A tool for understanding what a position spread across an exceedance ladder costs and what it pays back. It opens on a made-up example; the picker loads any live ladder on this site. Everything here is arithmetic on the numbers the user types and the exchange’s public prices. The site adds no forecast of its own, and none of this is investment advice.
For event contracts applied to variables on a continuum, ForecastEx typically lists a ladder of overlapping, non-mutually-exclusive exceedance values. In a live hurricane wind contract, for example, the exceedance ladder might contain ≥150, ≥140, ≥130, ≥120 and ≥110 mph.
If the wind reaches 100 mph, all of the Nos pay out and none of the Yeses do. If it reaches 135 mph, the Yeses on 130, 120 and 110 pay out and the Nos on 140 and 150 pay out. If it reaches 155 mph, all of the Yeses pay out and none of the Nos do.
It helps users understand net payouts for different allocations of a position across these overlapping exceedance strike ladders, for both hypothetical market prices and actual live prices for the contracts of interest. It takes as input the user’s prediction, a user-defined measure of uncertainty in that prediction, and the amount of capital they want to put up.
By default the calculator uses a normal distribution to represent uncertainty. Skewed representations are also available, in either direction, for quantities whose misses are not symmetric. A wind speed or a rainfall total with a long tail above, a crop yield with a long tail below. Both keep the prediction as the median and the stated span as the 95 percent interval; what changes is how that span is divided between the two sides.
The calculator then compares the market’s prices for Yes and No against the prices the user’s own distribution implies across the entire ladder, and marks which exceedance strikes are most mispriced relative to that distribution. In the second column the market’s Yes price is the green-to-red split, and an arrow runs from it to the value the user’s curve implies, so the length of the arrow is the disagreement.
Allocation is confined to strikes the market prices between 5 and 95 percent. Outside that range the book thins out and a position sized against those prices could not reliably be filled. The payout multiples that make deep strikes look attractive are the least attainable numbers on the board. Strikes outside the window stay drawn, faint, and take no capital.
Even with a prediction and an uncertainty distribution fixed, the question remains how to allocate capital according to a risk appetite. A participant could take an aggressive strategy and place the entire position in the few contracts their distribution implies are most mispriced and which carry the highest payout multiples, accepting the risk that most of the capital may well be lost. A participant could equally take a conservative strategy and distribute capital broadly across contracts, accepting lower payout multiples in the best case in exchange for it being less likely that most of the capital is lost. The calculator provides an aggressive strategy, a conservative strategy and a middle ground.
The formal basis is the Kelly criterion (Kelly, 1956). The calculator chooses the allocation that maximises the expected utility of the payout under the user’s probability curve, computed jointly across the ladder rather than one strike at a time. The middle scenario uses the logarithm as the utility, which is Kelly’s fully-invested form. At a single strike it splits the money between Yes and No in the user’s own probabilities, whatever the prices; across the whole ladder it tilts toward the strikes the curve prices furthest above their cost. The conservative and aggressive scenarios replace the logarithm with a more and a less risk-averse member of the same power-utility family, which under the standard lognormal approximation correspond to quarter-Kelly and double-Kelly risk appetites, as set out in MacLean, Thorp & Ziemba, Good and bad properties of the Kelly criterion.
A more risk-averse utility is less tolerant of outcomes that pay nothing, so it is more prone to buy the cheaper contracts on both flanks, which produces a smoother payout curve in the fourth column. A less risk-averse one accepts the possibility of loss and concentrates capital on the best-priced strikes near the centre of the prediction. When the participant’s implied fair values and the market’s agree, no allocation split has an expected edge over another before the fee, and the differences between the scenarios are purely about payout smoothness. With the fee inside every cost, a split that buys more contracts gives up more to fees, which the expected values on the scenario cards show.
No split holds Yes and No on the same strike. The exchange nets opposing positions, so buying the second side would close the first at a combined cost above a dollar; spreads across different strikes remain available. The whole amount is always committed, so the calculator’s only decision is where it goes, never how much of it to hold back. Dollar shares become whole contracts by rounding down, and the loose change then buys one contract at a time, best first, until it cannot afford the cheapest thing left. Costs are what a buyer pays now, Yes at one dollar less the No bid and No at one dollar less the Yes bid, with the per-side fee inside every figure. On quantities settled in whole units, “above 84” is read as the settled figure rounding past it, so the working threshold sits half a unit beyond the strike, matching how the contracts settle.
The inputs define a probability curve. The predicted value m is its median and the typed band b the half-width of its central 95 percent interval, so the cumulative curve F satisfies F(m) = ½ and F(m+b) − F(m−b) = 0.95 for every shape. The symmetric shape is the normal distribution with σ = b/1.96; the skewed shapes are shifted lognormals with the same median and the same 95 percent span.
Each buyable side becomes a probability and a cost. On a board settled in whole units, Yes on “Above K” pays when the settled figure exceeds K, which the curve prices at
p = 1 − F(K + ½)
and the matching No at 1 − p; Yes on “Below K” is priced at F(K − ½). The half unit is the settlement convention, since a true value of K.4 rounds to K and does not pay. The cost of a side is
c = 1 − (bid on the other side) + fee
so a dollar on it buys 1/c contracts and returns 1/c dollars if it pays, which is the payout multiple printed in the third column.
The thresholds cut the value axis into intervals, and between two neighbouring thresholds every contract’s outcome is fixed, so those intervals are the complete outcome space. A split is a set of fractions fj ≥ 0 summing to 1, one per buyable side. When the value lands in interval s, each dollar committed returns
x(s) = Σj fj aj(s), where aj(s) = 1/cj if side j pays in s and 0 if it does not.
Each scenario takes the split that maximises expected utility under the curve,
maximise Σs P(s) u(x(s)), with u(x) = (x1−γ − 1) / (1 − γ) and fYes(K) fNo(K) = 0 at every strike
and u(x) = log x at γ = 1. Conservative sets γ = 4, Middle γ = 1 and Aggressive γ = ½. A larger γ punishes intervals that pay little more heavily, so the split hedges with cheap contracts on both flanks; a smaller γ tolerates them and concentrates on the strikes priced furthest below the curve. In every case the maximiser moves money toward outcomes the user’s curve rates more likely than the prices imply, and 1/γ sets how hard it leans.
The probabilities belong to the user. The page does the arithmetic that follows from them, so if those numbers are wrong the expected values shown are wrong with them. Nothing here is a forecast, a recommendation or a fair value.