OlympusDAO attempts to be a decentralized reserve currency backed by the value of its Treasury. The underlying token for the protocol is OHM and is supposed to be backed by at least $1 in stablecoins. This is a very broad overview of how the protocol is intended to work and I will touch on how to decide whether you should stake or bond. I will not, however, opine on whether I believe it is a sound or flawed protocol.

Bonding is the process of purchasing OHM at a discount. For example, assume the price of OHM is \$500 and the discount is 10%. To bond, an individual needs to give the protocol \$450 and in 5 days the bond fully vests and the individual is given 1 newly created OHM. If the price does not change, the newly created OHM can be sold for \$500 in the secondary market for a 10% profit. Bonding is considered to be a short-term strategy, which means the risk is the price of OHM falling below its discounted price before it can be sold. Also, instead of using dollars, bonds also accept liquidity pool tokens so the Treasury can earn the fees from OHM trading, a practice is known as Protocol Owned Liquidity, which are used to back new OHM to reward to stakers.

There are two variables that determine the bond discounts: the debt ratio and the Bond Control Variable (BCV). The debt ratio $D_t$ is:

\[D_t=\frac{B_t}{S_t} \tag{1}\] \[\Delta{ULC} = \Delta{C} - \Delta{P} \tag{2}\]

where $B_t$ is the amount of bonds outstanding at time $t$ and $S_t$ is the amount of OHM in circulation. The price of the bond is:

\[P_{b,t}=1+(D_tBCV_t) \tag{3}\]

where the term in parentheses is the bond premium. Logically, a lower premium results in a greater discount to the current market price. A higher debt ratio, or greater demand for bonds, lowers the discount on bonds. The BCV is controlled by the protocol and is inversely related to the debt ratio to stabilize changes in bond prices.

To take part in the profits of the protocol, OHM holders can stake their tokens and earn a yield that is compounded every eight hours, or one epoch. To continue with the previous example, the Treasury now has \$449 in profits. Again, since 1 OHM is supposed to be backed by at least \$1, the protocol can create 449 new OHM tokens and distribute them to stakers. Also, as mentioned in the previous section, rewards to stakers can potentially be enhanced by investments made in the Treasury.

It is important to also address the risks of the protocol and the mechanisms in place to mitigate them. The floor price is the backing per OHM. For example, if the Treasury has \$1,000 and there are 500 OHM in circulation, the floor price is \$2. Theoretically, the price should never go below the floor price. Should that not hold, the Treasury will purchase OHM and destroy them, pushing up the price and reducing the supply.

Deciding whether to bond or stake

There are two key elements in determining whether it is more profitable to bond or stake: the bond discount and the reward yield. In the previous section, our example glossed over a nuance in the bond vesting process. A portion of the bond value is accrued in each epoch over the course of 5 days, or 15 epochs. Individuals have two choices: let that value accrue in your account until it fully vests or stake the cumulative value that has been accrued at each epoch. To compare the whether to bond or stake, we will use the latter strategy. To determine the bond discount:

\[d_t=\frac{P_{b, t}}{P_{m,t}}-1 \tag{4}\]

where $d_t$ is the discount and $P_{m,t}$ is the current market price. The implied 5-day rate of return on the bond $r_{b, t+5}$ is therefore:

\[r_{b, t+5}=\left(\frac{1}{1+d_t}\right)-1 \tag{5}\]

However, to determine the total return of a strategy that stakes the cumulatively accrued value, we must take into account the returns to staking. First, the total number of coins that accrue at the end of the vesting period $C_{b, t+5}$:

\[C_{b, t+5}=\frac{i_t}{P_{b, t}} \tag{6}\]

where $i_t$ is the amount of capital invested. At the end of every epoch, the number of coins that vest $c_{t,b}$:

\[c_{b,t}=\frac{C_{b, t+5}}{15} \tag{7}\]

where 15 is the number of epochs per day, 3, times the number of days in the vesting period, 5. The total number of coins earned from the bonding and staking process is:

\[C_{bs, t+5}=\sum_{t=1}^{n}c_{b,t}\left(1+r_{s,t}\right)^n \tag{8}\]

where $r_{s,t}$ is the staking reward per epoch and $n$ is the epoch number.\footnote{For brevity, we assume that the reward rate stays constant over 5 days} The total percentage return to bonding and staking is:

\[r_{bs,t+5}=\frac{C_{bs,t+5}P_{m,t+5}}{i_t}-1 \tag{9}\]

The total return to staking only $r_{s,t+5}$ is:

\[r_{s, t+5}=\left(1+r_{s,t}\right)^{15}-1 \tag{10}\]

If $r_{bs, t+5}$ is greater than $r_{s, t+5}$ it is more advantageous to bond, and vice versa. The issue with bonding and staking, as opposed to only staking, is practicality. It requires immediately staking the bond value as it vests every eight hours. This also requires paying gas fees on Avalanche every time that value is staked. This cost is generally negligible but it is not zero.