# Adjacent Event Contract Index Mathematics Methodology **Adjacent Markets, Inc.** Version 1.3 Adjacent uses AI and agents to assist with methodology development under [Adjacent’s AI Disclosure Policy](https://cdn.sanity.io/files/ddr9slt2/production/06cfe0b40d87e2291b313451461b10a0b9f37844.pdf). Humans remain responsible for themes, product decisions, and publication readiness. ## Table of Contents - [1. Introduction](#1-introduction) - [2. Index types](#2-index-types) - [Total Return](#total-return) - [Price Return (equal-weight price level)](#price-return-equal-weight-price-level) - [Implied Level](#implied-level) - [3. Weighting](#3-weighting) - [4. Rates](#4-rates) - [5. Total Return calculation](#5-total-return-calculation) - [Example](#example) - [6. Price Return calculation](#6-price-return-calculation) - [Settlement](#settlement) - [Example](#example-1) - [6A. Implied Level calculation](#6a-implied-level-calculation) - [Example](#example-2) - [7. Reconstitution](#7-reconstitution) - [7.1 Total Return](#71-total-return) - [7.2 Price Return](#72-price-return) - [7.3 Implied Level](#73-implied-level) - [8. Settlement and successor](#8-settlement-and-successor) - [9. Zero and halt](#9-zero-and-halt) - [10. Publication frequency and rounding](#10-publication-frequency-and-rounding) - [11. Changelog](#11-changelog) - [12. Approvals](#12-approvals) - [13. Legal Notices and Disclaimers](#13-legal-notices-and-disclaimers) ## 1. Introduction This document defines how Adjacent event-contract indices are calculated. Adjacent event-contract indices are calculated as **Total Return**, **Price Return**, or **Implied Level**, with Total Return the near-term default construction. It assumes acquaintance with mathematical notation and simple operations. The calculations are presented as equations, which are excluded from the individual index methodologies except by reference. Universe, inclusion, sleeve definitions, how sleeve readings combine, the reconstitution or reference-month calendar, and publication clocks for a given index live in that index’s methodology, not here. Constituent inputs `P` come from the public rates layer. **60-second indicative** values use the real-time rate published under [*Adjacent Event Contract Real-Time Rate Mathematics Methodology*](https://cdn.sanity.io/files/ddr9slt2/production/a85890e68d25ac741caaf256b31134318feeb647.pdf). **Official daily values** and **reconstitution admission** use the reference rate published under [*Event Contract Reference Rate Methodology*](https://cdn.sanity.io/files/ddr9slt2/production/5d9a472b54ceb98518c871be989fa5a39197af35.pdf). An individual index methodology may name a different split; the default is this one. Indices consume those published values. They do not recompute a mid, last trade, or second blend. An Implied Level index consumes those rates on an “at least X” strike ladder and publishes the implied print in Section 6A. --- ## 2. Index types ### Total Return A Total Return index measures the percentage change in the net asset value (NAV) of a specified portfolio of event contracts. Contract quantities `Q` are set under the Section 3 weighting option and then **held** until the next reconstitution calendar date. Between reconstitutions, NAV changes only with constituent rates, including when a rate publishes a terminal value. The index compounds that percent NAV change. The portfolio is fully invested at reconstitution. There is no unallocated cash sleeve. Calculation is gross of fees, spread, slippage, financing, and taxes. Fractional contract quantities are permitted. --- ### Price Return (equal-weight price level) A Price Return index is a published **equal-weight price (probability) level** of event-contract rates. There is no share count, no NAV, and no cash. Equity index families often publish Price Return and Total Return on the same portfolio, with dividends the difference; Adjacent Price Return is the analog of tracking prices, not that dividend machinery, and is not identical to an equity Price Return. It is not Total Return without settlement reinvestment. Equal weight is applied across constituents at reconstitution. `P_(j,t)` is the rate. The published level is a scaled simple average of those rates, with a sticky divisor so the level is 1,000.00 at inception. Quantities are not an input. When the rate publishes a terminal value (typically 0 or 1), that value is a print in the average; a name may leave the roster only on the reconstitution calendar. Calculation is in Section 6. --- ### Implied Level An Implied Level index is a published reading in official-print units, inferred from event-contract rates. On each sleeve, the reading is the live 50% pair of a