This article was compiled and organized by BlockWeeks
On Robinhood's newly launched L2 chain, the hottest trading target is not meme coins, but tokenized stocks. Should they be thrown into automated market maker (AMM) pools? If the entire S&P 500 were stuffed into one pool, what would happen? A deep research report from Galaxy Research provides the answer with a bunch of arithmetic.
The Problem of Three Semiconductor Stocks
In a corner of Robinhood's new chain, there is a Curve liquidity pool containing three semiconductor stocks, with no dollars at all. Only NVDA, AMD, and SNDK, quoting against each other, and anyone can swap one chip stock for another at 4 a.m. on a Sunday. No fiat leg. Someone looked at some of the most neurotic stocks in the market and decided they should automatically and permanently trade with each other. That person is me—I was the first depositor in these pools. This is either the future of finance or an elaborately designed way to donate to arbitrageurs. I decided to find out with arithmetic.
Over the past few years, the crypto world has been debating whether stocks can become tokens. That question has been settled: they can. It is just an ERC-20 token, 18 decimal places, (in this case as a non-issuer-sponsored token) with no voting rights. Now the question becomes: once it is sitting in your wallet, what should you do with it? Where on-chain should it go? What assets should it be paired with? What is the on-chain opportunity cost of tokenized stocks, and what are the trade-offs?
The entire promise of DeFi was supposed to be an open system for everyone—all the plumbing that banks provide.
The Mirror-Image Dilemma of Treasuries and Stocks
There are currently nearly $15 billion in tokenized U.S. Treasury funds on Ethereum. If you wanted to meet all the holders of the two largest projects—Circle's USYC and BlackRock's BUIDL—a medium-sized conference room would be enough; there are fewer than a hundred holders. This is both the dream of tokenization and almost its opposite: real assets, real scale, on-chain, yet doing almost nothing.
The problem with tokenized stocks is exactly the opposite: many holders, not much scale, and sparse trading. Then, over the past month, Robinhood launched an L2 chain, and the situation suddenly changed.
Daily trading volume on the decentralized exchange (DEX) on that chain surged to nearly $5 billion, making it the third-largest public chain by DEX trading volume after Solana and Ethereum, and by a huge margin the number one chain for real-world asset (RWA) DEX trading volume. Within weeks, the AMM liquidity providers (LPs) behind these trades earned APYs of hundreds or even thousands of percent.
The timing could not have been better. In mid-September, the SEC released proposed text for its innovation exemption, opening a path for fully tokenized stocks (rather than the "mostly" tokenized versions on Robinhood's chain) to legally trade on AMMs—at least for the next two years.
Regulators nod and smile, real demand finally appears, and only one core question remains: are AMMs really a good place to trade stocks?
The frenzy of Robinhood chain's first month has subsided, but savvy traders can still earn APYs of hundreds of percent by depositing tokenized stocks into AMM pools. Is this an equilibrium rate, or a flash in the pan that will dissipate as more tokenized stocks flood in and compete for the same fees? If stocks do belong in AMMs, how should they enter? Each stock in the portfolio entering the pool individually, only some entering, or the entire portfolio tokenized and pooled as a whole?
Core Conclusion: Do Not Split an Index into Individual Stocks
The research works through the math behind these choices: when a pool expands to many assets, what drives returns, and once assets are on-chain, which operations make sense and which do not.
The conclusion is: tokenizing every asset in an index or portfolio and running them in one AMM is likely a bad idea. Using the S&P 500 as a test case, an S&P AMM pool containing 500 assets underperformed simply holding by about 3% year-to-date, and merely to break even it would need to achieve about 45x annual turnover at a 5 basis point (0.05%) turnover fee—more than 3 times the turnover of SPY in TradFi (16x).
The conclusion is not that tokenized assets should not enter DeFi, but that most stocks should not be indiscriminately placed into passive AMMs. Broad exposure is expressed more efficiently with index tokens, or by depositing a tokenized portfolio as a whole into an AMM; individual stocks are usually better suited for lending or holding; and AMMs should be reserved for assets that are structurally related and have low dispersion.
Dispersion: The Number One Determinant of Impermanent Loss
When choosing the asset composition of an AMM pool, the most important factor is dispersion: the degree to which the assets in the pool diverge from one another. Skewness, kurtosis, and other features of the return distribution further adjust estimates of LP returns, especially when the pool is dominated by a few extreme winners or losers.
The S&P 500 is a very bad liquidity pool. An AMM holding all 500 constituents lost about 3% relative to simply holding over the past year, and would need about 45x annual turnover at a 5 basis point fee just to break even.
