On the Development of Systematic Crypto Trading Strategies: Lessons from Bayesian Optimization and Game Theory

Cryptocurrencies, and in particular alt-coins, offer a new horizon for investors. Illiquidity and market inefficiencies lead to volatile markets that have the potential for high returns relative to traditional equities. When these inefficiencies are correctly exploited, investors can achieve an outsized return that is virtually impossible to obtain in better-known tokens or traditional markets.

Here, we examine the inefficiencies present in the markets of lesser-known tokens, focusing on liquidity beta and strategies to generate alpha around the phenomenon.


In low-liquidity equity markets, buyers often pay an illiquidity discount due to the decreased ability to offload the asset. Crypto assets tend to mirror low-volume traditional equities, these assets have shown increased risk premiums and volatility but have illustrated the opportunity for annualized returns notably higher than the greater market.² This is likely attributable to delayed price formation and wider bid-ask spreads along with an initial illiquidity discount.

The above graph illustrates the liquidity premium in Bitcoin during a portion of November 2012 when it was significantly more illiquid than the present-day. After WordPress announced its acceptance of BTC, the illiquidity discount decreased as there was an additional widely used outlet to spend Bitcoin.


Volume fluctuations are also very common when dealing with these tokens. An increase in volume tends to be accompanied by a rise in the value of the token, given that mechanisms such as short selling and futures are not supported for many low-volume altcoins. It has been hypothesized that this phenomenon when combined with the resale option hypothesis, leads to an overvaluation among tokens and lower levels of return against tokens that do not exhibit the same level of positive heterogeneous beliefs.⁸

Units of Precision

Units of precision vary greatly between tokens, depending on the trading venue and the necessity of a more precise denomination. Some tokens have asset values that translate to minuscule amounts of Bitcoin. Even though BTC can be denominated in up to 10 decimal places, the value of some tokens is close to this threshold. Traditional equities diverge from crypto in this sense because the process of underwriting assets results in the primary sale to highly sophisticated market makers; this ensures that there is liquidity from inception. In crypto, these types of market participants are largely absent and those that are present tend not to participate in markets outside of the larger capitalization assets, making techniques such as increased units of precision more critical for market maturation. This burden falls on the exchanges that support those altcoin markets, where an increase in units of precision lowers the barriers for minimum positions paving the wave for a greater trade flow, especially among retail investors.

While it would seem that exchanges that offer greater units of precision for tokens tend to have higher volume and liquidity, this is not necessarily the case. It is true that markets being quoted in higher fidelity denominations create more price levels; however, volume and liquidity do not always have a causal relationship with these factors. For nearly all spot markets of assets supported on Binance and other competitors such as Huobi Global and KuCoin, Binance regularly maintains greater trade volume and more liquid order books. Binance offers few units of precision for these common markets though. Also, though there are a handful of dominant players in the space, the large number of cryptocurrency exchanges further contributes to market inefficiency.

Exchanges have vastly different levels of efficiency, and in some cases, single exchanges boast nearly all the volume of a trading pair, while in others, there is a much more even divide across venues. Haslag and Ringgenberg found that within low volume equities, fragmentation causes “increased bid-ask spreads, worse price efficiency, and more variability in liquidity,” a problem that has plagued cryptocurrencies. However, this level of cross-venue inefficiency creates repetitive trading opportunities.

State of Cryptocurrency Markets

There are a wide variety of cryptocurrencies that span from defensible utilities and tokens to tokens with questionable value propositions. However, a sizable amount of trading volume comes from quantitative traders who are exploiting market inefficiencies. These participants, who deploy strategies, such as liquidity provision, can help dampen volatility and lead to an increased efficiency among the tokens. Although the price of a defunct asset can drastically drop if it is removed from an exchange, events like this are rare, portfolio impact can be mitigated with appropriate diversification. The sheer number of cryptocurrency exchanges also increases the degree of fragmentation compared to traditional equities, creating further pricing inefficiencies. These rapidly evolving market conditions offer constantly evolving trading opportunities. The models postulated by modern game theory provide a compelling paradigm to develop optimal capital allocation strategies.

Modeling Markets with Competitive Coevolution

Competitive coevolution presents a highly applicable framework to model our interaction in cryptocurrency markets. In short, competitive coevolution is used to describe the interactions and development of strategies between players over time. Using competitive coevolution to model markets better prepares us for conditions down the road that are much harder for traditional models to predict, namely the interactions of market participants in cryptocurrency markets.