published “at least X” strike ladder, published as strike midpoint or price interpolate, as the index methodology states. There is no contract quantity and no net asset value. The published level is that implied print, in the units of the official print. Inception is the first official implied level. The level is not scaled to 1,000.00. The index methodology names the series, the sleeves, how sleeve readings combine, the current reference month and the next reference month, and the official publication window. Calculation is in Section 6A. --- ## 3. Weighting Weighting is a parameter of each construction. - **Total Return:** the index methodology is one of the following, equal dollar or equal contract. Both hold `Q` until the next reconstitution calendar. This is not equal weight on probability. - **Equal dollar**: `Q_i = W_i / P_(i,a)`. Cheap names get more contracts. - **Equal contract**: same prescribed `Q` in every sleeve (Section 5). - **Price Return (default):** equal **weight** across constituents. Each name is `1/n` of the average. A name marked 0.10 and a name marked 0.90 count the same. - **Implied Level:** no contract quantity. The index methodology names strike midpoint or price interpolate (Section 6A). The index methodology states how sleeve implied levels combine, including any blend of the current reference month and the next reference month. That combination is a parameter of the index, not a new mathematics type in this document. An individual index methodology may specify a different published scheme (for example, name equal-dollar instead of sleeve equal-dollar). That is a parameter of that index, not a new mathematics type in this document. --- ## 4. Rates Each constituent is marked at the published rate for that clock (Section 1). The 60-second indicative mark is the real-time rate from [*Adjacent Event Contract Real-Time Rate Mathematics Methodology*](https://cdn.sanity.io/files/ddr9slt2/production/a85890e68d25ac741caaf256b31134318feeb647.pdf). The official daily mark and the reconstitution admission mark are the reference rate from [*Event Contract Reference Rate Methodology*](https://cdn.sanity.io/files/ddr9slt2/production/5d9a472b54ceb98518c871be989fa5a39197af35.pdf), unless the index methodology states another split. The approved mark `P_(j,t)` is that rate in `[0, 1]`. A published print of 63.00 is `P_t = 0.63`. If no rate is available, the index holds the last valid rate. If there is no valid rate at reconstitution, reconstitution is deferred under the index methodology. Settlement and void treatment enter the index only as the rates publish them (Section 8). This document does not write 0.00 or 1.00 itself. A carried-forward last valid rate produces no NAV change for that quantity (Total Return) and no change in that name’s contribution to the average (Price Return) until a new rate or a terminal rate is published. On an Implied Level index, the rates are the published “at least X” strike rates (Section 6A). A carried-forward last valid rate leaves that sleeve’s implied level unchanged until a new rate is published. If the sleeve has no valid bracket, it holds its last valid implied level. --- ## 5. Total Return calculation Let `P_(i,a)` be constituent `i`’s rate at admission. `P_(i,a) ≤ 0` is not an admissible admission rate. Quantity `Q` at reconstitution is set by the Section 3 weighting option: **1. Equal dollar.** Let `W_i` be the reconstitution target dollars for sleeve `i`, with `Σ_i W_i = 1,000.00` and equal `W_i` across sleeves. Cheap names get more contracts. ``` Q_i = W_i / P_(i,a) ``` If a sleeve has more than one constituent, the sleeve target is split equally among those constituents unless the index methodology states another split. **2. Equal contract.** `Q_i = Q*` for every sleeve, with `Q*` prescribed in the index methodology (not a number in this document). A 0.20 name and a 0.80 name hold the same `Q`; more dollars sit on the expensive name. ``` Q_i = Q* ``` If a sleeve has more than one constituent, the prescribed `Q*` is split as stated in the index methodology. Let `P_(j,t)` be the rate, including a terminal rate when published, of constituent `j` at time `t`. Modeled NAV is: ``` NAV_t = Σ_j Q_j × P_(j,t) ``` The index level compounds the percent change in NAV. Every Total Return series is published with level `I = 1,000.00` at inception. That is a scale convention only; it does not force a rebase to 1,000.00 at later reconstitutions. NAV at inception is not always 1,000.00. Under equal dollar, `NAV = 1,000.00` because `W` is scaled that way. Under equal contract, inception NAV is `Σ Q* × P_a` (not forced to 1,000); `Q*` stays prescribed. Intra-window compounding is the same for both