August 2, 2021

## Overview

LVL Market Making users earned a portfolio return of 76% in Q2 2021. The average user return for the quarter was 15% and the standard deviation among user returns was 24%. Cash-on-cash returns for the same period were -2.9%, outpacing Bitcoin and Litecoin by 65% and 11% respectively, while under pacing Ethereum by 17%.

LVL Market Making holds cash and crypto, earns income in cash and crypto, and the returns are calculated in terms of cash and crypto. You can find more information on how returns are calculated in the Results section below.

## Exchange Liquidity

Investopedia defines market liquidity as follows:

Market liquidity refers to the extent to which a market, such as a country's stock market or a city's real estate market, allows assets to be bought and sold at stable, transparent prices.

For a cryptocurrency exchange like LVL, Coinbase, or Gemini, liquidity breaks down into:

1. Price efficiency - How close the exchange spot price is to the prevailing price of the asset in the broader market. The prevailing price could be based on prices on other high volume exchanges or a volume-weighted average of the prices, for example as can be found on CoinMarketCap.
2. Depth - How much inventory can be bought or sold for close to the exchange spot price. This incorporates the concept of slippage into the definition of liquidity. An exchange with poor depth may have a spot price very near the prevailing price, but slippage causes trades to execute at a different, less efficient price. CoinMarketCap incorporates the concept of slippage by reporting the 2% depth of the order book in their analysis of exchanges.

In order to operate continuously, a cryptocurrency exchange must maintain price efficiency and depth at all times. Liquidity providers satisfy this need by maintaining a pool of assets (or credit) on an exchange, which is continuously priced to sell at a small premium to the prevailing price. For example, if an exchange has one liquidity provider, and that liquidity provider is offering to sell 1 Bitcoin for 1% more than the prevailing price, then that exchange has a price inefficiency of 1% and a sell depth of 1 Bitcoin. Liquidity providers earn income from the 1% spread, are asset agnostic, and attempt to hold cash and Bitcoin at all times.

Traditional exchanges like Coinbase and Gemini incentivize third-party liquidity providers (LPs) by offering discounts based on trading volume and for trades that make liquidity. LPs factor out trading and compliance risk for exchanges in return for access to retail order flow and steeply discounted pricing. Exchanges and LPs work together to help millions of new users buy Bitcoin each year and create enormous value for the cryptocurrency ecosystem. However, the exclusive nature of liquidity providing and obscure structure of the cryptocurrency markets makes it difficult for the markets to efficiently price the value exchanges and LPs create. Here are two problems:

• Information asymmetry - For retail traders using its app, Coinbase charges a 0.5% spread fee, a 1.5% trading fee, for a total cost of 2%, and an additional "Coinbase Fee" for any trades less than \$200 in value, presumably the vast majority of retail trades. The Coinbase Fee raises the commission charged by Coinbase to as high as 10% for orders less than \$10. This 2-10% consumer fee imposed on retail users is 50-250 times the 0.04% institutional fee imposed on high volume liquidity providers. LPs take substantial commercial risk and deserve to get paid, but it comes at the expense of the consumer.

The cryptocurrency market, like Bitcoin itself, is a network of trust. Exchanges, LPs, and retails traders are all required for the efficient functioning of the market. And the more decentralized the network participants become, the more robust the network is. Retail participation in Bitcoin is exploding. Exchanges, while still oligopolistic, are becoming more competitive with new platform entrants such as Binance and BlockFi wrestling significant market share from incumbents in recent years. Liquidity providing, on the other hand, is still largely exclusive and concentrated amongst few market participants. This leads to inefficient market pricing and startling concentration of profits.

## LVL Market Making

LVL's mission is to level the financial playing field by providing premium financial services to everyone. To ensure a level playing field on our own marketplace, LVL Exchange was designed with two key design objectives:

1. No trading fees - LVL would not charge a trading fee (like Coinbase) to allow an even playing field for all users.
2. User generated liquidity - Liquidity providing tools would be provided by LVL and made available to all Premium users.

In April 2019, we introduced Automated Market Makers (AMM), an automated user account that provided continuous, automated market making on LVL. At the time, LVL only supported crypto-to-crypto trading and had less than a hundred users. Uniswap v1 had launched at Devcon 4 only four months earlier, and decentralized liquidity providing was a brand new idea. Over the following two years we iterated on AMMs until they functioned as a reliable provider of liquidity on LVL. We learned how to make AMMs work in the typical fashion of doing it wrong for a while and then using data to fix it. Two significant breakthroughs in AMM performance were the introduction of Constant Product Pricing—an idea from decentralized exchanges—and introducing arbitrage with SFOX, Kraken, and BitGo. After introducing arbitrage in March 2021, LVL has experienced continuous liquidity and no sell outs. This unbroken period of liquidity has allowed us to release our first longitudinal study on AMM performance for Q2.

