The VIX Is Not the Price of Every Future State
The subject of this series is the conditional pricing kernel: the way financial markets assign prices to different future states of the S&P 500. The question is why the same VIX reading can coexist with different prices for those states. The practical value of answering it is simple: a volatility index can tell us how much movement the options market is pricing in, but not necessarily which direction of movement is expensive, how investors’ outlook has changed, or how much compensation is attached to a particular loss.
That distinction matters whenever a market indicator is treated as if it were a complete diagnosis. A VIX of 20 and another VIX of 20 look identical as numbers. Yet the options behind those readings can have different shapes. In one market, investors may be paying especially heavily for protection against a sharp fall. In another, the same overall variance may be distributed more evenly between upside and downside outcomes. The volatility summary is unchanged; the prices assigned to specific states need not be.
The evidence for this argument comes from two complementary studies. A 2026 Federal Reserve paper estimates a forward-looking, time-varying pricing kernel and finds that the VIX and the Treasury term spread are especially informative about it. A 2013 BIS study examines Federal Reserve policy episodes and finds that option measures of downside risk often responded more clearly and more quickly than broad volatility measures such as the VIX. The studies do not estimate the same object, but together they make the central problem concrete.
A volatility index is not a map of states
To see what a VIX reading leaves out, start with what it does measure. The BIS study describes the VIX as a risk-neutral expectation of S&P 500 return volatility. In ordinary language, it is a market-price measure of expected dispersion under the probability system used to price options. It is often called a fear gauge, but its more precise role is as a broadly symmetric measure of the second moment: it summarizes how much variation is being priced, not the entire shape of the distribution.
That “not the entire shape” is doing important work. Two return distributions can have the same variance while differing in skewness. One can put more weight, or more price, on unusually bad outcomes and less on unusually good ones; another can be less lopsided while preserving the same average squared movement. A single second-moment statistic cannot distinguish those arrangements. The same point holds in options markets. The VIX aggregates information across option prices into a volatility measure, while the relative prices of out-of-the-money puts and calls reveal how the market values different parts of the distribution.
The BIS paper uses risk reversals for this purpose. A risk reversal compares the implied volatility of an out-of-the-money call with that of an out-of-the-money put at the same maturity and delta. Equity markets usually have negative skew: out-of-the-money puts are more expensive because investors place a high price on protection against a large fall. The absolute difference therefore acts as a proxy for the cost of insuring against a crash or for the skewness risk premium. It is not a direct probability that a crash will occur, but it tells us that the market is pricing the downside differently from the upside.
That is the first answer to the title. The same VIX can be accompanied by a different risk reversal because the average amount of priced volatility and the relative price of downside protection are different pieces of information. A market can become more concerned about a narrow set of severe losses without experiencing an equal change in its broad volatility summary. Conversely, the VIX can move while the relative price of downside protection changes less.
The Federal Reserve paper makes the same distinction from another direction. It begins with 12 possible conditioning variables, including the VIX, risk-neutral skewness and kurtosis, a left-tail-risk index, sentiment, the Treasury term spread, measures of economic activity, credit spread, and the lagged market return. The list is not a claim that all of these variables are equally useful. It is evidence that the pricing problem is multidimensional before the estimation even begins. Volatility is important, but it is one signal among several about the environment in which future returns will be priced.
What “state price” means here
A state price is easier to understand as the present price of a payoff that arrives only if a particular future state occurs. In a simple two-state example, one dollar paid after a good outcome and one dollar paid after a bad outcome need not have the same economic value today, even if the two payments are the same size. In a continuous market, the states are narrow ranges of future returns rather than two named boxes. The pricing question is therefore not only how much the market may move, but how the market prices a payoff delivered in each part of that movement.