Dispersion is the main determinant of impermanent loss (IL). How far the assets in the pool diverge explains about 90% of impermanent loss in multi-asset pools, with skewness and kurtosis explaining most of the remainder.
How Distribution Shape Affects Impermanent Loss
The research further tested several distribution shapes.
A left-skewed sample showed the opposite shape: most assets ended together, while a few suffered large losses. It produced only 1.75% impermanent loss. Negative skewness subtracted about 26.8 basis points from the dispersion estimate, while kurtosis added back about 4 basis points. This does not mean downside skewness is a desirable investment strategy; it merely reduces AMM LP losses relative to holding, rather than eliminating them.
A fat-tailed distribution produced 2.30% impermanent loss: the common dispersion term contributed 1.98 percentage points, skewness contributed less than 1 basis point, kurtosis contributed about 19.8 basis points, and fifth-order and higher effects contributed another 11.7 basis points.
A distribution with a tight center and rare outliers was worse, at 2.80% impermanent loss. In that particular sample, positive skewness contributed 14.2 basis points, kurtosis contributed 56.1 basis points, and higher-order terms contributed another 11.7 basis points.
A balanced bimodal distribution was less severe. Two compact return clusters produced 1.96% impermanent loss, almost identical to a normal distribution with the same dispersion. Skewness contributed less than 1 basis point, kurtosis contributed 1 basis point, and the residual contributed less than 1 basis point. If a basket is reasonably symmetrically split into two blocks, the histogram may look very different without creating much additional impermanent loss.
Therefore, the practical rule is not "avoid kurtosis" or "chase negative skewness." Look at dispersion first, because it still explains most of the LP cost. Then examine the distribution details and their impact. A few runaway winners are especially harmful to AMM LPs, making the apparent dispersion number less reliable. A concentrated downside tail may reduce relative impermanent loss at the same dispersion, but that only reduces the magnitude of the loss relative to holding, rather than eliminating it entirely.
These calculations provide a method for evaluating a pool—after someone else has already chosen the assets. But the more useful question is: how should assets be chosen so that these distribution problems are unlikely to arise in the first place?
Pool the Index, Not Individual Stocks
The answer is: pool the index, not individual stocks. Relative to depositing its constituent stocks, depositing a single index token can reduce the break-even turnover rate by more than 60%. Beyond that, AMMs are best reserved for assets that have a durable reason to stay close, such as dual-class share structures (different voting rights shares), mature industry pairings, and perhaps short-term Treasuries.
Treasury Pools and Stock Lending: The Same Species
Circle has already delegated a large amount of reserve management infrastructure to BlackRock. The question is not whether smart contracts can replace everything BlackRock provides—(currently) they cannot. Reserve managers provide custody, operational control, liquidity, and connections to financial infrastructure, for which there is no comparable cost in DeFi. The narrower question is: in highly standardized short-term government paper, how much of the repetitive work of buying, rolling, and providing liquidity can ultimately become programmable.
Under the reserve framework established by the GENIUS Act, this question becomes even more relevant, because stablecoin growth brings additional demand for cash and short-term government debt. A yield-aware AMM directly connected to minting and redemption rails might eventually return some of the economics of reserve management to the stablecoin or its holders. But it may also forever be vulnerable to being hunted by sophisticated off-chain flows. Both outcomes are plausible; current market infrastructure is not sufficient to pretend there is only one possibility.
Stock lending raises a similar parallel problem. Brokers and other intermediaries provide real credit, collateral, and operational services, but they also retain the spread generated by assets owned by clients. On-chain lending proves that at least part of the spread can flow back to holders. Reserve management and stock lending are essentially the same species: large, redundant, low-information intermediary layers whose profits survive mainly because the infrastructure to bypass them does not yet exist.
Conclusion
I started with three chip stocks and a pool that anyone can create. This framework does identify several legitimate uses for tokenized assets on-chain: index tokens, carefully selected AMM portfolios, lending markets, and perhaps eventually treasury pools behind stablecoins. It also points out which mechanisms are best left alone.
This raises a serious question: for commoditized markets whose distribution characteristics happen to match the advantages of AMMs (low return dispersion, high information asymmetry, high trading volume), are AMMs really suitable? Or, as other papers speculate, will the programmatic nature of smart contracts, delayed settlement, and the slightly slower prices of blockchain transactions make AMMs forever prey to sophisticated off-chain capital flows?
Curve allows anyone to create pools permissionlessly, but the market is under no obligation to make your idea a good one.
