Rebalancing Strategy Research Articles

Sell the losers? Keep the winners? None of the above – Focus on the median!

This paper presents an approach to index portfolio re-balancing, focusing on the median slice of asset performance instead of the more traditional focus on “winners” and “losers.” In the proposed approach, one constructs an equal-weight portfolio from the index’s median (by returns) component. We consider the Dow Jones Industrial Average (DJIA) as a case study and introduce a systematic re-balancing strategy that targets the middle third (“median”) segment of asset performers within the index. The proposed methodology provides significantly better returns and mitigates drawdowns compared with a passive “buy-and-hold” strategy while promoting a disciplined and simple portfolio re-balancing strategy. The study empirically evaluates the effectiveness of the median-based re-balancing strategy over historical data. We compare our strategy to a benchmark portfolio closely tracking the DJIA index and other popular re-balancing strategies focusing on winners and losers, including the Dogs of the Dow strategy. We provide a simple model to compare factor loadings offered by such strategies and show that the median strategy provides broad diversification across sectors. We also analyze factor exposures of the proposed strategy using the 3-factor Fama-French model. The analysis demonstrates that the “median” rotation strategy consistently outperforms the Dow Jones and the broad market index S&P-500, yielding higher returns and reduced drawdowns.

Stochastic Analysis of Buy and Hold Versus Annual Rebalancing Portfolio Strategies

Numerous articles in the literature develop theoretical mathematical models that prove rebalancing investment portfolios will outperform a buy and hold strategy on a risk adjusted basis. However, a number of authors using varying asset classes and time periods have found instances where buy and hold outperforms a rebalancing strategy on a risk adjusted basis. This research shows that both can be correct. Most of the papers found in the literature use historical prices and price changes to validate their findings. The research effort detailed in this paper simulates a wide range of possible future asset pricing scenarios that do not rely on historical price patterns. These findings suggest that differences between these two strategies, at a more detailed level, favor the rebalancing strategy, but not exclusively.

A Data-Driven Optimization Framework for Static Rebalancing Operations in Bike Sharing Systems

Bike sharing systems have been widely deployed in urban cities for first- and last-mile transportation. However, because of the geographical and temporal imbalance of bike demand, bikes need to be reallocated system-wide among stations during the night to maintain a high service level while minimizing demand loss due to stockout or overcapacity. Two technical challenges remain in optimizing the static bike rebalancing operations. One challenge is to accurately predict bike pickup and dropoff demand at each station, considering demand substitution effects and subsequently determining the optimal rebalancing quantity for each station. The other is to efficiently optimize the routing of multiple rebalancing vehicles for large-scale bike sharing systems, considering outlier stations with rebalancing quantities exceeding vehicle capacity. To this end, we propose an end-to-end solution to tackle the aforesaid challenges. Specifically, we first develop deep learning-based predictors that capture the time dependencies of station-level demand, the impact of weather conditions, and the demand substitution effect by nearby stations. Based on the demand rate, a sequential simulation-based demand loss estimator is developed to find the optimal rebalancing quantities that lead to the minimum expected demand loss. Then, a mixed integer linear programming model is formulated to optimize the routing problem of rebalancing vehicles. To address the computational challenge, we propose a data-driven decomposition algorithm to support a multivehicle multivisit rebalancing strategy by decomposing the multivehicle routing problem into smaller and tractable single-vehicle routing problems, which can be solved in parallel. Finally, extensive numerical experiments using real-world data from New York City Citi Bike demonstrate the accuracy of the proposed bike demand predictors, the impact of demand substitution, and the efficiency of the data-driven optimization framework. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported by the National Natural Science Foundation of China [Grant 72201222] and the Hong Kong Research Grants Council [Grants CityU 21500220 and CityU 11504322]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0182 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0182 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Standby component replacement strategy for a balanced system with a standby pool

In this paper, a new rebalancing strategy is proposed by replacing the standby components for a balanced system with a standby pool. The working components are connected in series. All standby components are stored in a standby component pool. When the working components do not fail and the balance degree of the system does not exceed a threshold, the system can operate normally. The balance degree of the system is defined as the maximum state difference of all the working components. If the system becomes unbalanced or fails, a qualified standby component in the standby pool should be selected to replace the working component. The replacement strategy is given in detail. This paper uses the discrete-state continuous-time Markov process to derive the system reliability. Finally, a numerical example and sensitivity analysis are given. Considering the downtime cost and the cost of purchasing standby components, the number of standby components in the standby pool is optimized.

