalidate the idea of a volatility premium. They make the claim more specific: premium estimates describe a defined market, sample, payoff and financing capacity. Removing those qualifiers turns a risk-transfer result into an unsupported promise.

The volatility risk premium is best understood as compensation for supplying insurance whose cost is concentrated in difficult states. Buying that insurance can be economically sensible for a portfolio owner; selling it can be sensible for an investor with the right price, diversification and capacity to bear losses.

The analytical task is to connect the quoted premium to a particular future distribution and a fundable payoff. Once that connection is explicit, volatility ceases to be a vague fear gauge and becomes a precise question about which uncertainty is being transferred, at what price, and who can afford the adverse outcome.