reconstitution options in Section 7.1. It is also the same for both weighting options: `Q` is held until the next reconstitution calendar, and NAV is still `Σ Q × P`. Whether the **live** level is reset to 1,000.00 at each reconstitution or carried through a divisor / chain-link (continuous) is specified in the index methodology — not implied by this construction. Thereafter: ``` I_t = I_(t-1) × (NAV_t / NAV_(t-1)) ``` If `NAV_(t-1) = 0`, the index remains 0.00 until the next reconstitution. Admission of new quantities does not itself move the index. Subsequent NAV change is `Q × P_t` on the held quantities. ### Example **Equal-dollar example:** Sleeve target W = 250.00, admission rate 0.08: Q = 250 / 0.08 = 3,125. If that contract moves to 0.10, sleeve NAV is 3,125 × 0.10 = **312.50**. If the other sleeves are unchanged at 750.00, NAV = 1,062.50. With `I_(t-1)` = 1,000.00, `I_t` = 1,062.50. --- ## 6. Price Return calculation Let `n` be the number of constituents on the current reconstitution roster. Equal weight means each name is `1/n` of the average. Let `P_(j,t)` be the rate of constituent `j` at time `t` (Section 4), including a terminal rate when published. There is no `Q`, no NAV, and no sleeve cash. The simple average of rates is: ``` A_t = (1/n) × Σ_j P_(j,t) ``` The published Price Return level is one thousand times that average, scaled so the level is 1,000.00 at inception: ``` I_t = 1000 × (A_t / D) ``` `D` is the simple average of rates at inception, so `I = 1,000` then. On price-only calculation intervals, `D` is unchanged. Calendar membership changes and the sticky divisor reset are in Section 7.2. Equivalently, `I_t = (Σ_j P_(j,t)) / D_Σ` with `D_Σ` chosen at inception so `I = 1,000`. This document uses the average form. Indicative values are recalculated every 60 seconds, the same frequency as Total Return, using Section 4 rates on the current roster. ### Settlement When a constituent officially resolves, the terminal rate (typically 0 or 1) is a print in the average at the next calculation interval after that value is published. The name remains on the roster at 0.00 or 1.00 until the reconstitution calendar, when it is eligible to drop. There is no reinvestment of settlement proceeds and no mid-calendar successor. ### Example Four names, reconstitution rates 0.10, 0.30, 0.50, and 0.70. Simple average `A = 0.40`. Set `D = 0.40` so `I = 1,000.00`. The 0.10 name prints 0.20. New average `A = 0.425`. `I = 1000 × 0.425 / 0.40 = 1,062.50`. A move of 0.50 to 0.60 is the same +0.025 to the average and the same +62.50 on the index: a 0.10 name and a 0.90 name count the same. If that name then settles Yes, it prints 1.00. Average `A = 0.625`. `I = 1000 × 0.625 / 0.40 = 1,562.50`. The name stays in the average at 1.00 until the reconstitution calendar. --- ## 6A. Implied Level calculation Let the listed strikes for a sleeve’s current reference month be ordered from low to high, in the units of the official print. On each strike, the input is the published rate that the official print is at least that strike (Section 4). A published print of 50 cents is 0.50. An exact 0.50 counts. K is the largest strike still at or above 0.50. K+1 is the next listed strike. The index methodology must pick one published scheme for turning that pair into the implied print. Both schemes use the same live pair. **Strike midpoint.** Equal weight on the two strike levels. The published rates select the pair. They do not enter the print except by choosing K and K+1. ``` x̂_t = (K + (K+1)) / 2 ``` **Price interpolate.** Place the print between K and K+1 so the implied “at least X” rate is 0.50, assuming a straight line in rate between the two published rates. Let `P_(K,t)` be the published rate on K and `P_(K+1,t)` the published rate on K+1. ``` x̂_t = K + ((K+1) - K) × (P_(K,t) - 0.50) / (P_(K,t) - P_(K+1,t)) ``` If `P_(K,t) = 0.50`, the implied print is K. If `P_(K,t) = P_(K+1,t)`, use strike midpoint. If the 0.50 crossing is not between K and K+1, use the edge-case bullets below. The bracket is selected again at each calculation interval. The two strikes are not held as contract quantities. - If every listed strike is below 0.50, the implied print is the midpoint of the two lowest listed strikes. - If every listed strike is at or above 0.50 and there is no next strike, the implied print is the midpoint of the two highest listed strikes. - If only one strike is listed, that strike is the implied print. - If no pair or single strike exists, the sleeve keeps its last valid implied level. The rates layer publishes one rate per strike for the claim that the print is at least that strike, including where a venue listed thresholds and where a venue listed