APY Calculation Method

The initial sum of capital deposited or invested, upon which interest is earned. This is the baseline for all yield calculations. In DeFi, this is often referred to as the staked amount or deposited liquidity.

• Example: Depositing 10 ETH into a liquidity pool.
• Impact on APY: The principal directly scales the absolute returns; a higher principal earns more interest, though the APY percentage itself is independent of the principal size.

The base percentage rate at which the principal earns interest over a specific period, before compounding is applied. This is often the rate quoted for a single compounding period (e.g., daily, weekly).

• Also known as: Periodic rate, base rate.
• Relation to APY: APY is derived from this rate. For example, a 0.1% daily nominal rate compounds to a much higher effective annual rate (APY).

The number of times per year that earned interest is calculated and added to the principal balance, allowing subsequent interest to be earned on previously accrued interest. This is the core mechanism that makes APY differ from a simple APR.

• Common Frequencies: Daily, weekly, monthly, or continuous.
• Formula Impact: APY = (1 + (Nominal Rate / n))^n - 1, where n is the number of compounding periods per year. Higher frequency increases APY.

The duration over which the APY is annualized and projected. APY standardizes returns to a one-year timeframe for comparability, regardless of the actual investment horizon or the length of the compounding period.

• Critical Assumption: APY assumes the nominal rate and compounding frequency remain constant for a full year.
• Real-World Note: In volatile DeFi protocols, rates rarely stay fixed for a year, making APY a forward-looking projection, not a guarantee.

Additional tokens or value distributed on top of base protocol fees, often from liquidity mining or governance token emissions. These are a major component of "yield" in DeFi and must be accurately valued and annualized.

• Calculation Challenge: Requires pricing the reward token and estimating its future emission schedule.
• APY Impact: Can dramatically inflate stated APY. It's crucial to distinguish between sustainable fee-based yield and temporary incentive-based yield.

Costs that reduce the net return. Transaction fees (gas), protocol fees (performance/withdrawal fees), and impermanent loss (for liquidity providers) are critical subtractions often not reflected in a headline APY figure.

• Net APY: The true yield is Headline APY minus all applicable costs.
• Analyst's Task: A robust APY model must factor in these real-world frictions to estimate the investor's actual net return.

The base case where interest is calculated only on the principal amount, without reinvesting earnings. Common in fixed-term deposits or simple lending protocols.

• Formula: APY = (Interest Earned / Principal) * 100
• Example: A 10% annual simple interest rate on $1,000 yields $100 after one year, for an APY of 10%.
• Key Trait: APY equals the stated nominal interest rate when no compounding occurs.

Interest is calculated and added to the principal at regular intervals (e.g., per block, hourly, daily), allowing subsequent interest to be earned on the accumulated total.

• Formula: APY = (1 + (r/n))^n - 1, where r is the nominal rate and n is compounding periods per year.
• Real-World: A 10% nominal rate compounded daily (n=365) results in an APY of ~10.52%.
• Protocol Example: Many lending markets like Aave and Compound use per-block compounding, making n extremely large.

The theoretical limit of compounding, where interest is reinvested an infinite number of times instantaneously. It provides the maximum possible APY for a given nominal rate.

• Formula: APY = e^r - 1, where e is Euler's number (~2.71828) and r is the nominal rate.
• Application: A 10% nominal rate under continuous compounding yields an APY of ~10.52%, very close to daily compounding for practical purposes.
• Use Case: Often used in financial mathematics as a benchmark for yield optimization.

APY is driven by the protocol minting and distributing its native token as a reward, often on top of base yield. This APY is highly variable and depends on token price and emission schedule.

• Calculation: APY = (Value of Tokens Distributed / Total Value Locked) * 100
• Volatility: This APY can change dramatically with token price fluctuations and emission rate adjustments.
• Critical Note: High APYs from emissions are often unsustainable long-term and represent inflationary yield.

Yield generated from a protocol's real revenue, such as trading fees, loan origination fees, or gas reimbursements. This is often considered 'sustainable' or 'real yield'.

• Source: Fees collected from protocol users are distributed to stakers or liquidity providers.
• Calculation: APY = (Total Fees Distributed to Stakers / Total Staked) * 100
• Example: A DEX distributing $1M in fees to $10M of staked liquidity tokens offers a 10% fee-based APY.

APR (Annual Percentage Rate) is the simple interest rate without compounding. APY (Annual Percentage Yield) includes the effect of compounding.

• Rule: APY >= APR. They are equal only with no compounding.
• DeFi Context: Protocols often advertise APY to show the boosted effect of auto-compounding. Always verify which metric is being displayed.
• Impact: For a 10% APR compounded daily, the APY is 10.52%. The difference grows significantly with higher rates and more frequent compounding.

Compounding is the process where earned interest or rewards are reinvested to generate additional earnings in subsequent periods. It is the critical factor that differentiates APY from APR.

• Mechanism: Rewards are added to the principal, and the next period's yield is calculated on the new, larger balance.
• Frequency: Compounding can occur continuously, daily, weekly, or at other intervals. More frequent compounding results in a higher APY for a given APR.
• Formula Impact: The APY formula APY = (1 + (APR / n))^n - 1 directly incorporates the compounding frequency n.

Rewards Emission refers to the scheduled release of new tokens or fees distributed as incentives to participants in a DeFi protocol, such as liquidity providers or stakers.

• APY Driver: The rate and schedule of emissions are primary determinants of a protocol's advertised APY.
• Inflationary vs. Fee-Based: Emissions can be inflationary (new tokens minted) or come from protocol-generated fees (e.g., swap fees).
• Dynamic APY: APY fluctuates based on emission rates, the number of participants, and the total capital (TVL) in the system.

Impermanent Loss (IL) is the potential loss in dollar value experienced by liquidity providers in an Automated Market Maker (AMM) pool compared to simply holding the assets, caused by price volatility of the pooled assets.

• APY Consideration: Advertised APY for liquidity provision must be evaluated against the risk of IL. High APY may be necessary to offset potential losses.
• Mechanism: IL occurs when the price ratio of the two assets in the pool changes after deposit. The loss is 'impermanent' if prices return to their original ratio.

Real Yield refers to protocol-generated revenue (e.g., trading fees, loan interest) that is distributed to token holders or stakers, as opposed to yield sourced from inflationary token emissions.

• Sustainability: Considered a more sustainable and desirable form of APY, as it is backed by actual protocol usage and economic activity.
• Calculation: A protocol's APY can be decomposed into its inflationary yield component and its real yield component. Analysts often scrutinize the real yield percentage.