The Convex Index

Abstract
The Convex Index offers broad and diversified exposure to an integral part of Decentralized Finance, the Curve ecosystem. A user can gain exposure through a single deposit, receiving tokens tracking the index. The index is low-risk, giving consistent returns from liquidity rebates, and useful for diversifying both traditional and crypto portfolios. Periodic rebalancing and reinvestment are optimally executed, greatly reducing the costs associated with the Ethereum blockchain.
Introduction
With the emergence of cryptocurrencies as a new and promising asset class, many institutional investors are wondering how to gain exposure in a safe manner that does not require significant overhead. “Crypto”, as it is called, is infamous for its lack of user-friendliness, high transaction costs, and constantly shifting environment requiring vigilance against hacks and panics.
From the turmoil, a handful of “blue chip” decentralized finance (DeFi) protocols have emerged unscathed. In particular, Curve Finance, and its symbiote, Convex Finance, together have total liquidity greater than 15% of the total value in DeFi. These protocols rely heavily on fees and rebates generated from providing stablecoin liquidity and offer safer and more consistent returns than outright bets on individual assets such as Bitcoin or Ethereum.
While these opportunities are very much real, for the investor seeking to participate in these protocols, the challenges of ease-of-use and high transaction costs still remain.
The solution we offer is “The Convex Index”, a well-diversified portfolio of Convex positions that gives exposure to the highest quality yield sources in the Curve ecosystem.
Background
The following background may be useful as a brief refresher on investment basics and as a common foundation for discussing the Convex Index.
The need for diversification
The saying “don’t keep all your eggs in the same basket” has been known since the 17th century, but until the Nobel Prize-winning work of Markowitz in 1954, it was not generally recognized that multiple baskets could only eliminate certain kinds of risk, diversifiable risk. Markowitz showed careful portfolio construction could greatly reduce risk by removing diversifiable risk while maximizing return.
The selection of assets with different exposures and the correlations between them is therefore of primary importance. Additionally, asset managers avoid choosing very similar assets to limit exposure to the same tail risk. An approach that works in both ways is to select across categories, such as economic sectors, or by geography. This can reduce correlation and avoid excessive exposure to the same risk, e.g. US stocks and European stocks are subject to different political regimes, while stocks and government bonds respond differently to monetary policy or global trade conditions.
The needs of an institutional investor are quite different from that of an individual investor. The former is seeking new exposures that complement their existing allocations, ideally providing additional returns while reducing diversifiable risk. It is important that any new exposure be to an instrument that is transparent in design and construction, as otherwise it is difficult to properly manage risk.
Building blocks for portfolio construction
Diversification is of key importance in investing. In an efficient market, you can only expect to be compensated for risk that is non-diversifiable. This explains why financial advisors advocate creating a suitably diversified portfolio; however, lack of access to a variety of markets and instruments has hindered the ability to properly diversify a portfolio. Many large institutions still found themselves handcuffed to mutual funds who charged expensive fees and offered limited liquidity.
This began to change in the 1970s with the birth of index funds, whose sole value proposition was to cheaply track a stock market index such as the S&P 500. While initially pooh-poohed by mutual fund managers who could not believe people would pay to be “average”, a large body of academic research developed, suggesting that “beating the market” was at best only achieved by a very tiny elite of fund managers. Large institutions increasingly began investing in index funds. Through the popularization efforts of John Bogle and others, retail investors also began to flood the index fund market.
Exchange-traded funds (ETFs) started with the SPDR ETF in 1993 and grew out of the seeds laid by index funds. If an index fund offers investors an inexpensive and convenient exposure to a broad selection of assets, then an ETF is like an index fund “on steroids”. An ETF share is extremely liquid and trades like a stock, unlike an index fund whose shares can only be redeemed at the end of the trading day. The diversity and low-cost of ETFs lets investors easily achieve their chosen mix of risk and reward.
To see the impact of ETFs, consider that for decades common wisdom stated a stock and bond portfolio is beneficially diversified by the addition of commodities; however, access to commodities markets has been difficult for the average investor. With the rise of commodity ETFs, the average retail investor can diversify a stock and bond portfolio with a commodities ETF. Further diversification into real-estate ETFs or other sectors is cheap and accessible, with new kinds of ETFs being created every year.
