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Decomposing APY: base, reward, assumption

One percentage, three statements — and an assumption that rarely comes with it.

This lesson has had no expert review. It was written for this platform and against the evidence it cites; nobody has gone through it independently.

Learning objectives

  • You can decompose a quoted APY into its components and name each of them.
  • You can name the assumption every APY figure silently makes.

Check your prior knowledge

Answer these for yourself before reading on. Wherever you hesitate is where this lesson pays off.

Core concept

Assumption

The silent assumption

Every APY figure projects the just-observed rate over a year — as if it stayed constant. For a variable rate in a lending market that is a strong assumption: the rate moves with every change in utilization. The APY is therefore a snapshot in annual dress, not a forecast.

Fact

Base and reward are different promises

The base component comes from use of the market: trading fees or borrowing interest. The reward component comes from a distribution of additional tokens. Both appear in the same percentage but are subject to different conditions: one falls with demand, the other ends with the emission schedule.

Risk

A high APY is a question, not an answer

An unusually high APY indicates that someone is paying unusually much. The useful reaction is not to read it as an opportunity or as a warning, but to ask who is paying and why. Possible answers: strong borrowing demand, an incentive program, a thin market with little capital, or a risk others have already priced in.

Definitions

APY in the glossary
Return projected to one year including compounding.
Base APY in the glossary
The part of the return from use of the market itself.
Reward APY in the glossary
The part of the return from additionally distributed tokens.

Model

  1. Note the total APY

  2. Split into base and reward

  3. Compute the emission share

  4. Check the rate's volatility (sigma)

  5. Formulate the statement: what would remain without emissions, and how reliable is the base?

One percentage, four checks

Formulas

Compounding

APY = (1 + r/n)^n − 1
r
nominal annual rate
n
number of compounding periods per year

Limit: The formula assumes r holds for the whole year and that reinvestment actually happens. Both are questionable with variable rates and where transaction costs arise.

Emission share

Emission share = Reward APY / APY
Reward APY
return component from distributed tokens
APY
quoted total return

Limit: The share is valued at the reward token's price today. Where that token's liquidity is thin, the valuation is itself the open question.

Worked example

What would remain without the emission?

Quoted APY
11.4 %
Base APY
1.9 %
Reward APY
9.5 %

Emission share = 9.5 / 11.4 ≈ 0.83

Around 83 % of the quoted return comes from emissions.

Reading: If the incentive program ends, what remains on paper is a market at 1.9 %. Whether the deposits stay is the real question — and the reason this decomposition comes before a position decision.

Interactive model

The worked example, with movable figures. Estimate first what happens — then check.

Compounding and emission share

How often interest is credited changes the APY — and how much of it is emission changes how long it lasts.

Estimate first, then check

Before you move the slider: how much does a 10 % APR gain from daily instead of yearly crediting — closer to 0.5 or to 5 percentage points? And what share of the example's 11.4 % remains without emissions?

The starting values are the worked example's own figures — change one input at a time.

1× per year365× per year

APY: 10.47%. Emission share: 83%.

What the model does not show: The model assumes a constant rate for the whole year. Variable rates, the cost of reinvesting and the reward token's price are missing — exactly the three things that make a displayed APY diverge in practice.

Retrieval

A pool quotes 11.4 % APY, of which 9.5 % is reward. What is the most defensible statement?
Which assumption does every APY figure make silently?

Exercise on real data

Find two markets with a similar total APY but distinctly different base components. Compute the emission share for both and also look at sigma.

Compare two markets with the same APY →

This platform's flag points take the ratio of reward to total return into account. Read how — and where the methodology names its own limits.

Read how this platform assesses reward dependence →

Application

A pool shows 11.4 % APY, of which 9.5 % reward, with a sigma well above the median of comparable pools. Which three sentences do you write into an analysis?

Related case studies

Institutional reading

Bank
Which part of this return could enter a revenue plan?
Asset management
May the vehicle hold the reward token at all — and if not, who sells it, and when?
Advisory
Which of the two figures has the client seen: 11.4 % or 1.9 %?

Metrics in this lesson

Key takeaways

Evidence