> ## Documentation Index
> Fetch the complete documentation index at: https://docs.beliefsystems.xyz/llms.txt
> Use this file to discover all available pages before exploring further.
# NAV Per Share
> How NAV per share is computed for Alpha Program participants, and how it differs from the published index level.
These pages document functionality available to approved participants in our **private,
invitation-only alpha program**. The program is not open to the public, and nothing in this
documentation is an offer to sell or a solicitation of an offer to buy any security.
The published **Index Level** is the benchmark: theoretical, fee-free, and computed for everyone. **NAV per Share** exists only inside the Alpha Program – it is the actual per-unit value of a participant's shares, accounting for real custody holdings, cash, and fees. This page explains how each is computed, why they differ, and what drives each one.
## Two Metrics, Two Purposes
| Metric | Purpose | What It Reflects | Used For |
| ----------------- | --------------------- | ------------------------------------------------------- | ------------------------------------- |
| **Index Level** | Performance benchmark | Theoretical index movement from inception | Tracking how the basket has performed |
| **NAV per Share** | Share valuation | Actual value of one share, accounting for real holdings | Minting and redeeming shares |
Think of the Index Level like a stock market index (e.g., the S\&P 500 level) – it tracks performance. NAV per Share is like the price of an ETF share that tracks that index – it reflects what you actually own, including cash holdings and fees. Just as an ETF's price can slightly differ from its benchmark index due to expenses and cash drag, NAV per Share can differ from the theoretical Index Level.
## Index Level (Theoretical Benchmark)
The Index Level is derived directly from the Raw NAV using a rebasing formula:
```
index_level = 100 x (raw_nav / inception_raw_nav)
```
**In plain English:** The Index Level starts at 100 when a series launches and moves proportionally with the weighted-average price of the underlying markets. If the basket's aggregate probability increases, the Index Level rises; if it decreases, the Index Level falls.
The Index Level is purely theoretical – it does not account for cash holdings, trading costs, or fees. It answers the question: "How has the underlying basket performed?"
A series launched with an inception Raw NAV of 0.62000000.
At a later NAV window, the Raw NAV is 0.58900000:
```
index_level = 100 x (0.58900 / 0.62000)
= 100 x 0.95000
= 95.00
```
The Index Level of 95.00 indicates the basket has declined 5% from inception.
If the Raw NAV later recovers to 0.68200000:
```
index_level = 100 x (0.68200 / 0.62000)
= 100 x 1.10000
= 110.00
```
The Index Level of 110.00 indicates a 10% gain from inception.
## NAV Per Share (What Your Shares Are Worth)
NAV per Share is the actual per-unit value of shares in a series. It accounts for all real assets held in custody:
```
NAV per Share = (Position Value + Custody Cash - Accrued Fees) / Shares Outstanding
```
This is the price at which shares are minted and redeemed. It answers the question: "What is one share worth right now?"
| Component | Description | How Determined |
| ---------------------- | -------------------------------------------------------------------- | ------------------------------------------------------- |
| **Position Value** | Current value of all prediction market positions held in custody | On-chain token balances multiplied by current midprices |
| **Custody Cash** | pUSD held as per-series cash (liquidity buffer, settlement proceeds) | Ledger balance |
| **Accrued Fees** | Management fees that have accumulated since last collection | Computed at each NAV window |
| **Shares Outstanding** | Total number of shares currently issued for this series | Ledger balance (increases on mint, decreases on redeem) |
The Index Level is a pure mathematical construct – the weighted average of market prices. NAV per Share reflects what the series actually holds:
* **Uninvested cash:** If not all cash has been deployed into positions, the series holds pUSD that isn't captured by the index formula. This cash provides a buffer but also means the share value may differ from the index.
* **Accrued fees:** Management fees reduce the actual value of holdings over time, creating drag relative to the gross index.
* **On-chain reality:** Position values are based on actual token balances held in custody, not theoretical allocations. The actual number of tokens purchased depends on execution prices, which may differ from theoretical midprices.
* **Execution differences:** When cash is invested, equal dollar amounts at different prices produce different token quantities. Over time, actual holdings may not perfectly match theoretical index weights.
When all cash is fully deployed and no fees have accrued, NAV per Share closely tracks the Raw NAV.
## Worked Example
Suppose a series has:
| Component | Value |
| --------------------------------------- | ------------- |
| Position Value (from on-chain holdings) | \$85,000.00 |
| Custody Cash (uninvested pUSD) | \$12,000.00 |
| Accrued Fees | \$500.00 |
| Shares Outstanding | 10,000.000000 |
```
NAV per Share = ($85,000 + $12,000 - $500) / 10,000
= $96,500 / 10,000
= $9.65
```
Each share is worth **\$9.65**.
Meanwhile, the Index Level might show 97.2, reflecting a 2.8% decline from inception based on theoretical pricing. The difference arises from the cash buffer (which adds value beyond what the index formula captures) and accrued fees (which reduce value).
