The Hormuz Curve: A Persistent Front-Loading Anomaly

The observation

Since the Hormuz normalization market opened on Kalshi in mid-March, we have been tracking something unusual in how the term structure is priced. Near-term contracts have consistently implied a materially higher monthly probability of normalization than far-dated ones, and that gap has not closed in over three months of continuous observation.

This post documents the pattern, walks through the methodology, and proposes three candidate explanations. We are not claiming this is definitively a mispricing. We are saying it is an anomaly worth watching, and that it has been persistent enough to warrant rigorous attention.

Methodology

The "When will traffic at the Strait of Hormuz return to normal?" series on Kalshi consists of sequential binary contracts, each resolving YES if the 7-day moving average of daily transit calls through the Strait exceeds 60 (420 per week) before a given date, as verified by IMF PortWatch data.

Because these contracts are cumulative by construction, the implied probability of normalization occurring specifically within a given calendar window can be derived directly from the difference between consecutive contract prices. If the Before Sep 1 contract prices at 48.9¢ YES and the Before Aug 1 contract prices at 34.5¢ YES, the market is implying a 14.4 percentage point probability of normalization occurring specifically between August 1 and September 1. Dividing by the number of months in that window gives the implied monthly rate for that segment of the curve.

This is the same methodology used to extract forward rates from a yield curve in fixed income, stripping implied period-specific probabilities from cumulative contract prices rather than reading them off the headline price directly. The historical snapshots in the table below were derived from Kalshi's exported price history data. The current snapshot can be independently verified by subtracting consecutive YES prices on the Kalshi market page directly.

The data

We computed implied monthly normalization probability for each window across six snapshots spanning April 1 through June 30. The pattern is consistent across every date.

Implied probability of normalization per month, by window

The near-term window has consistently priced in 18-22 percentage points of normalization probability per month throughout the entire observation period. The 3-6 month window has consistently priced in only 4-5 percentage points per month. That is a 4-5x differential that has been stable for over three months.

For context, if the true underlying monthly probability of normalization were constant, say a Poisson-like process where each month has an independent probability of being the month normalization occurs, then all windows should imply roughly the same per-month rate. They do not, and the gap has not compressed despite repeated near-term contracts resolving NO.

Three candidate explanations

1. Rational front-loading of diplomatic probability

The most generous interpretation is that this pricing is correct. Diplomatic breakthroughs, if they come, are more likely in the near term when political pressure is highest, attention is most concentrated, and negotiating parties are most engaged. Under this view, the monthly probability of normalization really is higher in July and August than in November and December, because if a deal hasn't been struck by then the situation may have calcified into a longer-term standoff. The market is pricing a decreasing hazard rate as time passes, not a constant one, and that could be entirely rational.

We cannot rule this out. It is consistent with the data.

2. Behavioral front-loading bias

A less generous interpretation is that retail flow on near-term contracts is systematically influenced by recency bias and headline sensitivity. When a diplomatic development surfaces, the near-term YES contract is the most visible and liquid instrument for expressing that view. Retail traders who want to bet on a resolution buy the closest available contract, pushing near-term YES prices up disproportionately relative to their informationally justified level. The far-dated contracts, being less salient and less discussed, escape this headline-driven flow and price more conservatively.

This would predict that the gap should widen after positive diplomatic news and compress or disappear in periods of sustained negative data. Looking at the Jun 30 snapshot, where the near-term implied rate spikes to 36.8pp per month for the Jul 15 to Aug 1 window, it does appear that recent headlines around the MOU have pushed short-end pricing to unusually elevated levels relative to the stable 4-6pp per month range further out the curve.

3. Liquidity and sophistication differential

Near-term contracts are significantly more actively traded and have thinner bid-ask spreads than far-dated ones. This cuts both ways. On one hand, more liquid markets should be more efficiently priced. On the other, more liquid markets attract more retail flow by volume, and if retail flow systematically misprices near-term contracts as described above, higher liquidity could amplify the anomaly rather than correct it. The far-dated contracts, being primarily traded by participants with longer time horizons and more deliberate positioning, may simply be harder to systematically misprice.

What this is not

This is a single-market observation on a novel, geopolitically-specific contract series over a three-month window. We are explicitly not claiming:

• That this pattern generalizes to other Kalshi markets or other prediction market platforms
• That the near-term NO contracts are definitively mispriced rather than rationally priced
• That this represents a persistent, exploitable alpha source beyond the specific Hormuz situation
• That the far-dated contracts are the correct benchmark for "true" monthly probability

All three explanations above are consistent with the data. Further research across multiple similar contract series over longer time horizons would be needed to distinguish between them.

Why we think it warrants attention

Three months is long enough for sophisticated participants to observe and correct a structural mispricing if one exists. The fact that the gap has not compressed, and has in some cases widened, is notable. Either the rational front-loading explanation is correct and the market is actually well-calibrated, or this is an anomaly that is either too small to arbitrage at current liquidity levels or too opaque to attract the right corrective flow.

We will continue tracking the implied monthly probability differential as new contracts open and existing ones resolve. If the NO side of near-term contracts continues to outperform the long-dated equivalent on a per-month basis, the case for a systematic structural inefficiency strengthens. If the gap closes as volumes grow and institutional attention on prediction markets increases, that is equally informative.

The data so far is interesting. Whether it is actionable is a separate question, and one we are not yet prepared to answer.

The data, in full

Every figure in this post comes from Kalshi's public daily price history for the "When will traffic at the Strait of Hormuz return to normal?" market ( KXHORMUZNORM-26MAR17). The full daily close series for all contract legs is available below so anyone can reproduce the forward-rate math and the per-window implied probabilities.

All price data from Kalshi's public market feed. Implied monthly probabilities computed using consecutive contract price differentials, analogous to forward rate extraction from a fixed income yield curve. This is not financial advice.