The low cost, diversity, and flexibility of ETFs lets even active managers engage in tactical tilts or handle rebalancing costs more effectively, while letting more passive managers fill in gaps in their strategic allocations. Not surprisingly, ETFs have grown tremendously in popularity, with currently 3.9 trillion in AUM.
The Curve and Convex protocols
Curve Finance is the largest DeFi protocol with almost 20 billion USD in value locked across multiple chains, which is almost 9.5% of total value locked across all of DeFi.
Curve’s main claim to fame is an extremely low-cost swap between assets that maintain a peg, such as stablecoins. Since the fees are low, Curve incentivizes liquidity providers (LPs) with “rewards” (rebates), not only their own CRV token, but with tokens from partner protocols, such as Compound, Synthetix, Frax, among many others.
Curve also enhances rewards (the “boost”) for LPs who choose to time-lock CRV tokens. In order to achieve the maximum rate of rewards, an LP must typically lock a sizable amount for 4 years. The locked tokens are no longer tradeable and so this represents a significant commitment.
Lockers gain voting power proportional to the time and amount locked. They can vote in weekly gauge votes, which determine the rewards rates for the different Curve pools. They also receive a portion of the fees generated by the platform.
The Convex protocol was created with the goal of maximizing the boost for LPs. Convex continually locks CRV and also participates in gauge votes in an effort to maximize earned CRV. An LP can delegate liquidity shares to Convex, who then earns the enhanced rewards rate and gives the LP boosted rewards minus a suitable fee.
In addition, Convex offers its own rewards for LPs who choose to delegate to them. The CVX token has outperformed the CRV token since inception. The boosted CRV rate and CVX rewards have made Convex the biggest holder of locked CRV (~50%), with many choosing to delegate their liquidity shares to Convex. The CVX token can also be locked to provide voting power and determine how Convex distributes its votes.
Curve and Convex have both been rigorously audited for security by top firms. APY.Finance has also closely scrutinized their contracts and found them to be very carefully designed and well-written. Neither protocol has ever been hacked nor has any major exploit been found.
The Index Portfolio
The Convex Index balances diversity, returns, and transaction costs.
Overview
A useful index gives broad exposure to a particular category. By “broad exposure”, we mean the opportunity to make the potential returns of the category, without picking winners over losers. The category must be specific enough to constrain the return and risk characteristics of the index. This makes it easier to fit into a portfolio and manage overall performance.
Figure 1: While US Treasuries have become highly correlated to the S&P 500, a portfolio of Curve positions offers lower correlation while hedging Bitcoin exposure. (Feb. 2021 - Feb. 2022)
For the Convex Index, we have focused on the specific strategy of providing liquidity to stablecoin pools, particularly those on Curve, the dominant stablecoin platform. This is an important source of yield for crypto traders, particularly during bear markets. We believe this is a good entrypoint for many institutional investors, as the index’s volatility is not only much lower than that of the mainstay cryptos but offers diversification to them and traditional assets.
​
Bitcoin
Ethereum
Curve Portfolio
S&P 500
Treasuries
60/40 Portfolio
Volatility
74.4%
94.3%
1.1%
12.6%
3.7%
7.8%
Sharpe ratio
0.331
1.08
8.31
0.937
-0.975
0.716
Figure 2: A Curve portfolio has less volatility than Treasuries with a compelling Sharpe ratio compared to equities and mainstay crypto (Feb 11 2021 - Feb 17 2022)
The platform provides exposure to the index by managing a portfolio of liquidity provider positions in Curve (through Convex). A user can buy tokens representing shares of the index. These tokens accrue yield instantly with no additional steps. Since these tokens follow the ERC20 standard, they can easily be managed by a custodial wallet as with other crypto assets following the standard.
The platform is significantly cheaper than managing the components of the index directly. The cost of a deposit into our platform is less than the cost of an allocation to a single Convex position. These costs easily multiply due to rebalancing and the periodic claiming of rewards.
The risks of the Convex Index come from several areas. Fundamentally, there is smart contract risk from APY.Finance, Curve, and Convex. Since rewards are primarily given in CRV and CVX tokens, there is market risk from those tokens, although somewhat limited due to the short duration held before they are reinvested into the portfolio. There is also liquidity risk, as transaction costs and the supply vs demand of stablecoins changes due to overall market conditions, which affects rebalancing. Last but not least, there is stablecoin risk, as each stablecoin has different tail risks that may cause them to deviate from the peg.