The pricing kernel is the device that connects those questions. In the Federal Reserve paper’s projected one-month market-return setting, it is defined from two probability densities: the risk-neutral density inferred from option prices and the physical density representing probabilities of realized returns. In simplified notation, the pricing kernel at a future return is proportional to
[ M_t(r) = \frac{1}{1+r_{f,t}\tau}\frac{f_t^*(r)}{f_t(r)}. ]
The risk-neutral density is not simply the market’s neutral forecast. It is the distribution that makes option prices internally consistent after risk compensation is incorporated. The physical density is the probability distribution used to describe realized outcomes. Their ratio tells us how the market’s price of a state differs from what its physical likelihood alone would suggest, with the risk-free discounting included.
This is why a VIX reading cannot be the whole pricing kernel. The VIX constrains a summary of the risk-neutral distribution’s variance. It does not by itself specify the distribution’s skew, its far-left-tail behavior, or the physical probability assigned to those outcomes. Even if two observations have the same VIX, they can differ in the other ingredients of the ratio. Their option-implied tail shape can differ. Their economic outlook can differ. Their physical density can differ. The resulting price assigned to a negative-return state can consequently differ as well.
The term spread is useful in this explanation because it is not another volatility gauge. The Federal Reserve study defines it as the 10-year Treasury yield minus the 2-year yield and treats it as a leading economic indicator. In its estimates, the VIX and term spread emerge as the most informative pair among the tested combinations. That result does not make them a universal sufficient statistic. It does show, within the study’s sample and specification, that a volatility signal and a forward-looking outlook signal contain distinct information about how future states are priced.
The diagram also shows why the phrase “same VIX” must be handled carefully. It identifies one input, not the entire route from market information to a state price. The research material does not contain a matched-date experiment that holds the VIX exactly constant and then compares every other input. The supported claim is narrower and more useful: the VIX is not enough, in principle or in the Federal Reserve study’s conditional evidence, to describe how the market prices all future return states.
The questions that make the VIX interpretable
Once volatility is understood as a summary rather than a complete map, four questions become unavoidable whenever the VIX is used to characterize risk.
First, what happened to the shape of the option-implied distribution? Risk reversals and other measures of skew can reveal a repricing of downside insurance that a symmetric volatility index may compress away. In the BIS study, the 10-delta and 25-delta risk reversals were strongly correlated with a more direct monthly tail-risk measure, but the authors still treated them as proxies rather than as probabilities. That distinction keeps the interpretation honest: an expensive put can reflect a high price of insurance, a high perceived likelihood of loss, or both.
Second, what does the market believe about future conditions? The Federal Reserve paper finds that the conditional kernel varies over time, particularly in negative-return states. That means the price of a future loss depends on the information environment in which the loss is being evaluated. A negative return that appears unlikely during a calm, favorable outlook may command a high state price because it would be especially damaging if it arrived. The same return may receive a different price when an adverse outlook already makes it part of the expected risk environment.
Third, are we discussing a price, a probability, or compensation for bearing risk? These are related but not interchangeable. The risk-neutral density is extracted from option prices; the physical density describes realized-return probabilities; the pricing kernel relates them. Risk reversals describe the price of a particular kind of protection. The VIX describes a variance summary. Collapsing all four into “fear” produces a vivid phrase but a poor analytical model.
Fourth, what does the evidence actually identify? The Federal Reserve paper is a preliminary staff working paper and estimates a kernel projected on the aggregate market return, not the complete pricing kernel for every asset. The BIS study covers a historical policy window and uses option-based proxies, event studies, and structural VARs. Its announcement results can combine asset purchases with forward guidance and other information released at the same time. Neither study licenses a universal trading rule or a claim that every equal-VIX observation must have different state prices.
The useful conclusion is therefore not that the VIX should be ignored. It is that the VIX should be read as one coordinate in a larger conditional system. To interpret it, we need to ask which states are expensive, what the market’s outlook is, and whether the observed quantity is a probability or a price of risk. The next unresolved step is to see how a pricing-kernel estimate incorporates those distinctions rather than leaving them as separate indicators.