APY, APR, and Impermanent Loss in Crypto Explained in Depth

5tGG...kNBo

27 Aug 2023

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Cryptocurrencies and blockchain technology have introduced new financial concepts and mechanisms that are still unfamiliar to many people. Among these are APY, APR, and impermanent loss - terms frequently used in decentralized finance (DeFi) applications. Understanding what they mean is key to making informed decisions in crypto investing.

What is APY?

APY stands for Annual Percentage Yield. It measures the real rate of return on an investment over one year, taking into account the effect of compounding interest. In DeFi applications, users can lend their crypto assets to earn interest or provide liquidity to earn trading fees. APY represents the total earnings a user would receive in one year, including interest compounding.

For example, if a user deposits 100 USDC into a lending protocol offering 5% APY, at the end of one year they would have 105 USDC. The 5 USDC interest payment gets compounding, generating more interest in the next period.

The power of compounding makes APY the most accurate measure of real yields from crypto investments. The higher the APY, the greater the earnings potential from compound interest over time.

What is APR?

APR stands for Annual Percentage Rate. This measures the simple interest rate earned on an investment, without taking compounding into account.

Using the same example above, a 5% APR would mean 5 USDC interest earned on 100 USDC deposited over one year. The interest does not compound.

APY and APR are similar but distinct metrics:

APY includes compounding, APR does not.
APY will always be higher than APR for the same rate.
APY reflects actual annual earnings, APR reflects the rate before compounding.

DeFi protocols may use APR to represent the base interest rates before compounding. Users should look for APY to understand true yearly yields.

Compounding Interest and Crypto Yields

Compounding is powerful because interest accrues on both the original principal and accumulated interest. With each compounding period, the interest amount grows.
For example, say a user deposits 100 USDC at 10% APY daily compounding:

Day 1: 100 USDC deposits earns 1 USDC interest. Total = 101 USDC
Day 2: 101 USDC earns 1.01 USDC interest. Total = 102.01 USDC
Day 3: 102.01 USDC earns 1.02 USDC interest. Total = 103.03 USDC

The interest earned each day is added to the balance, which generates more interest the next day. The earnings and balance grow at an increasing rate with continuous compounding.

Most DeFi lending protocols offer daily compounding. The higher the compound frequency, the higher the APY. Compounding makes a big difference over longer time periods.

DeFi Yields and Compounding Returns

DeFi protocols can offer double-digit or even triple-digit APYs. How is this possible?

High crypto yields are driven by:

Demand for borrowing crypto assets
Rewards for providing liquidity to trading pools
Protocol revenue and governance token rewards

Lenders can earn high interest when borrowers compete for limited supply of funds. Liquidity providers may get rewards from swap fees on trades. Protocols distribute a portion of revenues to liquidity pools. Governance token rewards incentivize participation.

For users lending stablecoins or the major cryptocurrencies,compounding high yields can generate significant gains over months or years:

10% APY compounded daily returns 113% gains after 1 year
20% APY compounded daily returns 149% gains after 1 year
50% APY compounded daily returns 545% gains after 1 year

However, crypto interest rates can be variable and rewards have risks. Users should account for potential rate fluctuations and risk parameters when estimating returns.

Impermanent Loss

Impermanent loss refers to the temporary loss of funds experienced by liquidity providers on decentralized exchanges (DEXs) like Uniswap or PancakeSwap.

Liquidity providers deposit equal values of two tokens into a trading pool to facilitate swap trades between the assets. In exchange they earn trading fees and protocol rewards.

However, impermanent loss can occur when the price ratio between the two assets changes compared to when funds were deposited. Due to arbitrage by traders, the investor's portfolio value decreases.

How Impermanent Loss Occurs

Let's look at an example:

Alice deposits 10 ETH ($2,000) and 2,000 DAI ($2,000) in a Uniswap ETH/DAI pool, when ETH is $200. So she has $4,000 total.
Later ETH doubles in price to $400. Her ETH is now worth $4,000 and the DAI worth $2,000.
But to maintain the 50/50 price ratio in the pool, some ETH is sold for DAI. So her pool share may be worth ~$5,500, less than the $6,000 if she just held the assets.
This $500 loss is impermanent loss. If ETH later drops back to $200, the full $4,000 value is restored.

Impermanent loss happens because DEX pools need to maintain constant pricing to facilitate trades. Price changes create arbitrage opportunities that rebalance the assets. Investors bear the loss.

Avoiding Impermanent Loss

There are a few ways to mitigate impermanent loss:

Provide liquidity in stablecoin/stablecoin pairs, like DAI/USDC. These tend not to change value relative to each other, avoiding imbalance.
Stick with correlated assets or indexes, like ETH/BTC or DeFi index tokens. Their prices tend to move together, limiting arbitrage trades.
Hold liquidity pool tokens and wait for the asset price ratio to return to original levels before withdrawing.
Factor impermanent loss into yield expectations. Require higher APY to compensate for potential loss from volatility.
Take advantage of "impermanent loss insurance" through protocols like Unslashed Finance, which provide compensation for loss.
Withdraw liquidity before major price swings, then re-deposit after. This requires active management.

Impermanent loss is an inherent risk in providing crypto liquidity, one that is difficult to avoid completely. Fortunately losses tend to be temporary during periods of volatility.

Impermanent Loss Calculations

Impermanent loss can be quantified based on the change in asset price ratios. The formula is:
IL = 2 * (1 - (Ratio1 * Ratio2)^(1/2))
Where:
IL = Impermanent loss
Ratio1 = Current value asset 1 / Original value asset 1
Ratio2 = Current value asset 2 / Original value asset 2
This calculates the difference between holding the assets separately versus as a pooled portfolio. The greater the change in price ratios, the higher the impermanent loss.
Many DeFi analytics tools calculate IL online for specific pools. Investors can monitor loss in real-time as prices fluctuate.

Comparing DeFi Yields With and Without Impermanent Loss

To account for impermanent loss, DeFi users should compare:

APY earnings on staked assets
Value change from impermanent loss
Net portfolio value over time

For example:

Alice stakes $10K USDC at 10% APY
Bob provides $10K in ETH/USDC liquidity, earning 15% APY
ETH price drops 25% in one month causing Bob 5% IL
Alice earns $83 interest. Bob earns $125 but has $500 loss.
Alice is ahead in this case.

Even with IL, liquidity yields often compensate for moderate volatility. But users should model out scenarios to estimate risk-adjusted returns.

Impermanent Loss and Taxes

A final issue is taxes. In many jurisdictions, impermanent losses realized when withdrawing liquidity are seen as taxable events.

Investors may owe taxes on capital losses they incurred from IL, before the losses recover in the future. This exacerbates the temporary effects of impermanent loss.

APY and APR are key metrics for earning yields in crypto. APY reflects compound interest critical for maximizing returns over time. However, impermanent loss can cut into liquidity provider earnings during periods of volatility.

Learning to model projected yields accounting for compounding gains and potential impermanent loss is an important skill in DeFi. Analyzing risk-adjusted returns will lead to smarter investments and prevent unexpected losses. While promising high yields, crypto protocols still require research, caution, and risk management.