Basket Selection
Components are selected by filtering the universe of Convex listings with the following series of screens.
Underlying asset USD stability
The index focuses on delta-neutral returns from USD pegged stablecoin pools. If any assets in the pool show volatility relative to USD they are filtered out. This includes pools with assets pegged to BTC or ETH, and pools that could suffer impermanent loss because they pair a token with ETH.
Annualized pool returns
The index filters out a subset of the lowest APR Convex listings, which is currently 50% of the full set, that passed the underlying asset USD stability screen. This screen allows sufficient diversity without sacrificing yield.
Slippage
To ensure efficient rebalancing, the index requires the Curve pool for a Convex listing to have an amplification coefficient high enough to support low slippage for the pool's composition. The higher the value of the coefficient, the more imbalanced a pool's composition can be while supporting slow slippage when depositing or withdrawing.
Pool TVL
The index filters out Convex listings that have a TVL under a threshold, currently set to $50M, to reduce the risk of insufficient exit liquidity when rebalancing and dilution of returns.
Underlying asset volume
The index requires accurate pricing from a Chainlink aggregator to calculate index token price. To be included in the index, each underlying asset in the pool must have at least $3M in daily volume otherwise there is a risk of mispricing from market inefficiency.
Depeg risk
The biggest risk to the index is an underlying asset depegging from USD. Due diligence is done on each underlying asset to analyze the peg mechanics. If there are risks uncovered during the due diligence process, the pool is filtered out.
Discretionary overlay
The due diligence team reserves the right to veto the inclusion of a pool if there’s a red flag that does not fit into any of the existing screens. Additionally, the community of governance token holders has final approval for inclusion in the form of a governance proposal vote.
Index Weights and Enhanced Indexing
A score is calculated for each selected Convex listing using a proprietary algorithm that is fed historical data from the corresponding Curve pool. These scores determine the target weights for each listing.
Position sizes often deviate from the target weights to optimize transaction costs. The primary technique for optimizing transaction costs is transaction batching. To resize every position whenever capital is deposited or withdrawn, to keep the index in perfect balance, would have a significant impact on returns due to transaction costs. Instead, positions are resized incrementally, to bring the index closer to the target weights over time.
Similarly, when TVL stays constant, but the weights change, a rebalance of positions may be necessary to match the new target weights. Each potential rebalance between positions is tested for optimal trade execution before it is performed. If the test fails, the rebalance is not performed. The rebalance is periodically retested after failure and will be performed if a subsequent test passes.
When the test fails for an extended period of time, the position size will deviate from the target weights. The index’s preference for low slippage pools helps reduce the necessary deviation caused by enhanced indexing optimization.
Optimal trade execution for a rebalance is tested by calculating the estimated returns from the current date, to the Convex gauge weight voting period end date, for the unbalanced position and the rebalanced position. The difference between these two returns must exceed, by a certain threshold, the slippage and transaction costs of the rebalance between positions.
The Index Token
Currently, users participate in the platform by depositing one of three major stablecoins, USD Coin, Dai, or Tether. In return, they receive tokens representing a share of the index portfolio returns, denominated in the appropriate stablecoin. The majority of user deposits are deployed into the portfolio, leaving only a small remainder for withdrawals. The necessity of keeping funds unallocated for withdrawals creates drag on performance.
Wrapping the Convex Index portfolio in a single index token improves capital efficiency for the platform, reduces cost and complexity for the user, and allows cross-chain Convex exposure. Most users will not interact directly with the platform but buy and sell the index token on exchanges. Participants with sufficient capital to meet the platform’s minimum requirements would deposit and withdraw from the platform to engage in arbitrage and keep the value of the index token pegged to net asset value.
Platform Efficiency
When the primary method for modulating exposure to the Convex Index is exchanging index tokens, there is reduced volume of platform deposits and withdrawals. The benefits are twofold:
1.Lower volume means lower reserve requirements to fulfill instant withdrawals. Because reserve pool capital cannot be deployed to the Convex Index portfolio, it is a primary source of capital inefficiency. Reducing the reserve pool size directly translates to higher returns for the index.

