Optimizing AVS Allocations for Liquid Restaking Tokens (LRTs)

As the number of Actively Validated Services (AVSs) surpasses 10, with 1,300 operators securing them, the complexity of restaking continues to grow. This variety, and the risk-reward tradeoff accompanying it, is multidimensional and impacts numerous factors across the restaking landscape. 

In this report, we explore various potential options for ether.fi’s AVS allocation strategy, and determine how they may impact its yield accrual. We seek to understand how yield changes over time for some of these underlying factors, especially with committing security to an AVS (for some amount and duration) before slashing and payment mechanisms are finalized.

Contents

1. AVS allocation framework — How should AVSs be spread across the current amount of restake available?
2. Adding one additional AVS — How does onboarding an additional AVS partnership incrementally impact risk-adjusted yield?
3. Adding an nth AVS — At what point do we see diminishing returns given the amount of restake to the LRT?
4. Partnership considerations — What are the tradeoffs of bespoke exclusive AVS partnerships, relative to a more widespread, organic selection of AVS?
5. Conclusions

AVS allocation framework — How should AVS commitments be spread across the current amount of restake available?

We seek to find an optimal restake allocation to distribute ether.fi's $9.3B in AVS commitments. This initial allocation assumes no additional registration. We have kept a few assumptions in mind to design this allocation strategy:

• Given the unknown profile for slashing risks, we instead want to reduce the second-order downside of AVS slashing (e.g., correlated slashing).
• Commitments cannot be modified or “uncommitted.”

Allocation

A couple of constraints govern how we approach AVS allocation. The varying commitment amounts (i.e., Polyhedra’s $3B vs. Drosera’s $300M) and the total restake available to ether.fi imply that achieving a minimal restake allocation necessitates AVSs in each operator “pod” sharing security.

Isolating one operator to handle larger capital loads may cause other operators to juggle excess risk given the total number of registrations [refer to assumption 2 below]. Therefore, we choose a minimal restake allocation that spreads capital and registrations evenly across operators to ensure comparable operator exposure. Again, this does not bind or threshold additional registrations but rather helps give color to a minimum viable setup. Constraints are as follows:

• Large AVS commitments are split across multiple operators to lower drawdown risks. This reduces variance associated with unknown slashing specifications.
• Potential additional registrations (regardless of commitment nature) can start with operators registered to two AVSs.

Method

Our AVS selection framework highlighted a potential framework to balance AVS risks and rewards. Specifically, we discount rewards by slashing as a function of \( c_a, t \) which is a portfolio of the restake registered with the AVS over a rebalancing time \( t \).

While this framework was designed at the global level across an entire set of AVSs and operators, minimizing slashing terms \( s(\mathbb{c_{a,o}}, t) \) idiosyncratic to each operator \( o \) informs how to reduce risk across the whole set. At a high level, we can do this by creating the notion of an operator risk score \( \mathcal{O}_o \) for operator \( o \). Some factors that can help inform operator risk score include:

• AVS slashing implementations (magnitude, conditions, idiosyncratic elements, etc.)
• AVS restake quorums
• Number of AVSs registered

One way of formally expressing the risk score relationship between operators \( i \) and \( j \) is shown below. Operators with similar risk scores \( \mathcal{O} \) should probabilistically exhibit similar expected drawdown risk.

\( \mathcal{O}_i \sim \mathcal{O}_j \rightarrow \mathbb{P}(|K_i - K_j| < c) > 1 - \delta \)

• \( K_i, K_j \) are drawdowns due to slashing on operators i and j
• \( c, \delta \) are respective thresholds

As such, we choose to allocate across operators such that each operator risk score is equivalent. Without additional information on AVS slashing implementations or behavior across the restaking ecosystem, our ex-ante expectation for slashing is equal across AVSs. Therefore, at the start, our risk score hinges on the number of registered AVSs, where operators with fewer AVSs registered will have a higher risk score [refer to assumption 2 below].

Current Recommendations

• Given 13 operators, we recommend splitting commitments evenly between operators.
• Reduce the number of registrations per operator to lower second-order drawdowns.

