> For the complete documentation index, see [llms.txt](https://the-fedz.gitbook.io/the-fedz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://the-fedz.gitbook.io/the-fedz/fstocks-fractional-reserve-real-world-asset/peg-latency-window-plw-how-fstocks-discover-price.md).

# Peg Latency Window (PLW): How Fstocks Discover Price

Synthetic assets like **Fstocks** (e.g., FTSLA) are designed to track the value of a corresponding tokenized asset such as **TSLAx**.\
However, they do not need to match that price **instantly**.\
The Fedz architecture intentionally allows short-term deviations while ensuring long-term convergence.

This controlled delay in price convergence is called the:

> **Peg Latency Window (PLW)**

The Peg Latency Window defines the short period during which the market price of an Fstock may differ from the fundamental anchor price reflected in the PLP (TSLAx ↔ FTSLA), before returning to parity.

***

### **Why Price Deviations Are Allowed**

Traditional AMMs expose LPs to **Loss-Versus-Rebalancing (LVR)** because arbitrageurs can instantly enforce the true price.\
Every small price change is exploited with riskless arbitrage, and the LP is systematically “picked off.”

In Fstocks, this mechanism does *not* exist because:

* The **PLP is gated** and turn-based
* Redeeming FTESLA into TSLAx is **not instantaneous**
* Arbitrage flows have **bandwidth limits**
* Fstock minting follows the **sequential access mechanism**
* There is **no open, permissionless loop** between the AMM and the reference asset

As a result, traders **cannot** instantly arbitrage FTESLA to match TSLAx.\
This creates room for short-term price drift in the public FUSD–Fstock pool — and that drift is *beneficial*, not harmful.

***

### **Formal Definition of Peg Latency**

Let:

* **S(t)** = the fundamental anchor price of the stock as expressed via TSLAx in the PLP
* **F(t)** = the market price of FTSLA in the public FUSD–FTSLA pool

Define the deviation:

Δ(t)=F(t)−S(t)\Delta(t) = F(t) - S(t)Δ(t)=F(t)−S(t)

and define a small tolerance ε (e.g., 1–2%).

Following a shock at time t0t\_0t0​, the **Peg Convergence Time** is:

τconv=inf⁡{τ≥0:∣Δ(t0+τ)∣≤ε}\tau\_{\text{conv}} = \inf \left\\{ \tau \ge 0 : |\Delta(t\_0 + \tau)| \le \varepsilon \right\\}τconv​=inf{τ≥0:∣Δ(t0​+τ)∣≤ε}

The **Peg Latency Window (PLW)** is the typical or expected value of\
τconv\tau\_{\text{conv}}τconv​ for meaningful shocks (where |Δ| exceeds ε).

In plain language:

> **The Peg Latency Window is how long it usually takes for Fstocks to realign with their underlying asset after a price shock.**

***

### **Why PLW Matters for LPs**

Inside the Peg Latency Window:

* FTESLA may trade slightly **above** or **below** TSLAx
* External arbitrageurs cannot instantly correct the price
* Order flow consists mostly of **uninformed traders**
* LPs often buy Fstocks at a discount or sell them at a premium
* Arbitrageurs must take **directional risk**, not riskless profit

This breaks the assumptions behind the classical **LVR model**, which relies on:

1. Instant access to the reference asset
2. Ability to continuously rebalance to neutral exposure
3. Immediate arbitrage between AMM price and true price

Since these conditions do not hold, arbitrageurs cannot impose the “true price” on the public pool, and LPs are not systematically exploited.

Instead of suffering guaranteed LVR, LPs operate in a regime where:

* **Short-term deviations work in their favor**
* **Arbitrage becomes risky** rather than free
* **LP losses are no longer mechanically equal to arbitrage profits**
* The expected LVR cost collapses compared to traditional AMMs

***

### **Long-Term Price Discovery Still Holds**

Although the public pool price can drift inside the Peg Latency Window, The Fedz ensures long-term accuracy:

* The PLP maintains the canonical peg between TSLAx and FTSLA
* Sequential access and turn mechanics gradually repair deviations
* Arbitrageurs eventually close the gap once access becomes available
* FUSD printing and supply adjustments deepen liquidity over time
* Combined mechanisms guarantee **Mean Reversion to the Anchor Price**

Thus, the Fstock price path looks like this:

* **Short term:** noisy, temporarily misaligned
* **Medium/long term:** convergent, anchored, fundamentally correct

This allows Fstocks to replicate the economic exposure of a real stock while avoiding the structural losses that plague traditional AMM LPs.

***

### **Summary**

* Fstocks track real tokenized stocks over the **long term**.
* Short-term deviations are **intentional** and **necessary**.
* The interval before convergence is the **Peg Latency Window (PLW)**.
* During this window, LPs often *gain* from noise-driven order flow.
* Arbitrageurs cannot execute riskless loops, breaking the usual LVR mechanics.
* Long-term price discovery is preserved via the PLP and turn-based rebalancing.

The Peg Latency Window is the core mechanism that allows Fstocks to remain stable, track real-world prices, and avoid the loss-versus-rebalancing trap that makes traditional AMM-based synthetic assets unprofitable to support.