Index Methodology

Version: 1.0 Methodology Version: midprice-v1 Last Updated: January 2026

Abstract

This document provides a technical specification of the Net Asset Value (NAV) computation methodology used by Belief Systems. The system aggregates prices from Polymarket prediction markets into composite indices, producing two primary outputs: raw_nav (a probability-weighted aggregate bounded in [0,1]) and index_level (a rebased index starting at 100). The current implementation uses the midprice-v1 methodology, which derives market prices from the midpoint of best bid and best ask quotes in the Polymarket Central Limit Order Book (CLOB).

Table of Contents

1. Terminology
2. Data Source
3. Methodology: midprice-v1
4. Worked Examples
5. Resolution Handling
6. Staleness and Data Quality
7. Known Limitations
8. Future Methodology Versions

Terminology

Data Source

Polymarket CLOB API

All price data is sourced from the Polymarket Central Limit Order Book API (clob.polymarket.com):

• Order Book Endpoint: /book?token_id={token_id}
• Market Metadata: /markets/{condition_id}

The CLOB API returns bid and ask levels with the following sorting convention:

Precision Specification

All numerical values use the following precision:

Methodology: midprice-v1

Overview

The midprice-v1 methodology computes index NAV using the arithmetic midpoint of best bid and best ask prices from the Polymarket CLOB. This approach provides a simple, transparent, and deterministic price discovery mechanism.

Step 1: Market Price Determination

Active (Unresolved) Markets

For each unresolved market, the price is determined as follows:

1. Fetch Order Book: Query CLOB API for the tracked outcome token
2. Extract Best Quotes:
   • best_bid = highest bid price (last element in ascending-sorted bid array)
   • best_ask = lowest ask price (last element in descending-sorted ask array)
3. Compute Midprice:

   midprice = (best_bid + best_ask) / 2
   

4. Clamp to Valid Range:

   price = clamp(midprice, 0, 1)
   

Example:

best_bid = 0.995
best_ask = 0.996
midprice = (0.995 + 0.996) / 2 = 0.9955

Resolved Markets

When the CLOB API indicates a market is closed (closed == true), the engine uses settlement prices based on the winner field:

If tracked outcome token is winner: settlement_price = 1.0
If tracked outcome token is loser:  settlement_price = 0.0

Fallback Behavior

If the CLOB API call fails:

1. Retry up to 3 times with exponential backoff
2. If all retries fail, use the last successfully fetched price for that market
3. Mark the computation as stale

Step 2: Weight Normalization

Raw weights from the index composition are normalized to ensure the sum equals 1.0:

W = Σ w_i           (sum of all raw weights)
w'_i = w_i / W      (normalized weight for market i)

Invariant: Σ w'_i = 1

This normalization guarantees that raw_nav remains bounded in [0,1] regardless of the raw weight values specified in the composition.

Example (7 markets with raw weights of 0.1429 each):

W = 7 × 0.1429 = 1.0003
Normalized weight per market = 0.1429 / 1.0003 ≈ 0.14285714
Sum of normalized weights = 1.00000000

Step 3: Raw NAV Calculation

raw_nav = Σ (w'_i × p_i)

Where:

• w'_i = normalized weight for market i
• p_i = price for market i (midprice if active, settlement if resolved)

Proof of Boundedness:

• Since w'_i ≥ 0 and Σ w'_i = 1
• And p_i ∈ [0, 1] for all markets
• Therefore: raw_nav ∈ [0, 1]

The raw_nav is explicitly clamped to [0, 1] as a defensive measure.

