Strategy C beats spot Bitcoin in both the bullish and bearish regimes, but the bull-market result changes the nature of the claim. In 2024, the overlay raises return from +36.23% to +38.69%. A gain of 2.46 points while BTC is rising looks like compensation for a pricing gap, not insurance. The strategy harvests differences between Kalshi's quoted probabilities and the authors' model.
The authors trace the lower exposure to "inherent differences between market-implied odds (sentiment-driven) and theoretical pricing". Their explanation makes this a model-versus-market result, even as the title and abstract frame the paper around hedging. Three contracts provide a thin foundation for the broader pricing claim.
The position and its signal
Bhaskara and Jerfy use three Kalshi Bitcoin event contracts as binary options on BTC. Contract price supplies the market-implied probability, so 65 cents means 65%. The model probability comes from the risk-neutral Black-Scholes terminal expression, Phi((ln(S/K) - 0.5 sigma^2 T) / (sigma sqrt(T))). Sigma is BTC's realized volatility during the month before the market opened. If BTC has traded through the strike at any time, the model probability is overridden and set to 1.
The difference D between model and market feeds a five-level signal. Above +15%, the strategy buys 5000 contracts; above +5%, it buys 3000. A reading inside 2% closes the position. Below -5% and -15%, the trade reverses, buying NO in sizes of 3000 and 5000.
Three portfolios each begin with $100k. Strategy A holds BTC alone. Strategy B adds a static short of 1000 Yes contracts and holds it to expiry. Strategy C adds the threshold signal. The authors compute signals every minute, with execution restricted to the rebalance mark. Reported figures all use 1-hour rebalancing, which the paper says generally outperformed the monthly, weekly, daily, 12-hour and 6-hour settings it tested. Fees follow Kalshi's quadratic formula, ceil(0.07 * C * P * (1-P)).
The sample contains a Dec 2024 max-reach $100k contract, open from March to December 2024; a Dec 2025 close-above $100k contract, open from November to December 2025; and a Jan 2026 max-reach $100k contract. BTC returned +36.23%, -3.58% and -26.02% during those windows. Table 1 reports +38.69%, -3.04% and -22.96% for Strategy C. The paper says fees are included, although Table 1 itself carries no label.
Sharpe rises from 1.20 to 1.27 in 2024, from -0.76 to -0.10 in December 2025, and from -5.88 to -5.55 in January 2026. Drawdown improves by 1.83 points in 2024, moving from -31.73% to -29.90%. The corresponding gains are 1.33 points in December 2025, from -10.59% to -9.26%, and 1.34 points in January 2026, from -38.51% to -37.17%. Fees consume 25.2% of gross in 2024, 16.8% in December 2025 and 25.2% in January 2026.
Does the probability match the payoff?
The terminal model fits only one of the three contracts.
Two of the three markets settle on the maximum price reached. A vanilla terminal-ITM probability lies systematically below the one-touch probability for an identical strike and horizon, since a touch requires less than a finish above the strike. Before a breach, the model's p therefore runs low, D runs negative, and the signal tends to short Yes. That directional lean comes from the chosen pricing method.
The authors offer two reasons. They seek relative mispricing, and a barrier model introduces "increased risk brought on by raised parameter sensitivity". They also write that "limited liquidity impedes continuous price adjustment following threshold breaches". Those are defensible modelling preferences. The resulting mispricing measure still contains a known, signed model error: comparing a vanilla terminal probability with a max-reach payoff pushes D downward until the strike is touched.
Volatility creates another persistent tilt. Sigma is estimated once, using the month before opening, then carried through a contract whose T extends to ten months in the 2024 case. Pairing one stale volatility estimate with a fixed strike can keep D on the same side for long periods. A five-level threshold rule turns that persistence into a lasting position.
The December 2025 close-above contract is the case for which the terminal formula is the appropriate object. Table 1 also gives that hedge its smallest advantage, just 0.54 points.
Conflicting results in the same paper
The Results text assigns Strategy C a -0.96% return in December 2025 and -24.17% in January 2026. For the same strategy and periods, Table 1 shows -3.04% and -22.96%. Each pair contains an error, with opposite implications. The text improves December relative to the table and worsens January.
The same paragraph describes the exercise as "roughly a 3% reduction in exposure relative to the unhedged BTC position" across every regime. Using Table 1, the improvements are 2.46, 0.54 and 3.06 points. December falls well short. Until those figures are reconciled, the numerical basis for the headline remains unclear.
Position size further weakens the ranking. Strategy B holds one 1000-contract short, while Strategy C takes 3000 or 5000 contracts. Strategy C's 0.08 Sharpe advantage over Strategy B in 2024 may simply reflect a larger version of the same exposure.
Fees decide the December result
During the flat December 2025 window, the overlay moves Sharpe from -0.76 to +0.05 before fees, then back to -0.10 after fees. Its sign depends on the fee assumption. The abstract anticipates this problem by promising to "discuss further considerations which can erode profits in the future (i.e. fees)".
The authors state the effect plainly: "Initial deployment of a strategy with hundreds of trades saw complete erosion of PL." The published configuration is therefore the trade frequency that remained viable. Rebalance choice follows the same pattern. The 1 hour portfolios were "generally performing better than other time horizons", leading the analysis to "exclusively utilizes 1 hour rebalancing portfolios" from the six settings tested.
The description of the fee deserves an arithmetic qualification. The paper calls it "7% of its notional value". Yet 0.07 * P * (1-P), divided by notional P, equals 0.07 * (1-P). At 50 cents the charge is 3.5%; 7% is the limit for a contract priced near zero. The economically relevant figure is the reported 16.8% to 25.2% drag, already calculated under the assumption that trades fill at the quoted price.
Liquidity remains unmeasured. The authors acknowledge that "the strategies do not take into account latency and market liquidity concerns." They expect Kalshi to draw institutional and retail flow, "ultimately mitigating concerns and converging results." Future depth is carrying the argument for execution today.
Orders of 3000 to 5000 contracts would need to clear the available depth at hourly rebalances. The analysis includes no spread, depth or slippage, and reports no trade count. Slippage appears on the authors' list for later work. Their conclusion gives the constraint directly: "scalability is still limited by liquidity". Across three regimes, the evidence supports an apparent Kalshi pricing discrepancy more readily than a deployable overlay.
Evidence we could not reproduce
We could not test any of this. The tradable leg requires 1-minute Kalshi event-contract prices, including contract-specific strikes, expiries and the distinction between one-touch and close settlement. We hold none of those data. Two of the three windows also fall beyond the end of our crypto price coverage. Substituting spot or listed options would change the instrument.
Our earlier work has also left us sceptical that prediction-market edge survives choices in measurement. In our note on Polymarket longshots, three defensible aggregations of the same 560.9 million resolved purchases yielded -19.4%, -6.3% and +4.1%. This paper rests on three contracts, one asset, no significance test and 1-hour rebalancing selected after the fact. That base is thinner.
The authors already identify the work that could settle the issue. Their conclusion leaves "optimal rebalancing frequencies, alternative probability models" for later research. The same signal should be run across every BTC max-reach monthly contract listed by Kalshi. One-touch contracts should use a one-touch model, with execution charged at the offer. If gains of 0.54 to 3.06 points remain, the result becomes a trade. The paper currently makes its hedging claim from three contracts, one asset and the horizon that happened to perform best.