Equations

Stake

$$deposit = withdrawal$$

The swap between SOHM and sSOHM (stake and cancellation of stake) is always cashed out at 1:1

$$rebase = 1 - (deposits / sSOHMOutstanding)$$

The reserve will not require the return of sSOHM when depositing profits, which will cause an imbalance. The rebase sSOHM is to correct the imbalance between the outstanding deposits of SOHM and sSOHM. This rebase allows the outstanding return of sSOHM to ensure that sSOHM is equal to a SOHM.

$$APY = [(1 + reward Rate)*totalsupply /stakeAmount]^{3*365}$$

According to the reward rate of return tells you the annualized rate of return. It takes into account the effect of compound interest, because sSOHM rebases exponentially.

$$Total value deposited= stake * price$$

Measure the dollar value of all SOHMs in the SOHM DAO protocol

Bond

The bond price is determined by the value of the SLP and the number of outstanding bonds. The agreement considers SOHM and BNB to be equal, because the agreement measures SOHM by its intrinsic value. This means that we only need to care about the sum of the assets in the pool, not their value. According to the constant product formula x y = k, the risk-free value is the minimum value of x + y. This happens to be when x = y. We can use the square root of x and y to determine this.

$$RFV = 2sqrt (constantProduct) * (LP / totalLP)$$

The debt ratio is the sum of all SOHM bonds committed divided by the total supply of SOHM. This allows us to measure the debt of the system.

$$debtRatio = bondsOutstanding/sohmSupply$$

Premium is derived from the system’s debt ratio and ratio variables. This scaling variable allows us to control the rate of increase in bond prices.

Premium determines the income of the agreement, which in turn determines the rights and interests of the pledger. The LP collected at the premium is used to forge a new SOHM and distribute it to the pledgers and DAOs.

$$Premium = 1 + (debtRatio * BCV)$$

Sell

$$executingPrice = lastMarketPrice * (1 - discount)$$

If the last market price is greater than TWAP, the sales contract will execute the order at the last market price minus the discount controlled by DAO, thereby providing arbitrage to encourage liquidity.

Treasury

$$IV = reserves / supply$$

The intrinsic value is determined by dividing the total storage assets by the total supply of SOHM.

$$profitMint = (IV - 1) * supply$$

At the end of each epoch, the Reserve Bank will mint SAME to return the IV to our expected value of 1.

$$epochMint = (TWAP - IV) * supply * ICV$$

If TWAP is greater than IV, the Reserve Bank uses this equation to fund the SOHM sales contract. ICV is a scaling variable controlled by DAO, which allows us to adjust for inflation.

$$epochBurn = |TWAP - IV| * supply * DCV$$

The Reserve Bank uses this equation to fund the BNB sales contract. DCV is a scaling variable controlled by DAO, allowing us to adjust for deflation.

Dashboard

$$Support for each SOHM = Market value of the treasury / Circulation supply$$

Tell you the market value of Treasury bonds for each SOHM

$$Liquidity owned by the agreement = Treasury lp balance / lp total supply$$

Tell you the liquidity that the agreement has

$$Runway Available = [ln(RFV(RFV funds/Pledged SOHM) / ln(1 + reward rate)]/3$$

Runway Available price