Overcoming CRISPR-Cas9 off-target prediction hurdles: A novel approach with ESB rebalancing strategy and CRISPR-MCA model.

The off-target activities within the CRISPR-Cas9 system remains a formidable barrier to its broader application and development. Recent advancements have highlighted the potential of deep learning models in predicting these off-target effects, yet they encounter significant hurdles including imbalances within datasets and the intricacies associated with encoding schemes and model architectures. To surmount these challenges, our study innovatively introduces an Efficiency and Specificity-Based (ESB) class rebalancing strategy, specifically devised for datasets featuring mismatches-only off-target instances, marking a pioneering approach in this realm. Furthermore, through a meticulous evaluation of various One-hot encoding schemes alongside numerous hybrid neural network models, we discern that encoding and models of moderate complexity ideally balance performance and efficiency. On this foundation, we advance a novel hybrid model, the CRISPR-MCA, which capitalizes on multi-feature extraction to enhance predictive accuracy. The empirical results affirm that the ESB class rebalancing strategy surpasses five conventional methods in addressing extreme dataset imbalances, demonstrating superior efficacy and broader applicability across diverse models. Notably, the CRISPR-MCA model excels in off-target effect prediction across four distinct mismatches-only datasets and significantly outperforms contemporary state-of-the-art models in datasets comprising both mismatches and indels. In summation, the CRISPR-MCA model, coupled with the ESB rebalancing strategy, offers profound insights and a robust framework for future explorations in this field.

Modulating bacterial function utilizing A knowledge base of transcriptional regulatory modules.

Synthetic biology enables the reprogramming of cellular functions for various applications. However, challenges in scalability and predictability persist due to context-dependent performance and complex circuit-host interactions. This study introduces an iModulon-based engineering approach, utilizing machine learning-defined co-regulated gene groups (iModulons) as design parts containing essential genes for specific functions. This approach identifies the necessary components for genetic circuits across different contexts, enhancing genome engineering by improving target selection and predicting module behavior. We demonstrate several distinct uses of iModulons: (i) discovery of unknown iModulons to increase protein productivity, heat tolerance and fructose utilization; (ii) an iModulon boosting approach, which amplifies the activity of specific iModulons, improved cell growth under osmotic stress with minimal host regulation disruption; (iii) an iModulon rebalancing strategy, which adjusts the activity levels of iModulons to balance cellular functions, significantly increased oxidative stress tolerance while minimizing trade-offs and (iv) iModulon-based gene annotation enabled natural competence activation by predictably rewiring iModulons. Comparative experiments with traditional methods showed our approach offers advantages in efficiency and predictability of strain engineering. This study demonstrates the potential of iModulon-based strategies to systematically and predictably reprogram cellular functions, offering refined and adaptable control over complex regulatory networks.

Safe haven between European ESG and energy sector under Russian-Ukraine war: Role of sustainable investments for portfolio diversification

The shortage of oil and gas supply to Europe during the Russia-Ukraine conflict has triggered a price hike in the European energy sector. To mitigate the impact of higher energy prices on consumers, the EU introduced a price ceiling mechanism to curb gas prices from exceeding market norms. This interplay between supply shortages and price controls further heightened volatility in energy market prices. Consequently, our study aims to explore the efficacy of ESG indices as a safe haven against the highly volatile European oil and gas sectors to reduce portfolio losses during conflict. Using advanced analytical techniques such as cross-quantilogram to predict directional predictability, we find that bullish ESG markets are a safe haven against the bearish oil and gas markets in short, medium, and long-term investment horizons. Further, to identify the net receiver/transmitter of spillover between ESG indices and oil and gas sectors, our quantile time-frequency connectedness analysis shows ESG is a net receiver of spillover before the conflict and during wartime. Additionally, we explored the indicator of uncertainty that influences quantile spillover between ESG indices and European oil and gas sectors. We find that uncertainty's role in quantile spillover is significant and asymmetric, and it becomes more volatile during wartime. This feature tends to be amplified during short and long-term spillovers. Finally, the portfolio rebalance strategy suggests that a safe haven portfolio based on a one-month investment horizon yields positive returns during wartime. Hence, this study suggests investors include ESG indices as safe haven assets at times of crisis and for policymakers to understand the role of uncertainties in reducing price volatility and risk contagion among ESG and energy markets.

