Let us imagine you have $1000 in a savings account with the equally imaginary Monolith Bank, now—while we're being all imaginative—let us pretend this high street bank are actually paying interest on your fiat savings, we shall say at 11% APR.
So what does that actually mean?
APR vs APY
Firstly we need to understand that APR stands for Annual Percentage Rate, and the quoted percentage is the amount by which your savings would grow if you kept them in the bank for one year without any compounding between now and then.
The problem is that different products offer different compounding intervals, and the effects this has on our returns are dramatic. Let's make a comparison, between 11% APR without intra-term compounding and daily compounding.
$1000 at 11% APR with interest simply paid at the end of the year would return $110.
$1000 at 11% APR compounded daily would return $116.26.
As you can see the return here is amplified through compounding, so we must consider compounding interval when comparing the return on various products—APR alone will not tell us the whole story.
In the examples above the APR in both cases is 11%, but the APYs are 11% and 11.626% respectively. APY stands for Average Percentage Yield and tells us what our total yield gained will be over the year when taking compounding in to account.
DeFi challenges
In the DeFi space we often have to compare pools quoting returns in APR vs ones quoting returns in APY—comparing the two is not straight forward. The issue with crypto is that compounding is not generally something that simply happens by itself (except in auto-compounding pools, more on that coming up), generally we must chose when to compound and pay the appropriate fees to do so.
The implication of this is that there are optimum times for compounding to maximise APY, compound too often and your fees will eat up your returns—a loss is even possible—not often enough and you are letting yield sit on the DEX doing nothing.
Often you will find you are offered an auto-compounding staking pool, which quotes returns in APY, and a manual pool which quotes fees in APR - to know which one is best for you there are several variables to consider, we need to consider both the underlying maths and your behaviour.
Auto-compounding pools are straight forward, you stake your tokens and leave them alone, the pools are compounded as a whole periodically and at the end of the term you will receive the quoted APY—providing the APY doesn't change, which it probably will.
With a manually compounding pool gas fees add a layer of complexity, the larger the invested principle the lesser the implication of fees, I have created a spreadsheet for calculating optimum compounding interval, link in resources.
Some examples-
$1000 of CAKE at 56% APR with a gas fee of $0.40, compounded daily would return $554.41—an APY of 55.44%
$1000 of CAKE at 56% APR with a gas fee of $0.40, compounded every 17 days would return $726.84—an APY of 72.68%
Calculating the optimum compounding interval for an APR pool, based on your invested principle, will allow you to decide which pool is right for you. We also need to consider behaviour—if the optimum period is impractically frequent, or you think you'll forget to compound, then a slightly lower APY in an auto-staking pool may still be your best option.
Added complexities
Of course, this is crypto, so nothing is simple—unlike what we already covered—the problem is we can't always just rely on these calculations to remain accurate because crypto is full of multiple floating points.
Your staked token changes in value
Your pool rewards are not paid in the staked token or in multiple tokens
Gas fee changes
To compound you have to buy more LP tokens that have associated fees
Your native fiat currency has changed in value
The APR/APY offered has changed
These added complexities can be taken into account to some degree, but are largely out of our control.
DISCLAIMER - I offer my calculator as a template tool only. I am neither an accountant nor a financial advisor, please do your own research.
https://docs.google.com/spreadsheets/d/1YmvOORhRSXW8OHNgkPvVwKB4fLoPjXyC/edit