Printer Financial — DeFi 101.1: What is APR and APY?
Welcome to the first article in our DeFi 101 series! We hope this series will provide answers to common DeFi questions, and arm you with information to perform better research and avoid getting rekt. We begin with a discussion of APR and APY, including what they are, and how they’re calculated.
Annual percentage rate (APR) is the yearly rate of return one is paid on a deposit. For example, if you deposit $100 into a savings account that pays 10% APR, at the end of year you will have $110, which includes your initial deposit ($100) plus the return from that year (10% of $100 = $10). This is different from annual percentage yield (APY), which takes into account the compounding effects of the return. For example, if you deposit the same $100 into a savings account that pays 10% APR, but instead of only paying out the return at the end of the year they compound twice per year (every 6 months), you will end up with a higher value at the end of the year. Calculating this can be a bit of chore, but it’s fairly straightforward: First, calculate the 6 month return, which is the APR divided by two because we’re compounding at half-year intervals (10%/2 = 5%). Then calculate your return after 6 months ($100 + (5% of $100) = $105). Now, do that one more time for the next 6 months ($105 + (5% of $105) = $110.25), and we end up with $0.25 more as a result of the additional compound.
In DeFi, it’s common to express returns in “daily APR,” which is technically incorrect because “daily annual percentage rate” makes absolutely no sense (how can something be “daily” and “annual” at the same time?). A better way to describe the daily return is “daily rate”, which can be calculated by taking the APR and dividing by 365. For example, an APR of 1000% would be equivalent to a daily rate of 2.74% (1000%/365). If we compound that rate daily, using an online calculator we find a corresponding APY of 1927158% (which, according to the degens on crypto Discord, is “decent”).
In general, the more often we compound, the higher the APY will be for a given APR, which is the main reason auto-compounding vaults in DeFi are so powerful (they compound multiple times per day!). However, it’s important to remember that the APYs displayed on these auto-compounding vaults are often insanely high (especially with new projects paying 10% daily or even more) but it’s highly unlikely you’ll actually realize those gains because those APRs (and often the token price) will almost certainly drop over time. In fact, even with these monster APYs, it’s very easy to lose money! Let’s look at a quick example:
Multiple times per day, Chad scrolls through the “Shill Me” channel on every one of his 3246 crypto Discord servers, and today he found an absolute gem: Shitomb Finance, an innovative Tomb fork pegged to the price of 1 Bitconnect ($BCC). With Shitomb, Chad can stake $FOOD in the Bathroom to earn $SHIT rewards, but he’s decided to ape into the $SHIT-$FOOD LP, currently earning 3650% APR, or 10% daily, which compounded daily is about 13 quadrillion percent (~13,000,000,000,000,000%) APY (which according to the degens on crypto Discord is “good”).
Chad apes hard and buys in for $10000: $5000 of $SHIT ($10 per token, about 10X peg), and $5000 of $FOOD ($1000 per token) to make the $SHIT-$FOOD LP, and then stakes it in the Bathroom. Chad’s goal isn’t long term… after all, he understands that Shitomb, as innovative as it is, likely won’t survive an entire year. So his plan is to get this juicy APR for three weeks (21 days), and then bounce with some serious profits. Using the same online calculator as above, we find that 10% daily return (compounded daily) will yield 640% over 21 days, turning the $10000 initial investment into ~$74000.
Much to Chad’s surprise, the next three weeks do not go according to plan. The prices of $SHIT and $FOOD slowly fall by about 15% per day, and while the juicy APR was stable at 10% daily, Chad’s balance at the end of the 21 days is much less than he expected. Instead of ~$74000, he now has only ~$3400 for a net loss of ~$6600. In this example, the tokens lost value at a higher rate than the rewards were paid (15% loss of token value versus 10% gain in token rewards, for a net loss of 5% per day). At the end of 21 days, he ended up with a much greater quantity of tokens, but they were worth far less than what he purchased them for. In other words, the loss of token value outpaced the number of tokens received as rewards. Always remember that the APR/APY tells you the return in token rewards, and only represents return in dollars when those tokens prices stay the same.
The example given here was very simple, with a fixed APR and both tokens changing in value linearly in a correlated fashion. Reality is usually much more complex, with token prices wildly fluctuating (often divergently), and daily rates changing by the minute. In the next article we dive into the dynamic nature of APR in DeFi, detailing the variables that define APR, and how to calculate it across common DeFi protocols such as yield farms and Tomb forks.
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