Assumptions

• [1] Allocations are designed ambivalent to operator reliability and quality. Given the lack of operator track records, we can not assume one operator is better suited to run a particular AVS than another.
• [2] A greater number of AVS registrations in a single operator increases the likelihood of negative second-order effects, such as correlated slashing.
  • There may be implicit curvature in these negative second-order effects.
  • For a defined operator, suppose \( H \) is the magnitude of negative drawdowns, and \( N \) is the number of AVSs that the operator is registered to. Then \( \frac{dH}{dN} \) is increasing with respect to \( N \).
  • Informally, this states that we assume the risk of excess drawdown accelerates the higher the number of AVS registrations.

Adding one additional AVS — How does onboarding an additional AVS commitment incrementally impact risk-adjusted yield?

The natural continuation is to explore how onboarding additional AVS commitments can impact that baseline commitment level. We find that:

• The overall benefit of additional registrations can be very sensitive to the quality of that AVS (in terms of yield and slashing potential).
• There can exist an AVS profile where additional registration does not meaningfully contribute to added ruin risk, but increases average returns.

Depending on operator setup, accommodating additional commitments may require rebalancing existing commitments across operators to ensure comparable operator scores.

Simulations

To give some ex-ante color on this yield expectation we need to somewhat assume rewards and slashing profiles [see Appendix A]. We assume:

• Commitment yields are equivalent across various AVSs at 100% APY, where individual slashing events incur a drawdown of 5%. Slashing probabilities for each AVS are 0.03.
  • Note: 100% APY is only for simulation purposes and not a characterization or estimate of potential AVS yields.
• The operator is greedily registered with 10 existing commitments, given slashing implementations are not finalized. This allows for stronger color on lower bounds and baselines.
• We fix a correlation strength between AVS slashing events to 0.2. The closer the correlation strength is to 1, the stronger the tendency for slashes to occur together.

An initial examination of registering an additional AVS suggests that there is likely a positive expectation in yield. However, this may depend on the additional AVS’s assumed slashing probabilities, magnitudes, and AVS yield. These initial explorations motivate varying reward potential and slash probabilities of the new AVS considered for registration. What is most interesting, is the potential for ruin via excess slash, as demonstrated by the individual simulation runs drawing down to -1.

We compare performance in terms of average returns and ruin risk between the two setups — one without the new AVS registration, and one with it.

Observations

Considering the yield spread and ruin spread heatmaps together, there may exist a potential two-dimensional phase transition between slashing probabilities / AVS yield with ruin risks (i.e., what sort of profiles can increase yield without adding to ruin potential).

• We observe a phased transition with the dark indigo corresponding to 0 ruin spread, extending from (1.5 annualized reward / 0.04 slash probability) → (0.5 annualized reward / 0.02 slash probability) to the top row.
• Additional AVS with a significantly lower quality profile likely adds to ruin risk.

When assessing average returns spread to baseline over this same range of rewards/slashing pairs, we find that there is a potential 10-20% increase in performance compared to baseline, while maintaining ruin risks constant (in simulation).

Ultimately, this phased transition likely shifts more conservatively with higher correlation strengths of slashing among AVSs, or >10 commitments we already have. With more AVS commitments, it may be less beneficial to use the same restake to register to increasing number of AVSs.

• There is likely some convex relationship with the risk of ruin, so the viability of onboarding additional commitment depends on how concentrated the operator AVS registration is.

Accommodating additional commitments to lower-quality AVSs may require rebalancing some AVS load to other operators. Since these relationships were examined from the perspective of one operator greedily registering with all AVS, one natural way to accommodate additional commitments without adding excess risk is to pursue a less greedy allocation.

To add color to that decision boundary on whether to support an additional AVS commitment and where those diminishing returns are, we naturally must vary across the size of the registration set and slashing correlations.

Adding an nth AVS — where do we see diminishing returns?

AVS commitment is applied globally and facilitated via multiple operators, suggesting that AVS commitments per operator can vary. Exploring these return/ruin spreads on different numbers of AVSs may yield additional color when operators are getting “maxed out,” and it becomes less beneficial to register with additional AVSs.

Decomposing to the operator level, suppose we have n AVSs registered on a particular operator and look to increase registrations set to n+1. Again, consider the same set of assumptions as in the previous section, where yields in our existing AVS set are equivalent at 100% APY and individual slashing events incur a drawdown of 5%. Slashing probabilities for each AVS are 0.03 [see Appendix A].

• If we fix the probability of slashing and correlation strength, how much reward does a new AVS need to output to justify inclusion, assuming we have n AVSs already registered?

