Where does the amplified yield in Chicken Bonds come from?

A core benefit of Chicken Bonds is the amplified yield that the boosted token captures. Before we explore how the amplification works, let’s quickly outline some key properties of the boosted LUSD token (bLUSD).

In LUSD Chicken Bonds, bonders receive bLUSD when they Chicken In, and bLUSD is always backed by the system’s LUSD Reserve.

The LUSD funds held by the system are allocated to two yield sources: B.Protocol and the Yearn Curve LUSD vault. The yields from these sources are harvested and auto-compounded. Crucially, all of the LUSD yields flow to the Reserve.

bLUSD is proportionally redeemable for LUSD in the Reserve: that is, if you hold x% of bLUSD supply, you can redeem it for x% of the Reserve (ignoring fees).

The redemption value of bLUSD grows faster than the underlying LUSD compounds. This means that the effective yield on bLUSD is greater than the yield generated by the LUSD that backs it.

Something for Nothing?

By now, we’re all skeptical of promises of unsustainable high APRs in DeFi - and on the surface, Chicken Bonds may sound too good to be true.

How can bLUSD mysteriously amplify the underlying natural yield of the system’s LUSD? Are some users losing out - and if so, why would they participate in the first place?

Yield Amplification Mechanics

Before we dive in, let’s define some terms:

Pending bucket: holds the LUSD from all open bonds (which have not yet been Chickened In or Out).

Reserve bucket: holds the acquired LUSD from Chicken Ins. The Reserve bucket backs the whole bLUSD supply. bLUSD is fully redeemable for the LUSD in the Reserve.

Permanent bucket: holds excess LUSD diverted from bonds that were Chickened In “early” (more on this later). The LUSD in here is protocol-owned and can never be redeemed.

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Yield amplification in Chicken Bonds stems from the fact that yields from all three protocol buckets (Pending, Reserve, Permanent) flow to the Reserve bucket. Therefore, the LUSD quantity in the Reserve grows faster than the “natural rate” at which LUSD compounds.

Over time, as all yields flow to the Reserve, the redemption price increases.

Let’s say 1 bLUSD redeems for x LUSD at some point in time t1.

Time passes, bringing us to time t2. Now, x LUSD would have naturally compounded to y LUSD, where y > x. But due to the yield amplification, 1 bLUSD will redeem for more than y LUSD.

So, who (if anyone) is “losing out”?

Actions that create the amplified yield

In Chicken Bonds there are three main actions:

• Bonding
• Chicken In (claim bond)
• Chicken Out (cancel bond).

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Chicken Outs (canceling a bond)

When a bonder Chickens Out, they reclaim their initial bonded LUSD. The yield their bond generated in its lifetime ends up in the Reserve and gets captured in the redemption value of bLUSD.  

By Chickening Out, a bonder gives up their right to claim bLUSD and effectively gives up the yield their bond earned to other bLUSD holders.

Now, let’s look at “early” and “late” Chicken Ins. Firstly, we need a quick detour…

Detour: Break-even time and Optimum Chicken In time

A bonder accrues a virtual bLUSD balance based on a plateauing curve. Due to the shape of this curve, a bonder’s bLUSD accrual rate decreases over time.

Their break-even time occurs when the market value of their accrued bLUSD equals their bonded LUSD.

If a bonder is willing to sell their bLUSD for LUSD and rebond it, then their optimal Chicken In time is the time that maximizes their bLUSD accrual in the long run.

Due to the plateauing bLUSD accrual curve, at some point, it’s better for the bonder to do this. They Chicken In, sell their bLUSD for LUSD, and rebond it to achieve a higher bLUSD accrual rate. Exactly when this optimal Chicken In time occurs is tricky to determine since the market price of bLUSD fluctuates. However, it will occur later than the break-even time. The better bonders are in predicting market sentiment, the higher the amplification they can achieve.

Early Chicken Ins (claiming a bond)

As time passes, a bonder’s claimable bLUSD gets closer and closer to their bLUSD cap. When they Chicken In, some LUSD goes to the Reserve and some goes to the Permanent bucket.

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The earlier they Chicken In, the more of their bonded LUSD gets sent to the Permanent bucket. When a bonder Chickens in “early”, they get less bLUSD - and divert more LUSD to the Permanent bucket - than if they’d waited until reaching their optimum Chicken In time.