Step 4: Index Level Calculation

The index level provides a rebased representation starting at a base value of 100.

index_level = base_index_level × (raw_nav / inception_raw_nav)

Where:

• base_index_level = 100.00000000
• inception_raw_nav = raw_nav at first successful computation
• raw_nav = current raw_nav value

Worked Examples

Example 1: Equal-Weighted Index with 7 Markets

Index Composition (7 markets, equal weight):

Step 1: Normalize Weights

W = 7 × 0.1429 = 1.0003
w'_i = 0.14285714 for each market

Step 2: Compute Raw NAV

raw_nav = (0.14285714 × 0.9955) +
          (0.14285714 × 0.9885) +
          (0.14285714 × 0.0065) +
          (0.14285714 × 0.095) +
          (0.14285714 × 0.0175) +
          (0.14285714 × 0.335) +
          (0.14285714 × 0.0415)

        = 0.14221428 + 0.14121428 + 0.00092857 + 0.01357143 +
          0.00250000 + 0.04785714 + 0.00592857

        = 0.35421428

Step 3: Compute Index Level

inception_raw_nav = 0.35721428
index_level = 100 × (0.35421428 / 0.35721428)
            = 100 × 0.9916016795
            = 99.16016795

This indicates the index has declined approximately 0.84% from inception.

Example 2: Index with Resolved Market

Index Composition (2 markets):

Computation:

W = 0.50 + 0.50 = 1.0
w'_1 = 0.50, w'_2 = 0.50

raw_nav = (0.50 × 0.45) + (0.50 × 0.00)
        = 0.225 + 0.000
        = 0.225

Resolution Handling

Market Resolution States

Index Resolution States

Terminal NAV

When an index becomes fully resolved:

1. Final computation is persisted
2. Index status is set to RESOLVED
3. Future computations return the terminal NAV
4. The terminal value is definitive (not stale)

Staleness and Data Quality

Staleness Conditions

A computation is marked stale: true when:

1. Any underlying market price fetch failed, AND
2. A fallback (last-known) price was used, AND
3. The index is not fully resolved

Single-Sided Order Book

If a market has only bids or only asks:

• Midprice cannot be computed
• Market is marked as stale
• Falls back to last known good price

Known Limitations

Theoretical vs. Executable Pricing

The midprice represents a theoretical value, not an executable price. It does not account for:

• Trading fees (typically 0.5-2% on Polymarket)
• Slippage for market-sized orders
• Market impact of hypothetical replication trades

Implication: The NAV represents a theoretical value, not an executable portfolio price.

Liquidity Variance

Markets within an index may have vastly different liquidity:

Low-liquidity markets may exhibit:

• Wider bid-ask spreads
• Higher relative volatility
• Less reliable price signals

Static Weighting

Current indices use fixed weights assigned at composition time:

• Weights do not adjust for liquidity differences
• No automatic rebalancing based on market conditions
• May over-weight low-confidence or illiquid markets

No Correlation Adjustment

Markets within an index may be correlated. The methodology:

• Treats each market as independent
• Does not discount for information overlap
• May overstate diversification benefits

Future Methodology Versions

All methodology changes are tracked via methodology_version string recorded with each computation.

Proposed Enhancements

Liquidity-Weighted Midprice (v2)

Weight midprice contribution by order book depth:

effective_price_i = midprice_i × min(1, liquidity_i / target_liquidity)

Benefit: Reduces influence of thinly-traded markets.

Time-Weighted Average Price (TWAP)

Compute prices as time-weighted averages over a rolling window:

twap = (1/T) × ∫[t-T, t] midprice(τ) dτ

Benefit: Smooths short-term price volatility.

Volume-Weighted Average Price (VWAP)

Use recent trade data:

vwap = Σ(price_j × volume_j) / Σ(volume_j)

Benefit: Reflects actual executed prices rather than quoted prices.

Formula Reference

Midprice

midprice = (best_bid + best_ask) / 2

Weight Normalization

w'_i = w_i / Σw_j

Raw NAV

raw_nav = Σ(w'_i × p_i)    where p_i ∈ [0,1]

Index Level

index_level = base_index_level × (raw_nav / inception_raw_nav)

Questions?

Contact us for more information about our methodology.