RESEARCH NOTE R5 · Research notes · complete derivations

Choose the pair, not just the yield.

Measure relative-price volatility and understand why desirable inventory can change a market maker’s economics.

15 min · Explain, experiment, decide

Hayden Adams argues that correlated pairs and investors who want the underlying inventory can make AMMs more competitive. That is an economic thesis, not a claim that correlation guarantees profit. The practical question is which risk your pair removes, and which it keeps.

Jump to the interactive experiment ↓

Price the ratio, then price the portfolio

For assets A and B, let S_A and S_B be their USDC prices and P = S_A/S_B be B per A. An A/B range operates on P. Its USDC value is S_B[x(P)P+y(P)]. A quiet ratio can coexist with a large USDC drawdown if both assets fall. ETH/cbBTC therefore has relative ETH/BTC exposure plus the USD risk of both assets and the separate token/custody risks of cbBTC. It is not a stablecoin position.

Correlation needs matching volatility scales

For synchronized log returns, σ²_ratio = σ²_A + σ²_B − 2ρσ_Aσ_B. If both annualized volatilities are 60% and correlation is 0.90, ratio volatility is about 26.83%; at zero correlation it is about 84.85%. Even at correlation one, unequal volatilities leave |σ_A−σ_B| ratio volatility. These are hypothetical inputs, not current estimates for any listed market. Measurement horizon, sampling, lead-lag and changing regimes matter.

Risk of the ratio

{σ_{A/B}}^{2} = {σ_{A}}^{2} + {σ_{B}}^{2} - 2 ρ σ_{A} σ_{B}

σA, σB: volatility of synchronized log returns on the same horizon; ρ: their correlation.

AssumptionsDescribes relative-price volatility, not the USD drawdown or a stable future correlation.

Desired inventory is an advantage with a mandate

An investor who already wants both assets may accept exposure a neutral dealer would pay to hedge. That can lower the return required for providing liquidity. It does not imply free capital or zero downside. Specify acceptable final weights, concentration, liquidity needs and a loss budget. A portfolio tilt can make economic sense even if it trails static holding over a particular interval; report both the mandate outcome and the opportunity cost.

Related assets are not necessarily correlated

Economic themes do not establish a statistical hedge. A stock and its sector ETF can decouple on earnings; tokenized assets can face different transfer or redemption rules and market hours. Stablecoin pairs can depeg. Estimate normal and stressed dependence separately, including periods when a reference venue is closed. A tight range based only on a calm historical window can concentrate precisely the risk that appears during a break.

Bridge markets and why research still matters

Correlated liquidity clusters still need routes into settlement assets. Bridge markets such as ETH/USDC carry directional and execution risks that cannot be explained by correlation alone. A routing path also adds fees, gas and capacity constraints at each hop. In AMM Markets, use the pair and mandate to frame policy research; do not assume that every related-asset strategy, hedge or lending integration has already been implemented.

TRY IT YOURSELF

Make the mechanics visible.

Change the correlation and the two annual volatilities. Then stress both assets down by 30%: observe that their ratio can stay unchanged while the portfolio loses 30% in the common currency.

Risk of the ratio

{σ_{A/B}}^{2} = {σ_{A}}^{2} + {σ_{B}}^{2} - 2 ρ σ_{A} σ_{B}

σA, σB: volatility of synchronized log returns on the same horizon; ρ: their correlation.

AssumptionsDescribes relative-price volatility, not the USD drawdown or a stable future correlation.

Annual volatility A60%Annual volatility B60%Return correlation0.90

Implied ratio volatility26.83%annualized · hypothetical inputs

Both assets down 30%Ratio: unchanged

Common-currency portfolio value−30%same quantities, no fees or flows

Dependence sensitivity with the selected volatilities
ρ	Ratio volatility
-0.50	103.92%
0.00	84.85%
0.50	60.00%
0.90	26.83%
1.00	0.00%

Annual volatilities refer to synchronized log returns. This identity is not a forecast, an option implied volatility or a live ETH/cbBTC estimate. Correlation may fail in stress; low ratio risk does not remove joint USDC drawdown or token risk.

CHECK YOUR UNDERSTANDING

A/B has low ratio volatility. What follows for its USDC value?It cannot fall materially.Nothing guarantees stability: both assets may decline together.It must earn more fees.

What does this mean for you?

Would you still want both assets after their relationship breaks? Which stress period would invalidate your narrow-range assumption?

CONNECT IT TO AMM MARKETS

From understanding to a real decision.

For an ETH/cbBTC market, inspect the ETH/cbBTC price and units first, then its USDC valuation and policy. Discuss correlated-pair mandates with the team using specific inventory limits, not a generic “low risk” label.

Explore registered market pairs ↗Opens a live service. Exploring is separate from submitting a transaction.

References and scope

Course edition: October 2026. Distinguish protocol principles from product instructions; actual market parameters come from the live interface and on-chain state.

Answer the knowledge check correctly to record progress.