The excess LUSD diverted on early Chicken Ins in turn increases the future yield which flows from the Permanent to the Reserve - amplifying the bLUSD yield.

Late Chicken Ins

A rebonder that Chickens In late (after their optimum Chicken In time) ends up earning bLUSD more slowly than rebonders that manage to time their Chicken Ins well.

It takes longer for them to accrue a given value of bLUSD than if they’d followed an optimal rebonding strategy. Being bonded for longer to reach the same value means they have spent longer bearing the opportunity cost of bonding - i.e. “donating” the yield from their underlying bonded LUSD to the system.

The net effect is a transfer of value from rebonders who Chicken In late, to those who managed to Chicken In optimally.

Why would anyone Chicken Out, or Chicken In early or late?

We’ll now see that these yield-amplifying behaviors are rational and expected in certain situations.

There can be good reasons to Chicken Out - for example when you need your bonded funds back for other purposes, such as making a purchase or repaying a loan. Or if you simply change your mind - even a perfectly rational user sometimes pays an opportunity cost when their personal situation changes.

It can also be rational for a bonder to Chicken In early before they approach their bLUSD cap. Depending on the bLUSD market premium, a bonder can break-even and net a profit well before they accrue most of their eligible bLUSD. Since the bLUSD market price fluctuates, some bonders will prefer a guaranteed profit now over a possible future gain.

Late Chicken Ins are inevitable, since solving for an exact optimum Chicken In time is a difficult problem. It can be derived under idealized assumptions (see our whitepaper), but a “real-life” Chicken Bonds system will be fluid, and harder to analyze - so we’d expect a distribution of Chicken In times, even if all else was held equal.

Finally, users are never perfectly responsive, and they factor in gas costs too. As a bonder, even if you’ve accrued your optimum bLUSD amount, it could make sense to wait a while for network congestion to subside before Chickening In. A number of bonders will also simply be slow to react and end up leaving some value on the table due to a late Chicken In.

If there were no open market for bLUSD and everyone Chickens In at the same bond age, what would yields look like?

Let’s, for now, pretend there’s no open market for bLUSD. Let’s also assume bonders bond at different times, and all Chicken In when they’ve (almost) reached their bLUSD cap, and so the Permanent Bucket is negligible.

All bonders have an opportunity cost. That is, they gave up their LUSD yield to the protocol until they Chickened In - at which point, they can earn an amplified yield on bLUSD going forward.

At the moment they Chicken In, the redeemable value of their bLUSD is almost equal to the LUSD they gave up.

The yield they earn after Chicken In depends on how the Pending bucket evolves, and how they timed their Chicken In.

Some bonders will do better than others - though, almost all will still earn an amplified yield on their bLUSD due to the yield flowing from the Pending bucket, even in this conservative (and unrealistic) scenario.

In practice, the Permanent bucket will grow over time as some fraction of bonders do Chicken In well before they reach their bLUSD cap. This supports an enhanced yield for bonders even in the later stages of a “mature” system, when the Pending bucket is smaller.

Is it a zero-sum game for bonders?

We’ve seen how some bonders may “donate” yield to others, often for perfectly rational reasons. So is the Chicken Bonds system zero-sum for bonders? Not necessarily!

Ultimately, bond returns depend on the bLUSD market price dynamics, and how well the bonders time their bLUSD sale or redemption.

The bLUSD market price captures the market’s expectations of future growth as well as speculative sentiment. bLUSD should trade above the redemption price - at some point in future, 1 bLUSD will redeem for more LUSD than its redeemable LUSD now would have grown to by that point (from normal compounding). This future value boost translates to a market price premium.

The absolute return that a bonder ultimately gets from selling bLUSD depends on the sale price they can achieve.

If all bonders only redeemed bLUSD, the system would be zero-sum. However, due to the bLUSD market premium it’s possible for all bonders in aggregate to achieve better returns than the underlying LUSD compounding.

As for bLUSD traders: some will make a profit, and some won’t. Timing an entry point and buying the token at or below “fair” market value is the universal challenge for all investors.

In general, bLUSD holders can expect the bLUSD price floor to grow faster than naked LUSD compounded in the underlying yield source. The bottom line: simply holding bLUSD results in an enhanced yield over the long-term.