New intelligent empowerment for digital transformation ArXiv ID: 2406.18440 “View on arXiv” Authors: Unknown Abstract This study proposes an innovative evaluation method based on large language models (LLMs) specifically designed to measure the digital transformation (DT) process of enterprises. By analyzing the annual reports of 4407 companies listed on the New York Stock Exchange and Nasdaq from 2005 to 2022, a comprehensive set of DT indicators was constructed. The findings revealed that DT significantly improves a company’s financial performance, however, different digital technologies exhibit varying effects on financial performance. Specifically, blockchain technology has a relatively limited positive impact on financial performance. In addition, this study further discovered that DT can promote the growth of financial performance by enhancing operational efficiency and reducing costs. This study provides a novel DT evaluation tool for the academic community, while also expanding the application scope of generative artificial intelligence technology in economic research. ...

The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments ArXiv ID: 2407.09536 “View on arXiv” Authors: Unknown Abstract We engineer blockchain based risk managed portfolios by creating three funds with distinct risk and return profiles: 1) Alpha - high risk portfolio; 2) Beta - mimics the wider market; and 3) Gamma - represents the risk free rate adjusted to beat inflation. Each of the sub-funds (Alpha, Beta and Gamma) provides risk parity because the weight of each asset in the corresponding portfolio is set to be inversely proportional to the risk derived from investing in that asset. This can be equivalently stated as equal risk contributions from each asset towards the overall portfolio risk. We provide detailed mechanics of combining assets - including mathematical formulations - to obtain better risk managed portfolios. The descriptions are intended to show how a risk parity based efficient frontier portfolio management engine - that caters to different risk appetites of investors by letting each individual investor select their preferred risk-return combination - can be created seamlessly on blockchain. Any Investor - using decentralized ledger technology - can select their desired level of risk, or return, and allocate their wealth accordingly among the sub funds, which balance one another under different market conditions. This evolution of the risk parity principle - resulting in a mechanism that is geared to do well under all market cycles - brings more robust performance and can be termed as conceptual parity. We have given several numerical examples that illustrate the various scenarios that arise when combining Alpha, Beta and Gamma to obtain Parity. The final investment frontier is now possible - a modification to the efficient frontier, thus becoming more than a mere theoretical construct - on blockchain since anyone from anywhere can participate at anytime to obtain wealth appreciation based on their financial goals. ...

$\text{“Alpha”}^2$: Discovering Logical Formulaic Alphas using Deep Reinforcement Learning ArXiv ID: 2406.16505 “View on arXiv” Authors: Unknown Abstract Alphas are pivotal in providing signals for quantitative trading. The industry highly values the discovery of formulaic alphas for their interpretability and ease of analysis, compared with the expressive yet overfitting-prone black-box alphas. In this work, we focus on discovering formulaic alphas. Prior studies on automatically generating a collection of formulaic alphas were mostly based on genetic programming (GP), which is known to suffer from the problems of being sensitive to the initial population, converting to local optima, and slow computation speed. Recent efforts employing deep reinforcement learning (DRL) for alpha discovery have not fully addressed key practical considerations such as alpha correlations and validity, which are crucial for their effectiveness. In this work, we propose a novel framework for alpha discovery using DRL by formulating the alpha discovery process as program construction. Our agent, $\text{“Alpha”}^2$, assembles an alpha program optimized for an evaluation metric. A search algorithm guided by DRL navigates through the search space based on value estimates for potential alpha outcomes. The evaluation metric encourages both the performance and the diversity of alphas for a better final trading strategy. Our formulation of searching alphas also brings the advantage of pre-calculation dimensional analysis, ensuring the logical soundness of alphas, and pruning the vast search space to a large extent. Empirical experiments on real-world stock markets demonstrates $\text{“Alpha”}^2$’s capability to identify a diverse set of logical and effective alphas, which significantly improves the performance of the final trading strategy. The code of our method is available at https://github.com/x35f/alpha2. ...

An Improved Algorithm to Identify More Arbitrage Opportunities on Decentralized Exchanges ArXiv ID: 2406.16573 “View on arXiv” Authors: Unknown Abstract In decentralized exchanges (DEXs), the arbitrage paths exist abundantly in the form of both arbitrage loops (e.g. the arbitrage path starts from token A and back to token A again in the end, A, B,…, A) and non-loops (e.g. the arbitrage path starts from token A and stops at a different token N, A, B,…, N). The Moore-Bellman-Ford algorithm, often coupled with the ``walk to the root" technique, is commonly employed for detecting arbitrage loops in the token graph of decentralized exchanges (DEXs) such as Uniswap. However, a limitation of this algorithm is its ability to recognize only a limited number of arbitrage loops in each run. Additionally, it cannot specify the starting token of the detected arbitrage loops, further constraining its effectiveness in certain scenarios. Another limitation of this algorithm is its incapacity to detect non-loop arbitrage paths between any specified pairs of tokens. In this paper, we develop a new method to solve these problems by combining the line graph and a modified Moore-Bellman-Ford algorithm (MMBF). This method can help to find more arbitrage loops by detecting at least one arbitrage loop starting from any specified tokens in the DEXs and can detect the non-loop arbitrage paths between any pair of tokens. Then, we applied our algorithm to Uniswap V2 and found more arbitrage loops and non-loops indeed compared with applying the Moore-Bellman-Ford (MBF) combined algorithm. The found arbitrage profit by our method in some arbitrage paths can be even as high as one million dollars, far larger than that found by the MBF combined algorithm. Finally, we statistically compare the distribution of arbitrage path lengths and the arbitrage profit detected by both our method and the MBF combined algorithm, and depict how potential arbitrage opportunities change with time by our method. ...