In these theoretical setups, we find that ruin risk is very sensitive to variations across these factors. In particular, adding an additional AVS of similar quality (expected reward and slashing risk) to the existing registration set may start to increase ruin risks at 10+ AVS at lower correlation levels, while simultaneously increasing average returns. Ultimately, these boundaries on where ruin risks begin increasing depend on the quality of that additional AVS being considered (where quality is driven by slashing likelihood).

At lower levels of correlation strength

• The boundary sits at roughly 10+ AVSs for equal quality AVSs,
• And at 7+ AVSs for lower quality AVSs (unclear for higher quality AVSs)

At higher levels of correlation strength

• The boundary sits at ~6 AVS for equal quality AVSs,
• And at 4+ AVSs for lower quality AVSs (unclear for higher quality AVSs)

Results

For each mini heatmap below, the x-axis represents the number of AVSs registered on that operator, the y-axis represents the annualized reward of the additional AVS commitment. The large x-axis varies across slashing probabilities of the new AVS, and the large y-axis on correlation strengths.

Heatmaps A and B: Returns / Ruin counts of adding a new AVS with a defined probability of slashing in the basket of n AVSs

Heatmaps C and D: Returns / Ruin spread to baseline (without additional AVS)

Observations

The numerical experiments suggest potential convexity in drawdown that results from an increased AVS registration count, coupled with unknown slashing correlations and probabilities. Moreover, stronger correlations contribute heavily to ruin changes as rewards and AVS registration counts vary.

• Heatmap A — High net additional AVS returns can mitigate the effects of ruin.

• Heatmap B — Ruin risk accelerates as slashing correlation goes to 1.
  • Correlation may contribute more to ruin risk than slashing probability on the additional AVS.
  • This may be exacerbated by an increased AVS registration count.
• Heatmap C — Increased slashing probabilities draw down more on average returns than a lower AVS reward.
  • For two AVSs with approximately equal expected yield net of slashing, registering the AVS with lower slashing probability may have a lower impact on additional risk.
  • Intuitively, this aligns with reducing the variance of drawdowns associated with unknown slashing correlations.
• Heatmap D — Strong slashing AVS correlation seems to significantly add to ruin risk on the 5-10 AVSs / operator mark.
  • The added risk for a high AVS count (15+) seems juxtaposed to the increased risk of ruin for baseline.

Ultimately, any slashing correlation strength and other latent relationships are currently unknown, and any parameters that help guide intrinsic AVS quality are still unavailable. Despite this, we can form some very ex-ante notions on how to conservatively assess whether to add to our commitment set.

Understanding these tradeoffs allows us to adopt sophisticated allocation strategies and choose to register with an AVS without a commitment, should we believe the rebalancing associated with non-commitments allows us to avoid punitive slashing.

Partnership considerations — What are the tradeoffs between commitments relative to non-commitment for securing AVSs?

Ideally, pre-committing economic security to an AVS requires the commitment yield to exceed the non-commitment yield by some premium/buffer, since that commitment prevents deregistration. Let \( y_i, \gamma_i \) be the organic yield and commitment yield associated with AVS \( i \), respectively. Let \( s_i \) be the slashing penalty on AVS \( i \), and \( \mathcal{S}_i = \sum s_{i,t} \) the set of all slashing penalties over the time period. Assume that \( \gamma_i, y_i \) are insensitive to the size and duration of the commitment.

• \( y_i \) is the cost-adjusted APY obtained when operators register with AVSs organically.
• \( \gamma_i \) is the cost-adj APY obtained when an LRT signs a pre-commitment deal for a guaranteed amount of restake security.

Then, pre-committing economic security to an AVS requires \( \gamma_i \) to be greater than \( y_i \), both probabilistically and in expectation, considering some risk premium.

• \( \mathbb{E}[\gamma_i - \mathcal{S}_i] \geq \mathbb{E}[y_i - \mathcal{S}_i] + k_{prem} \) for some premium/buffer \( k_{prem} \) derived from commitment length risks, “early”-stage risks, inability to rebalance, etc.
• \( \mathbb{P}(\gamma_i - y_i \geq k_{prem}) \geq 1 - \delta \) for some probability bound.

Ultimately, rebalancing generally drags on average returns, and at lower slashing correlations the benefits of rebalancing are not as tangible. In worst-case scenarios it can significantly aid against ruin risk. Moreover, we find that the benefits of rebalancing are generally very sensitive to the added premium from commitment — the expected cost of rebalancing a similar quality AVS is roughly around ~5-10%. However, this accelerates as the additional AVS quality declines.

