Return on equity

Introduction

Return on Equity (ROE) is a crucial metric in Euler that helps users understand their overall yield relative to their invested capital. When you interact with Euler by depositing and borrowing assets, you earn Supply APY on your deposits while paying Borrow APY on your debts. ROE combines these factors to give you a clear picture of your position's performance.

Understanding ROE

ROE is calculated by comparing your net earnings (after accounting for both supply and borrow rates) to your equity in the position. The formula is:

$$\text{ROE} = \frac{( \text{Total Deposits} \times \text{Net Supply APY}) - ( \text{Total Debt} \times \text{Net Borrow APY})}{\text{Equity}}.$$

What makes ROE particularly interesting in Euler is that it can be calculated in two different ways, depending on how you've structured your position. This flexibility allows you to evaluate your returns in the context that makes the most sense for your strategy.

Ordinary Borrow Positions

When you simply deposit collateral and borrow against it, your equity is measured as the total value of your deposits. This approach is most useful for understanding the cost of a standard loan.

How It Works

In an ordinary borrow position, your equity is:

$$\text{Equity} = \text{Total Deposits}$$

Your ROE is:

$$\text{ROE} = \text{Net Supply APY} - \frac{\text{Total Debt}}{\text{Total Deposits}} \times \text{Net Borrow APY}$$

Since a user's Loan-to-Value (LTV) is their total debt divided by their total deposits, this simplifies to:

$$\text{ROE} = \text{Net Supply APY} - \text{LTV} \times \text{Net Borrow APY}$$

Example

Suppose you deposit $1000 into ETH paying 6.5% Supply APY and borrow $800 USDC costing 4.5% Borrow APY.

Your equity is:

$$\text{Equity} = \$1000$$

Your ROE is:

$$\text{ROE} = 6.5\% - (\frac{\$800}{\$1000}) \times 4.5\% = 2.9\%$$

Multiplied Positions

When you create a multiplied position, your equity is measured as the difference between your total deposits and total debts. This approach is particularly useful for evaluating yield farming strategies or long/short positions.

How It Works

In a multiplied position, your equity is:

$$\text{Equity} = \text{Total Deposits} - \text{Total Debts} = \text{Net Asset Value}$$

Your ROE is:

$$\text{ROE} = \frac{(\text{Total Deposits} \times \text{Net Supply APY}) - (\text{Total Debt} \times \text{Net Borrow APY})}{\text{Net Asset Value}}$$

Example

Suppose you deposit $200 into ETH paying 7.5% Supply APY and multiply 5× by shorting USDC, which has a 4.5% Borrow APY. Your total deposits and debts remain the same as the first example:

$$\text{Total Deposits} = \$1000$$ $$\text{Total Debts} = \$800$$

Your equity is now:

$$\text{Equity} = \$1000 - \$800 = \$200$$

Your ROE is now:

$$\text{ROE} = \frac{(\$1000 \times 7.5\%) - (\$800 \times 4.5\%)}{\$200} = 19.5\%$$

Choosing the Right Calculation

The Euler interface allows you to toggle between these two ROE calculations because the context of your position matters. The same numbers can produce very different ROE values depending on whether you're:

• Taking out a simple loan against your collateral
• Creating a leveraged yield farming position
• Managing a long/short strategy

Best Practices

When evaluating your ROE:

1. Consider your position's purpose when choosing the calculation method
2. Remember that higher leverage amplifies both gains and losses
3. Factor in all costs, including gas fees and potential liquidation risks
4. Monitor how changes in interest rates affect your ROE
5. Consider the impact of reward tokens on your overall returns
6. Be aware that ROE can change significantly as market conditions evolve