Overview
The VIX summarizes risk-neutral variance, but it does not determine the shape of downside risk, physical probabilities, or state-dependent compensation. This series moves from that measurement gap to the conditional pricing-kernel method, showing how the VIX and Treasury term spread reweight future S&P 500 return states, especially the left tail. Crisis estimates, option tests, and a historical Federal Reserve policy study improve interpretation without becoming a universal pricing model or proving causal changes in crash probability.
Learning outcomes
- The VIX summarizes risk-neutral variance, not the full distribution or the price of a particular loss state.
- Equal VIX readings can coexist with different downside-insurance prices when option-implied skew or the physical outlook differs.
- In the reported Federal Reserve study, the VIX and Treasury term spread change the estimated kernel, especially in negative-return states.
- Crisis estimates and option tests show relative improvement, but deep outright puts remain rejected and the kernel is not universal.
Keywords
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PlansFAQ
What does the VIX actually measure?
The VIX measures a risk-neutral expectation of S&P 500 return volatility, or a broad variance summary inferred from option prices. It is not a direct crash probability or a complete map of future state prices.
Why can the same VIX imply different state prices?
The same VIX can imply different state prices because it fixes a variance summary while option shape, physical outlook, and risk compensation can differ. A conditional pricing kernel maps those differences across future return states.
How do the VIX and Treasury term spread condition the pricing kernel?
In the reported Federal Reserve study, the VIX and Treasury term spread change the estimated state-price map, with the largest variation in negative-return states. The preferred pair is specific to that sample, horizon, and specification.
Does a cheaper risk reversal prove that a crash is less likely?
No. A cheaper risk reversal indicates a lower relative option-implied price of downside insurance, but it does not by itself identify a lower physical crash probability.