2.Lower volume means less rebalances between reserve pools. This saves on transaction costs and lowers the risk of a forced withdrawal from a Curve pool during a period of high slippage.
User Simplicity
Token swaps are one of the simplest to understand and cheapest DeFi actions a user can perform. Almost any user can figure out how to trade tokens, even if more advanced concepts such as staking, LPing, and collateralization are out of reach. When a user can purchase an index token to include the Convex Index in their portfolio, they no longer need to concern themselves with withdrawal fees, available reserves, boost-lock mechanics, etc.
Cross-chain Compatibility
One of the biggest challenges for cross-chain platforms is the operational overhead from running multiple instances of the platform on each network. An index token with the standard ERC20 implementation can be bridged to any EVM compatible L1 or L2 network to give users on those networks access to the platform without requiring additional platform instances.
An index token also solves the problem of liquidity fragmentation across networks. Liquidity concentrates on the network where the platform is deployed while ownership of the liquidity is distributed across other networks in the form of the index token.
Index Token Mechanics
Two groups of users contribute to the index token mechanics: the end-user, and the arbitrageur. The end-user acquires the index token because it has desirable properties that improve the performance of a wide range of portfolios, and the arbitrageur earns a return from the end-user by keeping the index token pegged to the index portfolio performance.
End-user
The end-user rarely exchanges the index token, but holds it for long periods of time. They care about index token liquidity, where it’s listed, and its compatibility with wallets.
Arbitrageur
The arbitrageur frequently exchanges the index token, but holds it for short periods of time. They care about platform features, gas cost, and index portfolio metrics, so they can perform effective arbitrage.
Arbitrage Mechanics
When investors in a traditional ETF purchase shares, they do not deposit capital directly into the fund, they purchase the shares on the market. To keep these shares priced accurately, an ETF has authorized participants that can deposit capital directly to mint new shares, allowing them to arbitrage the shares on the market for a return, and keep the share price pegged.
The index token uses a similar mechanic to hold its peg. Instead of authorized participants, the ability to directly deposit capital is permissionless, allowing any sufficiently sophisticated user to engage in arbitrage for profit.
The arbitrageur has two opportunities, when the index token is trading at a premium and when the index token is trading at a discount.
Premium Arbitrage
If the market price of the index token is at a premium relative to the index portfolio value, arbitrageurs can mint new tokens by depositing capital directly into the platform. These new tokens are sold on the open market, bringing the price down and earning a return for the arbitrageur.
Discount Arbitrage
If the market price of the index token is at a discount relative to the index portfolio value, arbitrageurs can purchase the tokens on the open market, which raises the price. These purchased tokens can then be redeemed directly on the platform to withdraw capital equal to the true value of the token relative to the index portfolio, earning a return for the arbitrageur. An arbitrageur needs to be mindful of withdrawal fees and the size of the reserve pools when performing discount arbitrage.
Platform
Overview
The smart contracts comprising the platform were built from the ground up to incorporate best practices in securing and managing capital. Different subsystems can only be operated by the relevant administrator role, with each role being protected by a separate multisig wallet.
The flow of funds through the platform is designed so that user deposits move to only one smart contract, the LP Account, which is permitted to only transfer funds to whitelisted destinations, registered Curve or Convex contract accounts. The whitelist registration is controlled by a more privileged multisig than the one operating the LP Account.
The only unauthenticated interactions with the platform happen through the liquidity pools to allow users to deposit and withdraw funds. However, users are limited to withdrawing what is available in reserve pools. At any given time, since most deposited liquidity is being managed by the LP Account, part of the portfolio must be periodically unwound to replenish the reserves for withdrawals. This means an exploit of the liquidity pools can only result in the loss of at most the funds in the reserve pools, a minority of deposited funds.
As the LP Account enters (and exits) positions, it receives (and redeems) tokens from the Curve or Convex protocols that represent deposited funds. These tokens are priced by an innovative Chainlink feed which also aggregates the total value for the portfolio. As yield is accrued by the portfolio, the feed ensures the user’s share appropriately reflects the increased value. The use of Chainlink as an oracle eliminates many dangers associated with blockchain pricing mechanisms, and the dynamic composition of our feed allows us to scale without introducing additional points of failure.