single-print bins. The index takes one median on that published ladder. It does not average medians computed venue by venue. It does not apply this rule to a raw single-print bin price. This document does not restate how the rates layer builds or blends that ladder. If the index has more than one sleeve, the index methodology states how the sleeve implied levels combine. That statement includes any blend of the current reference month and the next reference month. Indicative values are recalculated every 60 seconds from the real-time rate (Section 4). Official daily values use that day’s reference rate. The index methodology names the official window. The rates methodologies name Effective Time T. This document does not name that clock. ### Example Listed strikes 2.0, 2.1, and 2.2. Published rates 0.80, 0.46, and 0.12. K is 2.0. K+1 is 2.1. Strike midpoint is 2.05. Price interpolate is `2.0 + 0.1 × (0.80 - 0.50) / (0.80 - 0.46) = 2.09`. --- ## 7. Reconstitution This section states how each type treats the reconstitution calendar. ### 7.1 Total Return Membership and quantities change only on the reconstitution calendar published in the index methodology. There is no rebalancing between reconstitutions. Rates are revalued every calculation interval; quantities are not. At reconstitution, new `Q` are set from Section 5 using rates from the reconstitution pricing window stated in the index methodology. The index methodology must pick one Total Return weighting option. `Q` is set by the Section 3 / Section 5 weighting option. Intra-window, `Q` is held until the next reconstitution calendar. NAV is still `Σ Q × P`. Total Return reconstitution is either **rebased** or **continuous**, as specified in the index methodology. Continuous uses a divisor / chain-link so the live level is not reset to 1,000. **1. Rebased.** The **live** series starts each reconstitution window at 1,000.00. Prior vintage is frozen. That reprint is a rebase, not a period return. Live levels are not a continuous multi-period total-return series across reconstitutions. Where a **vintage** series is published, the completed cohort is frozen at its last official value, including 0.00. A vintage is not reset to 1,000.00. Held `Q` scale NAV to the 1,000 base at the start of each live cohort; composition change is not a market return. ``` I_R = 1000.00 ``` **2. Continuous** (divisor / chain-link). Intra-window math is unchanged: ``` I_t = I_(t-1) × (NAV_t / NAV_(t-1)) ``` At reconstitution, `Q` resets under the chosen weighting option (equal dollar or equal contract per sleeve). The **published level does not** reset to 1,000. A linking factor / divisor is set so ``` I_R = I_R- ``` The live series compounds across windows. The rebalance itself does not print a jump. After the link is set, compounding continues with the new quantities and the same ratio. Reconstitution pricing uses the reference rate at the reconstitution window stated in the index methodology. ### 7.2 Price Return Price Return does not set `Q`. Default weight remains equal weight `1/n` of the Section 6 average. Membership changes only on the reconstitution calendar. There is no intra-day add or delete. On reconstitution, names may be added or dropped. That can change the simple average even if no remaining contract’s rate moved. That roster change must not move the published level. Price Return reconstitution is a **continuity reset** (one rule, not a rebased-versus-continuous choice). Reset the divisor so the index **after** the membership change equals the index **immediately before**: ``` D_R = 1000 × (A_R / I_R-) ``` which makes `I_R = I_R-`. `A_R` is the simple average on the new roster; `I_R-` is the published level immediately before the change. Three names at 0.50 give an average of 0.50 and an index of 1000. Add a fourth at 0.10 and the average becomes 0.40. Without resetting `D` the index would print 800. Reset `D` so the level stays 1000. After that, real rate moves move the index as usual. ### 7.3 Implied Level Implied Level selects the 50% bracket again at each calculation interval (Section 6A) and applies the named scheme, strike midpoint or price interpolate. The index methodology states when the current reference month changes, and how a roll blends the current reference month with the next reference month. The published level stays in official-print units through that change. Section 7.1 applies to Total Return. Section 7.2 applies to Price Return. --- ## 8. Settlement and successor Official settlement is the event-contract analog of a final price (the analog of a corporate action that *does* affect the index). A new contract is admitted only on the reconstitution calendar (the analog of an add that