Yield Calculations

To understand how yield is calculated within the protocol, it is important to understand the following:

• The Principal Token effectively acts as collateral.

• The value of the Principal Token is the same for every user and determined by the ptRate, i.e. the price of the Principal Token in the underlying asset.

• The ptRate can only decrease.

• The ptRate starts as 1 and decreases if the ibtRate (i.e. the price of the IBT in the underlying asset) decreases.

If ibtRate increases

In this scenario, the yield attribution per user is simple. The Principal Token value in the underlying asset never de-pegs (i.e. 1 PT = 1 underlying asset).

In simple terms, the yield calculation is:

$$(ibtRate_{new} - ibtRate_{old}) * ytBalance_{user}$$

If ibtRate is volatile

If the ibtRate alternates between increasing and decreasing, then the calculation is more complex.

The reasons for the added complexity is that:

• the ptRate is the same for every user,

• when any user interacts with the protocol, it triggers a ptRate update.

This results in the Principal Token's price in the underlying asset to change for every user.

The following example will illustrate the challenge:

• If Alice and Bob both deposit 10 underlying tokens at time t0 when the ibtRate = ptRate = 1, then both will receive 10 PT and 10 YT.

  • At time t1, the ibtRate decreases to 0.5, and Alice decides to withdraw all of her funds. This will trigger a ptRate decrease of 50%, i.e. ptRate = 0.5. Alice will then receive 5 underlying tokens, which is expected.

  • At time t2, the ibtRate increases to 0.75, and Bob decides to withdraw all his funds. Intuitively, Bob should get 7.5 underlying tokens back.

    • However, since the ptRate can only decrease, the ptRate still remains at 0.5.

    • From Bob's perspective, the ibtRate decreased from 1 to 0.75, so there has been no positive rate for Bob.

    • Bob was impacted by the decrease in yield from 1 to 0.5, but wasn't rewarded for the increase in yield from 0.5 to 0.75.

    • Therefore the protocol needs to balance the loss in Principal Tokens value with appropriate positive yield.

This balancing between negative and positive yield is performed in the internal _computeYield function. It works by calculating how much a user should have gained or lost compared to what has actually been lost in Principal Tokens value (viaptRate decrease). The yield attributed to the user is thus:

• actualLoss - expectedLoss if the ibtRate decreased from the user's perspective (e.g. the example above), or

• actualLoss + expectedProfit if the ibtRate increased from the user's perspective (e.g. if in the example above at time t2 the ibtRate had increased to more than 1).

Note that the actualLoss above is due to the ptRate decrease and expectedLoss < actualLoss.