LVL combines market making and arbitrage in a single feature referred to simply as Market Making. The basic theory of operation of Market Making is as follows:

1. Hold 50/50 cash and crypto - Market Making is asset neutral, meaning it has no preference between cash and crypto. By default, Market Making holds 50% cash to post buys and 50% crypto to post sells. The crypto is held proportional to a volume-weighted index. This cash and crypto portfolio allocation is the multi-armed bandit solution to maximize order execution assuming sells and buys are equally likely. During Q2, the portfolio allocation was roughly 50% cash, 35% Bitcoin, 12% Ethereum, and 3% Litecoin. Note that, due to fluctuations in market price and the additional trading activities below, the portfolio allocation may deviate from this target allocation in part or in full. This position can be considered the "baseline" portfolio from which trading activities are conducted. Market Making results in the next section are evaluated relative to this baseline.
3. Arbitrage with external LPs - Market Making posts its overweight position of any asset as limit orders with external liquidity providers. For example, if Market Making is holding 25% cash and 75% Bitcoin by notional value (25/75), it will post limit sells for up to 25% of its notional value with external liquidity providers. The limit orders are executed using smart order routing. LVL currently has arbitrage relationships with SFOX, Kraken, and BitGo. During Q2, SFOX was the only enabled arbitrage counterparty.

We believe that a useful interpretation of Market Making is as a passive volume-weighted index strategy with opportunistic active trading via market making and arbitrage. The active trading is opportunistic because market making and arbitrage limit orders do not execute unless the the marginal spread profit is met. In exchange for this marginal income, Market Making users incur the opportunity cost of committing assets to Market Making and inventory risk experienced when the underlying portfolio deviates from the baseline strategy. To maximize marketplace health and order execution, the two active strategies are prioritized in order of liquidity objective. Market Makers first market make to ensure depth on LVL, then use only their overweight position to ensure price efficiency.

## Results

To motivate analysis of Market Making returns, consider the example of holding a portfolio of fixed interest accounts for cash and Bitcoin. The Bitcoin account is denominated in, and pays interest in terms of, Bitcoin. Both interest accounts offer a 3% APY. It's intuitive to declare the interest rate on the Bitcoin account as 3%, not "3% + volatility" because by opening a Bitcoin interest account at all, the user takes a long position and has risked-in asset volatility. The main difference between this example and Market Making is that Market Making pools together cash and crypto and earns income on both pro rata. Nonetheless, Market Making users expect roughly 50% exposure to Bitcoin and in doing so take a hedged long position on Bitcoin and risk-in Bitcoin volatility. Therefore, the returns of Market Making should be viewed as the appreciation of assets, less volatility of the underlying index position, over time. In this section, we review the volume-weighted index strategy and develop the yield of active Market Making relative to that passive index.

We first review the return profile of the volume weighted index strategy. A volume-weighted index holds a portfolio of assets proportional to trading volume. In the second quarter, the portfolio was allocated 50% to cash and 50% to crypto. The allocation among crypto, $(v_b, v_e, v_l)$, was 70% for Bitcoin, 24% for Ethereum, and 6% for Litecoin. For a given day $t$ and daily returns $r_c(t)$, $r_b(t)$, $r_e(t)$, and $r_l(t)$ for cash, Bitcoin, Ethereum, and Litecoin, respectively, the daily return of the index $r_0(t)$ is:

$$r_0(t) = \frac{1}{2}\left(v_b \cdot r_b(t) + v_e \cdot r_e(t) + v_l \cdot r_l(t) \right)$$

Given absolute returns $r_A(t)$ for Market Making, then the Market Making returns $r(t)$ are given as:

$$r(t) = r_A(t) - r_0(t)$$

To produce these results, we studied all 186 liquidity providers on LVL in Q2 with 30 days or more of active Market Making. For each participant, we calculated their daily return according to the above formula, excluding days with major deposits or redemptions (+ / - 50% of account value). Only account-days with balances of \$20 or greater were considered. In total, these results represent 15,020 study-days across 186 LPs for an average of 80.75 study-days per user. We believe this focuses the study on representative users who participated in Market Making throughout the quarter while not "cherry picking" longer holding times. For example, expanding the study criteria to users with at least 5 study days before (256 total users) impacted total returns by less than 1%. To analyze the overall performance of Market Making, we calculated average (by user) daily return$r(t)$and the portfolio total return$R = \prod_t (1 + r(t)) - 1$. The portfolio return$R$was 11% for the quarter. Absolute return$R_A$for the same period was -2.9%, outpacing Bitcoin and Litecoin by 65% and 11% respectively, while underperforming Ethereum by 17%. In comparison, the index return$R_0$was -12.5%. As seen below, the absolute total return$R_A$tracked very closely to the theoretical index return$R_0$. This resulted in predictable returns$R$. The average per-user total return for the quarter was 15% and the standard deviation among user returns was 24%, resulting in a Sharpe ratio of 0.64. Of the users considered in the report, 77% earned a profit in Q2 compared to the baseline strategy, while 23% of users experienced a loss. There was no correlation between account size and return ($R^2 = 0.0085$), while trading volume was predictive of return ($R^2 = 0.0557\$). Here, trading volume is measured as the total notional trading volume divided by the mean intra-period notional balance. This is sometimes called turnover. Market Making exhibited a beta of 0.64, demonstrating a substantial reduction in volatility compared to the baseline index, reflecting the utility nature of Market Making.

## Risk Disclosure

Market Making is a feature available with LVL Premium that allows users to automatically market make with their holdings on LVL. Market Making accounts are separated and separately directed by users. LVL does not pool user funds together, offer a hedge fund, or provide performance guarantees for Market Making.

No investment strategy can completely eliminate the risk of investment losses. You are responsible for the risks and the financial resources you use to determine an investment strategy. You should not engage in trading unless you fully understand the nature of the transactions you are participating in and the extent of your exposure and tolerance for investment losses. If you do not fully understand the risks involved in trading, we encourage you to seek independent advice from a financial advisor.

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