nToken return example

In this example, a liquidity provider mints nTokens by depositing a million dollars worth of cTokens in a currency's nToken account. End-users then trade roughly 1M$ of fCash assets over the course of a 3 month trading period. For simplicity, all fCash maturities (3 month, 6 month and 1 year) have the same interest rate path over the trading period.

In the figure presented above we can see that as interest rates increase from ~2.5% to ~7%, the nToken account has a larger net fCash position and a lower cToken position. This is because as end-users borrow cTokens from the fCash pools, the nToken account receives positive fCash assets (a lending position) and holds less cTokens. Conversely, as fCash rates decrease the nToken account effectively sells fCash assets and receives cTokens via its liquidity tokens position. When fCash interest rates go lower than the original interest rate at which the LP provided its liquidity (~2.5%), the nToken holds a negative fCash position.

To get the nToken's blended interest rate, we aggregate the nToken's account claims on cTokens and fCash tokens and weight each asset by its current market rate.

As we can see in the figure above, as the nToken gets increasingly long fCash its blended interest rate increases. This is because the nToken is lending at higher rates than the cToken supply rate. As long as fCash interest rates remain above the cToken supply rate, the nToken's account blended interest rate will benefit from positive fCash residuals relative to holding solely cTokens.

Conversely, when the fCash rates become lower than the cToken rate the nToken account's blended interest rate is lower than the cToken supply rate. This is because the nToken still has a positive fCash position and is now lending at a lower rate than the cToken supply rate.

Closer to the end of the quarter, the nToken account has a net negative fCash position (a borrowing position). Since the cToken supply rate is higher than the cost at which the nToken borrows fCash, the nToken's blended interest rate is still slightly higher than the cToken supply rate. This is because the nToken is borrowing at a fixed rate that is lower than the variable rate. In other words, the nToken's blended interest rate puts a bigger weight on high-yielding cTokens and a negative weight on low-yielding fCash tokens.

Liquidity fees

Over the 3 month trading period, the nToken account also accrues liquidity fees via its liquidity token holdings. These liquidity fees represent ~1,500$ or ~0.15% of the overall traded volume of 1M$. In our example the LP initially provided 1M$ in liquidity, the overall trading volume thus represents 1X its initial liquidity. We can think about the nToken return from liquidity fees as:

Liquidity fee return = Total traded volume x weighted average liquidity fee in BPS / total liquidity

The higher the amount of trading volume is generated per unit of liquidity, the higher the nToken return from liquidity fees will be. Moreover, if end-users actively trade longer-dated maturities over shorter ones, the average liquidity fee in BPS will be higher thus increasing the nToken return from liquidity fees.

As we can see in the figure above, the nToken account accumulates more fees in periods of high trading volume. In our example, these periods correspond to large fCash interest rate moves.

nToken return (excluding incentives)

The combined effects of the blended interest rate, liquidity fees, and impermanent loss result in an increasing nToken's NPV over the quarter starting at 1$ per nToken and finishing at 1.014$ or a yield of ~1.4% (~5.6% annualized).

As a comparison, the cToken return (excluding incentives) over the same time period would have been ~1.09% (~4.37% annualized)

A major difference between the cTokens and the nTokens is that contrary to the cToken value, the nToken NPV does not increase monotonically.

The nToken's NPV decreases at the beginning of the quarter because it holds an increasing amount of positive fCash residuals that are discounted at higher rates. As fCash interest rates stabilize, the nToken's NPV slowly increases as it is earning the blended interest rate. Subsequently as fCash rates decrease, the nToken's NPV increases rapidly as it is still holding positive fCash residuals that are now discounted at lower rates.

NOTE incentives

The NOTE incentive rate of return for an LP is a function of the NOTE token value and the LP's nToken holdings in a given currency and can be regarded as:

Note Incentive Return = Note Incentive Emission Rate * Note Token Price * LP nToken holdings proportion / Amount of liquidity deposited by the LP.

For simplicity, consider that the LP in our example holds all outstanding nTokens in a currency and thath the annual emission rate for this currency is 200,000 NOTE. After holding the nTokens for 3 months, the LP can claim the 50,000 NOTE to be issued during that period of time. If the NOTE token price is 1$ (implying a 100M$ fully diluted valuation) and the liquidity provider had initially provided 1M$ worth of liquidity, the LP would effectively be receiving a 5% NOTE incentive return on his liquidity (50,000$ / 1,000,000$) over the quarter.

Total nToken returns

In our above example the total nToken return over one quarter is 6.4% (25.6% annualized):

• Blended interest rate: 1.24% (4.96%)

• Liquidity fees: 0.15% (0.60%)

• NOTE incentives 5% (20%)

Let's note that the impact of impermanent loss on returns was negligible.