In order to be profitable, one needs a strategy more effective than those of other traders or competitors. As an increasing number of competitors deploy similar strategies, the gain of each individual market participant utilizing it decreases; thus strategies become less lucrative over time. Therefore, the return generated from any one strategy tends to follow a long-tailed distribution over time. Traders who use a diverse set of strategies with minimal correlation are able to adjust trading parameters better than those who do not in order to stay competitive.⁴

The above graph illustrates the return of strategies over a period of time. As the strategy is deployed for longer, it becomes less effective due to changing market conditions and the interactions of other firms in the space. For this reason, improvements or new strategies need to be deployed when return hits an inflection point in order to maintain consistent returns over a period of time. The labels given to the three S-curves only represent one of many possible scenarios in regard to our strategy development.


We determine the optimal arrangement of these signals by harnessing a technique known as hyperparameter optimization. This is a mathematical method used to determine the best combination of any number of parameters for maximizing or minimizing an outcome. Traditionally, hyperparameter optimization problems were solved by Grid Search or Random Search algorithms. However, these algorithms are very computationally intensive (expensive on scalable cloud service providers like AWS) and take far too long to solve to be appropriate in the asset management business. This is the case as they go about testing parameter combinations naively in an effort to “stumble upon” optimal combinations. However, Pareto Technologies utilizes an intelligent algorithm derived from Bayesian Search Theory. Bayesian search theory has been used by the U.S. Navy and Coastguard for locating lost ships by pinpointing areas of high probability of finding the lost object under consideration. At Pareto, Bayesian Search is tailored for triangulating into market signals from noise. Our system improves portfolio performance with respect to the aforementioned hyperparameters of our trading algorithms to achieve desired objectives (maximizing Sharpe Ratio, maximize Profit, minimize volatility).

This image is a sample plot of our portfolio allocation system which dynamically allocates AUM to various strategies during changing market conditions. Short strategies will perform best during downturns while volatility trading can squeeze out gains from resistance levels. During an upswing, long-focused strategies will generate the most return.

These parameters can even be surprisingly trivial, as exhibited by the success of quantitative hedge fund manager Jaffray Woodriff. Woodriff’s firm, Quantitative Investment Management, largely uses open, high, low, close data to derive internally created secondary variables. Furthermore, Woodriff explains that analyzing massive sets of data without developing hypotheses or assuming correlations can also lead to successful trading strategies that would not otherwise be detected.³ By employing Bayesian Search Theory, Pareto is able to rapidly comb vast swaths of data for search signals, similar to Woodriff’s low-conviction strategies.

At Pareto, we are guided by contrarianism that demands diverse and inventive approaches to thinking and problem-solving. For this reason, we utilize a multi-strategy approach that allows us to maintain a low portfolio beta and a high Sharpe ratio. Our advanced quantitative and qualitative strategies are continuously adjusted in order to best position ourselves to weather a wide array of market conditions.

By harnessing Bayesian optimized trading algorithms, Pareto’s systems seamlessly trade in hundreds of markets and obtain a risk-adjusted return, minimize concentration risk, and maintain a high degree of defensibility among strategies. At the same time, we focus on growth through the development of new strategies and improved trading techniques to our portfolio.

If you feel that a partnership with Pareto would align with your investment mandate or would like to learn more about our strategies, we encourage you to reach out and would be happy to speak in further detail about the opportunities with our fund.

Works Cited

[2] Damodaran, Aswath. (2005) Marketability and Value: Measuring the Illiquidity Discount.

[3] Ennkuutan. (2013) Notes and Quotes from Jaffray Woodriffs’s Hedge Fund Market Wizards Interview. Ennlightenment.

[4] Goetzmann, William N and Alok Kumar. (2008). Equity Portfolio Diversification.

[5] Haslag, Peter and Matthew C. Ringgenberg. (2015). The Causal Impact of Market Fragmentation on Liquidity.

[6] Koning, John Paul. (2012). How Bitcoin Illustrates the Idea of a Liquidity Premium. Moneyness.

[7] Wahal, Sunil. Entry, Exit, Market Makers, and the Bid-Ask Spread. (1997). The Review of Financial Studies, Volume 10, Issue 3.

[8] Wei, Wang Chun. (2018). Resale Options and Cryptocurrency Mispricing.



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