Simulations

How much buffer is needed to justify a commitment relationship to the AVS, rather than one with more optionality? We assess this by comparing:

• Commitment to an AVS with yield adjusted upward by that premium buffer, and
• Allowing for rebalancing to that same AVS, but for which we do not have that yield premium. Allow for rebalancing out of our allocation to that additional AVS if it is slashed.
  • Consider the accrued yield ratios between our commitment AVS portfolio vs. a hypothetical total AVS portfolio (including that non-commitment AVS).
  • This ratio informs us of the incremental effect of this additional AVS on the net yield.
  • Adjust the allocation to this additional AVS at t, by the ratio at t-1.

We follow similar experiments conducted previously [see Appendix A] and examine primarily returns and ruin spreads between these two strategies. This time, we vary by the buffer amount, correlation strengths, slashing probability, and AVS registration set count, but primarily fix the annualized reward of the additional AVS.

Interestingly, it seems the larger the AVS registration count, the less rebalancing can potentially help soften ruin risks — perhaps implying that a single rebalanced AVS has less overall effect when grouped with more AVSs. But, as the correlation approaches 1, this relationship shows signs of breaking down.

We observe that a 20% added buffer to a commitment yield (relative to non-commitment yield) may be sufficient under average-case scenarios to justify a commitment. We then lower the commitment premium/buffer amounts to find the minimum premium required to justify a commitment.

For AVSs of similar quality, 5% of additional reward may be sufficient to justify commitment. This gradually increases to 10%.

• For AVSs of lower quality, this may move to 15-20%.
• Increasing correlation strength generally shifts the benefit of rebalancing toward setups with fewer AVS.

Conclusions

Using a theoretical framework, we examined how the contours of the risk-reward tradeoff in AVS selection evolve across multiple dimensions and underlying factors, especially through the lens of committal AVS security. We found that:

• A minimal restake allocation adhering to all commitment magnitudes can balance capital and registration among all available operators.

• An AVS profile can exist where additional registration does not meaningfully contribute to added ruin risk but increases average returns by roughly ~10-20% (i.e., 1.1-1.2x existing allocation yield), under assumed conditions. Ultimately, the overall benefit of additional registration can be very sensitive to the quality of that AVS.
  • Accommodating an additional commitment may require rebalancing existing commitments across operators to ensure comparable operator risk levels.
• Ex-ante real data shows that ruin risk is very sensitive to variations across slashing correlations, the AVS registration count, and AVS slashing probabilities. In this framework, at lower levels of slashing correlation, adding an additional AVS of similar quality (expected reward + slashing risk) to the existing registration set may increase ruin risks at ~10 AVSs in the registration set.
  • If we consider committing to a lower-quality AVS, this lowers to ~7 AVSs.
• At lower slashing correlations, the benefits of rebalancing are less tangible. In worst-case scenarios, it can significantly aid against ruin risk if the added premium is not sufficient.
  • Under average-case simulated scenarios, commitment premiums of 5-10% (i.e., 1.05x - 1.1x of the non-commitment yield) can justify commitments. However, this accelerates as the AVS quality declines.

The dynamics between restakers and the AVSs they secure will become more complex as full functionality, slashing, and payments become live. While this framework approached most relationships from a hypothetical lens, careful agent-based simulation can further assess intricate risk-reward tradeoffs as more AVSs go online.

Appendix A

The presence of the EIGEN token and its role as a dual staking token along with native ETH-based restake suggests a potentially different classification of slashing penalty and yield accrual. The greater flexibility of this dual staking model may imply that EIGEN-based security suffers from a higher probability of slash (due to being primarily responsible for intersubjectively attributable faults), but as compensation gets rewarded with higher yield.

• The form of this yield (i.e., ETH or EIGEN-based) depends on the type of security. While we’ve assumed that yield remains fixed in fiat terms over the simulation’s lifetime, in reality this may vary, especially as EIGEN/ETH price ratios move.
• To reassess AVS registrations, one can apply different weighting factors to ETH / EIGEN-based yield in conjunction with expected slashing deltas.
  • The disambiguation between EIGEN and ETH-based security implies this AVS registration decision can further be split into whether we register EIGEN security or ETH security only.