must not itself move the index). When a Total Return constituent officially resolves: - `P_(j,t)` becomes the terminal rate as published. That terminal is typically 0.00 or 1.00, but this document does not write 0.00 or 1.00 itself. - That rate change is included in NAV exactly once, at the next calculation interval after the rate publishes it. - `Q` is unchanged. The settled contract remains in NAV at that published terminal rate until the vintage is frozen / the next reconstitution. - There is no reinvestment of settlement proceeds into other contracts between reconstitutions. Price Return settlement is the same published terminal rate, as a print in the Section 6 average, with the name eligible to drop only on the reconstitution calendar. Void, amendment, and non-binary settlement enter the index only if and when the rate publishes them. Until a terminal or void rate is published, the last valid rate is held. A voided or amended rate does not, by itself, drop the name off-calendar. A successor contract is not admitted mid-calendar, including when the next cohort’s contracts are already listed. Empty or settled slots wait for the reconstitution calendar. For an Implied Level sleeve, the official print and any terminal rate enter as the index methodology states, through the published rates. Until a valid bracket or a new rate is available, the sleeve holds its last valid implied level. The next reference month is admitted on the calendar in the index methodology. --- ## 9. Zero and halt No official value is published below 0.00. A print of 0.00 is permitted and is a continuing official value. Live and vintage series at 0.00 continue to be published. Zero is not, by itself, a halt, termination, or suspension. If `NAV_(t-1) = 0`, `I_t = 0.00` until the next reconstitution. On a Price Return index, if every constituent rate is 0.00, `I_t = 0.00` until the next reconstitution. Upside is uncapped. A halt or delayed publication may occur only if a disruption makes routine rates or rules unsuitable, as provided in the index methodology and applicable governance policies. A halted or suspended *contract* uses the last valid rate in Section 4; it does not, by itself, halt the index. On an Implied Level index, a sleeve with no valid bracket, no available rate, or no listed reference period holds its last valid implied level. The index keeps publishing. One thin sleeve, or a missing reference period, does not by itself halt the index. --- ## 10. Publication frequency and rounding - **Indicative values:** every 60 seconds, using the real-time rate in Section 4. Total Return applies that rate to the held `Q`. Price Return applies it to the equal-weight average in Section 6. Implied Level re-selects the Section 6A bracket and publishes the implied level. - **Official daily value:** the index calculated from the reference rate in Section 4, using the official window stated in the index methodology. The published index is that calculation. The rates methodologies name Effective Time T. This document does not name that clock. The official daily value uses that day’s reference rate. - **Reconstitution:** Total Return quantities use the reference rate at the reconstitution window stated in the index methodology. Price Return resets the divisor on that calendar as in Section 7.2. Implied Level reference-month changes follow the calendar in the index methodology (Section 7.3) and use the reference rate. Index levels are expressed to two decimal places. Contract quantities may be fractional. After a vintage has reached its official terminal value, including 0.00, that constant official daily value continues until the vintage is retired. --- ## 11. Changelog | Version | Date | Changes | | --- | --- | --- | | 1.3 | October 6, 2026 | Implied Level Section 6A: index methodology picks strike midpoint or price interpolate on the same live 50% pair. Strike midpoint unchanged. Price interpolate is new. | | 1.2 | September 25, 2026 | Added Implied Level (Section 6A): live 50% midpoint on a published “at least X” strike ladder, last valid implied level, and the same real-time / reference rate split. Later section numbers are unchanged. Universe, reference-month calendar, and official window stay in the index methodology. | | 1.1 | September 6, 2026 | Split constituent inputs: real-time rate for 60-second indicative values; reference rate for official daily values and reconstitution admission. | | 1.0 | September 2, 2026 | Initial mathematics methodology. | --- ## 12. Approvals | Role | Name | Signature | Date | | --- | --- | --- | --- | | Chief Executive Officer | | | | | Chief Operating Officer | | | | --- ## 13. 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