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LVR and the price of stale inventory

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A pool can trade at prices that lag new market information. Loss-versus-rebalancing measures the difference from a benchmark that holds the same changing exposure but rebalances at reference prices.

Do not confuse three quantities: market exposure from inventory, difference versus holding initial tokens, and adverse execution relative to rebalancing. The recent research checkpoint motivates this separation, but the example here is a discrete teaching comparison rather than the paper’s continuous-time result.

Define benchmark and pool values at identical timestamps and include the same external cash flows. Fees can offset part of the difference but are not automatically sufficient.

Apply it in a strategy

• Design an LP research ledger that isolates fee income from exposure and execution disadvantage.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: An arbitrary buy-and-hold comparison is not LVR; a reproducible same-exposure benchmark is necessary.

Research deliverable

Build and explain a lvr and the price of stale inventory worksheet. Design an LP research ledger that isolates fee income from exposure and execution disadvantage.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def rebalancing_comparison(reference,pool,fees,costs):
    if min(reference,pool,fees,costs)<0: raise ValueError("Nonnegative values required")
    difference=reference-pool
    return difference,fees-difference-costs

print(rebalancing_comparison(10030,10000,40,8))