Valuing fCash

As Notional strives to make the interest rates constant by inducing variability in the exchange rate.

The exchange rate (fCash:cToken) might fluctuate based on the lending and borrowing trades in the AMM and the time to maturity but the trader is guaranteed to receive fixed rates provided that they hold their fCash positions till maturity.

AMM / Dynamic Curve

It is certain that you would get a fixed interest unless you exit early. But what happens if when you exit before maturity? Why there is no certainty of fixed rates if you exit early?

To understand this, you need to understand how fCash accrues interest.

Interest accrual with fCash

If you wish to lend 100 USDC (cash) at an lastImpliedRate of 5% for 1 year at a 0.03% liquidity fee, you would get 105.095 fCash.

lastImpliedRate = 0.05 - 0.003 = 0.047 TimeToMaturity = 1 (1 yr) Cash = 100 USDC fCash = 100 * e^(0.047 * 1) = 104.81

Here the present value of 104.81 fCash is worth 100 USDC at the time of deposit. As we approach the maturity date, the value of that fCash will approach 104.81 USDC.

Once your trade has been executed, you can rest assured that your interest rate is fixed and that we guarantee your fCash position will be honored at maturity.

Context: fCash Use-case

$fCash = Cash* e^{(lastImpliedRate * TimeToMaturity) }$

The exchange rate between fCash to Cash approaches to 1 (1 fCash = 1 Cash) as we approach the maturity date. The trades happening in the Notional AMM would likely impact this exchange rate by altering the fCash proportion but the intensity of the change in exchange rates drops as we approach maturity. This same formula can be used to evaluate fCash's value.

Dependency on trades: As trades happen in the AMM the exchange rate would change due to the slippage.

Dependency on timeToMaturity: Exchange rates change due to the slippage caused in the trades and the impact of this slippage reduces as we approach towards the maturity date.

Q. Does the last implied rate come from the oracle rate?

A Walkthrough example of an early exit

We would build on top of our example of lending 100 Cash for 1 year at 5% APY. Let us assume you exit from the trade (sell your fCash in the AMM to get your Cash) in 6 Months. The interest rate at the time of exit is the same as you entered the trade i.e. 5%.

When you sell 104.81 fCash, you would receive 102.07 Cash making a profit of 2.07 Cash in the whole investment position. This equates to 4.1% APY. All the trade calculations can be referred to from the image above.

Let us take another example where the rates changed:

In the above example, at the time of exit, the interest was 6%. This rise in the interest rate impacted the profits (1.56 Cash now vs 2.07 Cash earlier) and the APY dropped to 3.1%.

If you exit before maturity, the exchange rates might be at a value where you might lose money or maybe gain some. This brings us to the risks due to the change in interest i.e. exchange rates.