Intro
Financial culture (or, more accurately, ignorance) is one of our country’s weaknesses, leaving so many speechless at the mercy of the bank clerk (or similar). Simple interest rates, compound interest, and the effective percentage rate (APR) are unfortunately still arcane topics for many.
Let alone APY, or Annual Percentage Yield, in Italian. Indeed, it’s simpler than it seems in financial terms, but more tricky in terms of communication and understanding.
The underlying logic is compound interest, in which compounding normally occurs on an annual basis. If I invest €100 at 5%, at the end of the first year I’ll have €105, and if I leave it invested (principal + interest), in the second year I’ll have €110.25, and so on.
The APY is simply a generalization of the concept of compound interest, in which compounding occurs more frequently than annually. The crucial point, however, is how the applied interest rate is expressed, or rather advertised for marketing purposes. We’ll see below how it can be used artfully and misleadingly, though generally not dramatically.
APY (Annual Percentage Yield)
Let’s return to our previous example, but with monthly compounding instead of annual compounding.
The applied rate will be 5%/12 = 0.4167%. Therefore, the 12-month compounding formula will be: 100*(1+0.4167%)^12 ≈ 105.12. If we repeat the exercise considering daily compounding, we arrive at 105.13. Therefore, the more frequent the compounding, the higher the APY rate is than the nominal rate. In our case, 5.12% and 5.13% on a monthly and daily basis, respectively. So, if I expect 5% at the end of the year, it means that the compound interest rate will be (somewhat) lower than 5%. Of course, the difference isn’t huge in many cases, but it can become significant with high compound interest rates or longer investments (remember Warren Buffet’s words: compound interest is a gift from God).
Compound interest rates can take on values unthinkable in the traditional world. Beyond months and days, which are still reasonable overall, they can take on frequencies in the order of hours or even seconds, if tied to block validation times in a blockchain (approximately 12 seconds for Ethereum).
In more general terms: APY = (1 + r / n)^n – 1, where r = interest rate and n = compound interest rate.
One could push this argument to the limit, assuming instantaneous compound interest, but here things get complicated. We’re no longer talking about interest rates, but about interest intensity, and the math gets tricky.
APY and Decentralized Finance (DeFi)
But what’s the reason for this long preamble? The reason is that APY is increasingly used, in place of more traditional capitalization logics, in the DeFi space, so-called decentralized finance (Decentralized Finance vs. TradFi, Traditional Finance), which relies on blockchains and cryptocurrencies for financial transactions.
There are essentially three reasons for this choice in the DeFi space, always keeping in mind that, like traditional finance, DeFi is not populated by disinterested benefactors.
- Marketing
Advertising the APY rate, our 5% from the previous examples, conceals the fact that the interest rate applied during capitalization periods (months or days, or even less) is actually lower. Over 12 months, a 5% APY corresponds to an effective 4.889%, which is slightly less than 5%, and which sounds much less attractive than a flat 5%.
- Economic convenience for fractions of a year (for the payer, not the recipient)
DeFi finance has much faster capitalization times than traditional finance. It’s rare to leave capital invested for an entire year. Therefore, while traditional capitalization grows linearly over the course of a year, fractional capitalization grows exponentially, only meeting linear growth at the end of the year. This is a complicated way of saying that if you stop investing before a year, you’ll earn less money with DeFi (not a lot, but a little) than with traditional finance.
- Adaptability to the DeFi dynamic
Such rapid capitalization times are well suited to managing the timescales of decentralized finance, where returns fluctuate significantly based on supply/demand, token issuance, liquidity usage, and incentives to attract deposits.
Ultimately, the APY has become the benchmark in DeFi because the ecosystem is optimized for rapid and automatic capitalization on the earnings side, where a higher and more accurate effective return helps protocols compete for capital. The APY provides users with the number that best reflects reality, and what they expect.pitale. L’APY fornisce agli utenti il numero che meglio corrisponde alla realtà, e quello che appare più attraente.
