nToken valuation

nTokens can be conceptually thought of as a cross between interest-bearing assets like cTokens and Uniswap LP tokens.

The value of nTokens depends on the assets sitting in the nToken account. As an example, if the assets in the nDAI account are worth 100 DAI and there are 10 nDAI tokens outstanding, each nDAI token is worth 10 DAI.

At any time, nToken accounts can hold:

• cTokens. Compound’s interest-bearing versions of underlying tokens like DAI or USDC. The value of a cToken steadily increases as borrowers on the Compound protocol pay interest to cToken holders.

• fCash. Notional’s zero-coupon bond like instruments. fCash represents a fixed amount of an underlying token like DAI or USDC that the holder can redeem at a specific maturity date. The present value of fCash increases as time to maturity decreases and is a function of a market’s current interest rate levels.

• Liquidity Tokens. Shares of the cTokens and fCash sitting in Notional’s liquidity pools. Liquidity tokens are freely redeemable into their claims on cTokens and fCash at any time. As users lend or borrow from Notional’s liquidity pools, a liquidity token’s claims on cTokens and fCash changes. For example, if end users lend to a liquidity pool (buying positive fCash and selling cTokens), the liquidity token will have a claim to more cTokens and less fCash assets.

Since liquidity tokens can be converted into their underlying claims at any time, the value of an nToken is defined by the value of the nToken account’s net cToken and fCash holdings.

It is important to note that as end-users lend or borrow from the various liquidity pools, liquidity tokens held by the nToken accounts will have a claim on either a long or short fCash position. This is what we refer to as “fCash residuals” or an nToken’s net fCash position after converting its liquidity token holdings into their constituent cash and fCash components. As an example, if end-users of a particular pool have been borrowers on a net basis, the nToken account will have a positive residual (net positive fCash position or a net lending position) in that maturity. Conversely, if end-users were lenders on a net basis the nToken account would have a negative residual (net negative fCash position or a net borrowing position). nToken residuals are extremely important as they influence an nToken return profile and its redemption cost.

In other words, although liquidity providers initially only add cTokens to the nToken account, the account will accrue a net positive or negative fCash position through its liquidity token holdings across active maturities as end-users trade on these liquidity pools.

Because nToken accounts can hold fCash assets, the net present value (NPV) of nTokens does not increase monotonically. An nToken's NPV can decrease if the nToken account:

• holds a net positive fCash position (positive residuals) and interest rates increase

• holds a net negative fCash position (negative residuals) and interest rates decrease