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# Unweighted Shares

Unweighted shares (US) is simply the amount of JOE tokens that 'back' a fNFT Bond. The NFT is backed by JOE tokens in the sense that it is entitled to receive rewards generated by that amount of JOE tokens. This metrics is utilised to issue shares to fNFT bond holders. Issued shares are used to account for reinvested revenue.
This means that at the time of issuing, the US of a bond will simply be its cost.
Bond level
Cost
US
1
10 JOE
10 Shares
2
100 JOE
100 Shares
3
1000 JOE
1000 Shares
4
5000 JOE
5000 Shares
The longer you hold a bond, the more the underlying US will grow. This is because during every reward emission, the part that is reinvested is accounted for through the increase of US for all bonds minted before the date of issuing. This is done in order to guarantee ownership of future passive income generated by the compounded amount.
Example
(1) 4 Level 1 and 4 Level 2 fNFT Bonds get minted at launch.
$4L_1 + 4L_2 = \begin{cases} \text{US} = 4 \cdot 10 + 4 \cdot 100 = 440\\ \text{TVL} = 4 \cdot 10 + 4 \cdot 100 = 440 \end{cases}$
Now, a Level 1 NFT will have 10 US and a Level 2 NFT will have 100 US.
(2) Now let's suppose that after 1 year, the protocol has earned revenue for 50% of its TVL.
$\text{Revenue} = 50 \% \text{ TVL} = 220 \text{ JOE}$
(3) We can now imagine being in Phase 1: TA where all revenue is reinvested. Even if bond holders won't earn any liquid rewards, they will be receiving shares accounting for their contribution to the revenue. As all rewards are reinvested, the protocol will be issuing 220 shares.
Shares issuance
$I_S$
- For every JOE reinvested within the protocol, 1 share is distributed to all bonds. Shares issued are divided between bonds according to their unweighted shares.
$I_S = 100 \% \text{ Revenue} = 220 \text{ Shares}$
To calculate how many shares a bond is entitled to claim, we must calculate its percentage of ownership over all unweighted shares.
$I_{S, L} = \frac{\text{US}_{L}}{\text{US}} \cdot I_S$
• $I_{S, L}$
: Shares issued to a bond of level
$L$
.
• $\text{US}_L$
: Unweighted shares of a bond of level
$L$
.
Thus:
• $I_{S, L=1} = 5 \text{ Shares}$
• $I_{S, L=2} = 50 \text{ Shares}$
Each NFT will now have the following unweighted shares
$\text{US}_{L=1} = 10 + 5 = 15, \quad \text{US}_{L=2} = 100 + 50 = 150$
Keep in mind that also weighted shares increase by the amount of claimable shares multiplied by the bond's weight. This is done in order to ensure NFT holders the right to claim payments generated by their compounded rewards.
The protocol will now look like this
$4L_1 + 4L_2 = \begin{cases} \text{US} = 4 \cdot 15 + 4 \cdot 150 = 660\\ \text{TVL} = 4 \cdot 15 + 4 \cdot 150 = 660 \end{cases}$