Figure 1: System architecture
User deposits and withdrawals
Users can deposit into the platform with any of three stablecoins: USD Coin, Dai, or Tether. For each stablecoin, there is a separate liquidity pool which will create APT tokens for each deposit. The total value of all three types of APT tokens for a user comprises the entire account value for the user. These tokens incorporate the accrued interest from the platform with no additional user actions required.
The amount of APT created for a user deposit is calculated simply to be the same percentage of the total APT created as the deposit as percentage of the pool’s total value. The pool’s total value is comprised of the USD value of its reserve and the USD value of its deployed capital, including any accrued yield. This latter value is tracked using another token, mAPT (see next section).
Transfers to and from the LP Account
When sufficient capital has built up in the reserve pools, most of it gets transferred over to the LP Account, with the remainder left to satisfy small withdrawals. The LP Account can also transfer unused capital back to the pools. Periodically capital is unwound from positions and swapped into USDC, DAI or Tether, if needed, to replenish reserve pools.
Every time capital is transferred from a liquidity pool to the LP Account, an amount of mAPT token is created for the pool. The mAPT token allows us to track how much is owed to each pool. When capital is transferred back to the pool, the corresponding amount of mAPT is destroyed.
Managing positions
A Curve pool allows swaps between any two tokens held by the pool. A liquidity provider (LP) provides the liquidity for swaps by depositing the requisite tokens into the pool. The depositor receives yield-bearing tokens, called “LP tokens”, that entitle the holder to a portion of the liquidity in the pool and any accrued fees. These LP tokens can be deposited into Convex to gain additional liquidity rebates. The result is what we call a Convex position.
A Convex position gains yield from trading fees and additional rebates from protocol tokens. The primary rebates comprising a bulk of the total yield are CRV and CVX tokens. Partner protocols can also contribute rebates, which can be an important source of additional yield (typically greater than the accrued fees, but less than the CRV & CVX yield).
Unwinding (part of) a position requires withdrawing LP tokens from Convex and then removing liquidity from the corresponding Curve pool. The received tokens from the pool may not match the token types needed (for either user withdrawal or adding to a position) and may require swaps.
A Convex position continually earns its rebate tokens. These tokens must be claimed (“harvested”) and then swapped for stablecoins so they can be reinvested into Convex positions.
Consideration of transaction costs for all these operations are crucial as poor execution can easily exceed the gains made during the rebalancing period.
Tracking and valuing positions
As mentioned in the section “User deposits and withdrawals”, in order to create or redeem APT, the pool’s deployed value must properly track the value it is owed by the LP Account.
The deployed value is calculated as the pool’s ownership percentage of total mAPT created multiplied by the Chainlink aggregator’s total value. The Chainlink total value must properly reflect the entire portfolio managed by the LP Account in order to create or redeem APT in the right amounts.
Rather than naively having Chainlink attempt to price all assets held by the LP Account, some of which are rather illiquid, APY.Finance has a system of allocation contracts that works with a custom Chainlink feed to value the entire portfolio.
Each Convex position is decomposed by an allocation contract into liquid base assets which can be safely be priced by Chainlink. Each allocation contract is registered with our Chainlink Registry contract. Chainlink queries this registry to obtain the symbol, balance, and decimal precision of each base asset in the decomposition. Using this information, Chainlink can price each asset balance and return the total value.
Summary
Whether your portfolio is composed of traditional assets or contains crypto assets such as Bitcoin, the Curve and Convex protocols offer beneficial diversification and competitive returns as compared to other safe haven assets.
The complexity of these protocols necessitate having sufficient technical prowess to operate them. Awareness of the dangers of the underlying assets and the protocols being plugged into Curve is critical for proper risk management. Obtaining consistent, compounding returns requires careful execution in order to avoid bleeding from costs.
Our team’s years of experience in traditional and decentralized finance lets us effectively navigate these challenges. The Convex Index’s evolving composition reflects our deep knowledge of Curve and Convex. Our rigorous screening process weeds out risks that may not be readily apparent to those without crypto native fluency.
The platform is designed to minimize loss of funds and role-based access is built into every operation. Efficiency in execution and managing the risk of the portfolio is only possible because of the idea at the heart of the platform: a single pool of liquidity participating in a dynamic portfolio, something not done by any other DeFi platform.
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