If a new investor mints \$5,000 at NAV per Share of \$9.65:
```
New shares issued = $5,000 / $9.65 = 518.134715 shares
```
After minting, the series has:
```
Position Value: $85,000 (unchanged until positions are acquired)
Custody Cash: $17,000 ($12,000 + $5,000 new deposit)
Accrued Fees: $500 (unchanged)
Shares Outstanding: 10,518.13 (10,000 + 518.13)
NAV per Share = ($85,000 + $17,000 - $500) / 10,518.13
= $101,500 / 10,518.13
= $9.65
```
NAV per Share is unchanged. New shares are issued at exactly the current NAV, so neither new nor existing investors are diluted. This is a fundamental property of open-ended fund mechanics.
## Position Value: On-Chain vs. Theoretical
Position values are based on **actual on-chain token balances** held in the series' custody wallet, not on theoretical index weights.
```
position_value = sum of (on_chain_balance_i x midprice_i) for each market
```
If the custody wallet holds:
| Market | On-Chain Token Balance | Midprice | Position Value |
| --------- | ---------------------- | -------- | -------------- |
| Market A | 1,000 tokens | \$0.65 | \$650.00 |
| Market B | 2,500 tokens | \$0.40 | \$1,000.00 |
| Market C | 800 tokens | \$0.82 | \$656.00 |
| **Total** | | | **\$2,306.00** |
These token balances are queried directly from the blockchain and can be independently verified by any investor through the Polygon block explorer.
When cash is invested into positions, the actual number of tokens purchased depends on market prices at the time of execution. Equal dollar amounts invested at different prices produce different token quantities – cheap tokens are bought in larger quantities, expensive tokens in smaller quantities.
Over time, this means actual custody holdings may not match theoretical index weights precisely. Using on-chain balances ensures the NAV reflects what is actually held, not what was theoretically intended.
If on-chain balance data is temporarily unavailable (e.g., network issues), the system falls back to the theoretical index formula as an approximation. Each computation records which valuation method was used, so investors can verify the data source.
## When They Diverge
NAV per Share may differ from the theoretical index value in several situations:
| Scenario | Effect on NAV per Share | Direction |
| ------------------------- | ------------------------------------------------------------ | ------------------------------------------ |
| **Uninvested cash** | Cash adds value not captured by the index formula | NAV per Share higher than implied by index |
| **Accrued fees** | Fees reduce the actual value of holdings | NAV per Share lower than implied by index |
| **Execution differences** | Actual purchase prices may differ from theoretical midprices | Either direction |
| **Partial fills** | Position sizes may not exactly match theoretical weights | Either direction |
Over time, with full deployment and minimal fees, the two metrics should track closely.
## What Moves NAV Per Share
Understanding what drives changes in your share value:
The primary driver. As the underlying prediction markets move – reflecting changing expectations about future events – the value of the positions held in custody changes proportionally. A series tracking monetary policy expectations will see its NAV per Share move as rate cut probabilities shift.
When a market resolves, its tokens become worth exactly \$1.00 (if the tracked outcome won) or \$0.00 (if it lost). This locks in that market's contribution to NAV. Favorable resolutions increase NAV per Share; unfavorable resolutions decrease it.
Management fees accrue continuously at each NAV window, reducing the numerator of the NAV per Share formula. Fee rates are configured per series and subject to change. See [Fees](/investing/fees) for details.
When new deposits are invested into prediction market positions, cash moves from pUSD into outcome tokens. The total value should remain approximately the same (minus any execution costs), but the composition of the numerator changes from cash-heavy to position-heavy.
Minting and redeeming shares does **not** dilute or boost NAV per Share. New shares are created at exactly the current NAV per Share, so existing investors' share value is unaffected. Similarly, when shares are redeemed, the proportional reduction in both assets and shares preserves NAV per Share. This is a fundamental property of the open-ended fund structure.
## Precision and Rounding
NAV per Share is calculated to 8 decimal places. When rounding is required, the system uses different approaches for different metrics:
| Calculation | Rounding Direction | Rationale |
| --------------------- | ----------------------------- | -------------------------------------------------------------------- |
| Raw NAV / Index Level | Round half up (symmetric) | Informational metric; symmetric rounding is fair |
| NAV per Share | Round down (in favor of fund) | Pricing metric; conservative rounding protects existing shareholders |
The difference is intentional. Raw NAV is an informational metric used for tracking performance – symmetric rounding is appropriate because small deviations don't affect anyone's economic outcome.
NAV per Share is used for actual share pricing. Rounding down ensures that small rounding differences do not systematically benefit new investors at the expense of existing shareholders. This is standard practice in fund accounting (sometimes called "defensive rounding" or rounding "in favor of the fund").
The practical impact is negligible – the difference is typically less than \$0.00000001 per share – but the principle matters for accounting integrity.
The complete methodology behind index computation.
How on-chain balances feed into position valuation.
How NAV per Share determines your share allocation.
How fees affect NAV per Share over time.