Optimizing Sparse Mean-Reverting Portfolio ArXiv ID: 2406.17155 “View on arXiv” Authors: Unknown Abstract Mean-reverting behavior of individuals assets is widely known in financial markets. In fact, we can construct a portfolio that has mean-reverting behavior and use it in trading strategies to extract profits. In this paper, we show that we are able to find the optimal weights of stocks to construct portfolio that has the fastest mean-reverting behavior. We further add minimum variance and sparsity constraints to the optimization problem and transform into Semidefinite Programming (SDP) problem to find the optimal weights. Using the optimal weights, we empirically compare the performance of contrarian strategies between non-sparse mean-reverting portfolio and sparse mean-reverting portfolio to argue that the latter provides higher returns when we take into account of transaction costs. ...

Profit Maximization In Arbitrage Loops ArXiv ID: 2406.16600 “View on arXiv” Authors: Unknown Abstract Cyclic arbitrage chances exist abundantly among decentralized exchanges (DEXs), like Uniswap V2. For an arbitrage cycle (loop), researchers or practitioners usually choose a specific token, such as Ether as input, and optimize their input amount to get the net maximal amount of the specific token as arbitrage profit. By considering the tokens’ prices from CEXs in this paper, the new arbitrage profit, called monetized arbitrage profit, will be quantified as the product of the net number of a specific token we got from the arbitrage loop and its corresponding price in CEXs. Based on this concept, we put forward three different strategies to maximize the monetized arbitrage profit for each arbitrage loop. The first strategy is called the MaxPrice strategy. Under this strategy, arbitrageurs start arbitrage only from the token with the highest CEX price. The second strategy is called the MaxMax strategy. Under this strategy, we calculate the monetized arbitrage profit for each token as input in turn in the arbitrage loop. Then, we pick up the most maximal monetized arbitrage profit among them as the monetized arbitrage profit of the MaxMax strategy. The third one is called the Convex Optimization strategy. By mapping the MaxMax strategy to a convex optimization problem, we proved that the Convex Optimization strategy could get more profit in theory than the MaxMax strategy, which is proved again in a given example. We also proved that if no arbitrage profit exists according to the MaxMax strategy, then the Convex Optimization strategy can not detect any arbitrage profit, either. However, the empirical data analysis denotes that the profitability of the Convex Optimization strategy is almost equal to that of the MaxMax strategy, and the MaxPrice strategy is not reliable in getting the maximal monetized arbitrage profit compared to the MaxMax strategy. ...

Computing the SSR ArXiv ID: 2406.16131 “View on arXiv” Authors: Unknown Abstract The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion setting, it is well-known that the short-term limit of the SSR is 2; a corollary of our results is that this limit is $H+3/2$ where $H$ is the Hurst exponent of the volatility process. The general formula for the SSR simplifies and becomes particularly tractable in the affine forward variance case. We explain the qualitative behavior of the SSR with respect to the shape of the forward variance curve, and thus also path-dependence of the SSR. ...

Covariance Matrix Analysis for Optimal Portfolio Selection ArXiv ID: 2407.08748 “View on arXiv” Authors: Unknown Abstract In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. This inverse covariance matrix also prescribes the hedge trades in which a stock is hedged by all the other stocks in the portfolio. In practice with finite samples, however, multicollinearity gives rise to considerable estimation errors, making the hedge trades too unstable and unreliable for use. By adopting ideas from current methodologies in the existing literature, we propose 2 new estimators of the inverse covariance matrix, one which relies only on the l2 norm while the other utilizes both the l1 and l2 norms. These 2 new estimators are classified as shrinkage estimators in the literature. Comparing favorably with other methods (sample-based estimation, equal-weighting, estimation based on Principal Component Analysis), a portfolio formed on the proposed estimators achieves substantial out-of-sample risk reduction and improves the out-of-sample risk-adjusted returns of the portfolio, particularly in high-dimensional settings. Furthermore, the proposed estimators can still be computed even in instances where the sample covariance matrix is ill-conditioned or singular ...

International Trade Flow Prediction with Bilateral Trade Provisions ArXiv ID: 2407.13698 “View on arXiv” Authors: Unknown Abstract This paper presents a novel methodology for predicting international bilateral trade flows, emphasizing the growing importance of Preferential Trade Agreements (PTAs) in the global trade landscape. Acknowledging the limitations of traditional models like the Gravity Model of Trade, this study introduces a two-stage approach combining explainable machine learning and factorization models. The first stage employs SHAP Explainer for effective variable selection, identifying key provisions in PTAs, while the second stage utilizes Factorization Machine models to analyze the pairwise interaction effects of these provisions on trade flows. By analyzing comprehensive datasets, the paper demonstrates the efficacy of this approach. The findings not only enhance the predictive accuracy of trade flow models but also offer deeper insights into the complex dynamics of international trade, influenced by specific bilateral trade provisions. ...

Asymptotic methods for transaction costs ArXiv ID: 2407.07100 “View on arXiv” Authors: Unknown Abstract We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems from optimally tracking benchmarks, hedging the Log contract, to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity. ...