Yield Mechanics

This section explains how the yield mechanics work for the RZR and how it's different from the OHM model

Below is a step-by-step “token-flow ledger” that shows exactly where RZR's yields come from, where they go, and why they can more sustainable than OlympusDAO’s model.

OlympusDAO Recap

We'll start with a 60-second refresher on OHM mechanics, then layer-in the Harberger-tax twist to undertand how the system is different.

Symbol	What it is	Typical 2021 value
$PCV_t$	Treasury assets at epoch t	$500 M (stablecoins + LP)
$S_t$	Total OHM supply	17 M
$sS_t$	Staked supply (≈ 97 %)	16.5 M
$B_t$	New bond deposits this epoch	$3 M
$r\_\text{epoch}$	Rebase reward rate	0.35 % per 8 h → 20 K % APY
$\Delta S_t$	OHM minted to stakers	sS_{t-1}\times r\_\text{epoch}

When OHM trades at a fat premium to its backing, discounted bonds become ultra-profitable, so $B_t$ soars → Treasury swells → policy can maintain (or even raise) $r_\text{epoch}$ without breaching the 1 OHM ≥ $1 backing rule.

In effect speculative inflows are alchemised into rebase yield.

RZR – adding a Harberger-tax fuel line

Symbol	What it is	Default
$H_t$	Harberger-tax inflow this epoch	Declared-value × 5 % APR × (epoch length)
$r_\text{max}$	Initial reward rate (5000 % APR)	0.359 % per epoch
$r_\text{min}$	Floor rate (1000 % APR)	0.092 % per epoch
$\tau$	Time since last bond sale (hours)

Reward-rate formula

The reward rate formula is enabled as long as the token price trades higher than the protocol backing and linearly decreases until a new bond is cleared.

$r_t \;=\; \max\!\Bigl(r_\text{min},\; r_\text{max}-\tfrac{\tau}{12}\,(r_\text{max}-r_\text{min})\Bigr)$

Resets to $r_\text{max}$ whenever a bond clears.

Treasury growth

Treasury growth (Or PCV growth) is the sum of all the new bond sales and the taxes collected from the Harberger tax.

$\Delta PCV_t = B_t \;+\; H_t$

Token emissions

$\Delta S_t = sS_{t-1} \times r_t \quad\text{distributed as:}\quad \begin{cases} 85\% &\text{→ stakers (sRZR)}\\ 10\% &\text{→ veDRE lockers (boost)}\\ 5\% &\text{→ referral payouts} \end{cases}$

Keeping each RZR “over-collateralised”

To keep every RZR token over-collateralized, the protocol continously checks a backing ratio and ensures that it is always above 1.

$\text{Backing ratio } \beta_t = \frac{PCV_t}{S_t} \ge 1$

If $\beta_t$ threatens to drop below 1 the protocol throttles $r_t$ toward $r_\text{min}$ (or pauses rebases) until fresh $B_t + H_t$ arrive.

Worked example – one 8-hour epoch

To understand the mechanics better, we go through an 8 hour epoch to see how the variables play out.

Item	Value
Starting PCV	$10 000 000
Starting supply	1 000 000 RZR
Declared sRZR value	$30 M
Bond inflow $B_t$	$100 000 (4,4,4 bond)
Harberger tax $H_t$	$30 M × 5 % / (365×3) ≈ $12 330
Epoch reward rate $r_t$	0.359 % (fresh bond just hit)
New HBA minted $\Delta S_t$	1 000 000 × 0.359 % = 3 590
PCV after epoch	$10 112 330
Backing per RZR	$10.03 (↑ from $10.00)

In this example,

• The Treasury absorbs $112k without selling any RZR.

• Only 3.6 k RZR are printed, boosting stakers yet barely denting the backing ratio.

• If no new bonds land for 12 h, $r_t$ decays to 0.092 % (= 1000 % APR) — still sky-high, but four-times lower inflation.

Rebase rewards are printed out of thin air, but they live or die by whether the Treasury can keep up. OHM relied purely on waves of speculative bonding to fund that backing.

RZR adds a second hose (Harberger taxes) that keeps dollars flowing even when hype cools—letting it maintain high yields without blowing up the collateral ratio.