Virtual shares accrue bad debt

[Rubilmax]

Context

The virtual assets to which virtual shares are entitled act like a borrow position that can't get liquidated. For this reason, these virtual assets behave like unrealizable bad debt that can grow to a significant value on a Morpho Blue market.

Analysis

The minimum time it takes for these virtual assets to reach the size $S$ on a market with $T \ge 1$ borrowed assets at rate $r$ can be under-estimated (worst-case scenario for lenders) using the formula:
$S \times T = (T + 1) \times \exp{(elapsed \times r)}$

Solve for elapsed and you get:
$elapsed = \frac{ln\frac{S \times T}{T + 1}}{r}$

Where $elapsed$ is of the same unit as $r^{-1}$

Calculation

If $r$ is 800% APR (maximum of AdaptiveCurveIrm) and $T = 1$:

• it takes at least 1.31 year for an almost inactive market (because $T = 1$) to grow this bad debt to 1 USDC
• it takes at least 1.77 year for an almost inactive market (because $T = 1$) to grow this bad debt to 1 WBTC

Mitigation

1. The implementation of $\exp$ is under-estimating the result in Blue, so the attacker needs to ping the market from time to time to accrue interest in an optimal manner
2. The share price can be observed before an interaction in order to quantify this bad debt and decide whether this market is considered sane
3. The duration grows with $\frac{ln(T)}{r}$ so a non trivial borrow on a market guarantees a sufficiently large order of magnitude (3.4 years for a market with 1k USDC borrowed, 3.8 years for a market with 10 WBTC borrowed)