Identifying the Nonlinear Impacts of Road Network Topology and Built Environment on the Potential Greenhouse Gas Emission Reduction of Dockless Bike-Sharing Trips: A Case Study of Shenzhen, China

Existing studies have limited evidence about the complex nonlinear impact mechanism of road network topology and built environment on bike-sharing systems’ greenhouse gas (GHG) emission reduction benefits. To fill this gap, we examine the nonlinear effects of road network topological attributes and built environment elements on the potential GHG emission reduction of dockless bike-sharing (DBS) trips in Shenzhen, China. Various methods are employed in the research framework of this study, including a GHG emission reduction estimation model, spatial design network analysis (sDNA), gradient boosting decision tree (GBDT), and partial dependence plots (PDPs). Results show that road network topological variables have the leading role in determining the potential GHG emission reduction of DBS trips, followed by land use variables and transit-related variables. Moreover, the nonlinear impacts of road network topological variables and built environment variables show certain threshold intervals for the potential GHG emission reduction of DBS trips. Furthermore, the impact of built environment on the potential GHG emission reduction of DBS trips is moderated by road network topological indicators (closeness and betweenness). Compared with betweenness, closeness has a greater moderating effect on built environment variables. These findings provide empirical evidence for guiding bike-sharing system planning, bike-sharing rebalancing strategy optimization, and low-carbon travel policy formulation.

When to efficiently rebalance a portfolio

A constant weight asset allocation is a popular investment strategy and is optimal under a suitable continuous model. We study the tracking error for the target continuous rebalancing strategy by a feasible discrete-in-time rebalancing under a general multi-dimensional Brownian semimartingale model of asset prices. In a high-frequency asymptotic framework, we derive an asymptotically efficient sequence of simple predictable strategies.

Multi-class imbalance problem: A multi-objective solution

Multi-class imbalance problems are frequently encountered in real-world applications of machine learning. They have fundamentally complex trade-offs between classes. Existing literature tends to use a predetermined rebalancing strategy and mainly focuses on overall performance measures. However, in many real-world problems, the true level of imbalance and the relative importance between classes are unknown, making it difficult to predetermine the rebalancing strategy and the evaluation criterion. In this paper, we explicitly consider the between-class trade-off issue in the multi-class imbalance problem. We consider all the classes to be important and find a set of optimal trade-offs for the decision-maker to choose from. To reduce the computational cost of this process and make it a practical method, we seek the help of selective ensemble and multiple undersampling rates, and propose the Multi-class Multi-objective Selective Ensemble (MMSE) framework. We further equip the objective modeling with margins to reduce the number of objectives when the task has many classes. Experimental results show that our proposed methods successfully obtain diverse and highly competitive solutions within an acceptable running time.

Safe haven properties of industrial stocks against ESG in the United States: Portfolio implication for sustainable investments

This study explores the safe haven role of industry sectors classified by the Global Industry Classification Standards (GICS) for global Environmental, Social, and Governance (ESG) stocks in the United States. Our study applies the novel cross-quantilogram and quantile time-frequency connectedness approach for daily time series data from November 2019 to October 2023. Our findings confirm that industry sectors, mainly financials, industrial, communication, information technology, energy, consumer staples, and consumer discretionary, are the safe haven avenues at down, normal, and up market conditions; however, these safe haven avenues vanish for the long-term investment horizon. We also explore the risk spillover patterns for the total time domain and the decomposed spillover level for the short- and long-term spillovers. Our connectedness finding shows that the net transmitters and net receiver patterns are similar for the extreme markets but dramatically change for the normal markets. Finally, based on the portfolio rebalancing strategy, the returns of our portfolio, comprised of industry sectors and the ESG index, outperform the overall market. Moreover, our portfolio yields lower negative returns and a higher Sharpe ratio when compared with the overall market returns. These findings confirm the benefits of diversification by reducing downside portfolio risk. This study is primarily relevant for socially responsible portfolio and risk management investors.

Induced dual-target rebalance simultaneously enhances efficient therapeutical efficacy in tumors

Multiple gene abnormalities are major drivers of tumorigenesis. NF-κB p65 overactivation and cGAS silencing are important triggers and genetic defects that accelerate tumorigenesis. However, the simultaneous correction of NF-κB p65 and cGAS abnormalities remains to be further explored. Here, we propose a novel Induced Dual-Target Rebalance (IDTR) strategy for simultaneously correcting defects in cGAS and NF-κB p65. By using our IDTR approach, we showed for the first time that oncolytic adenovirus H101 could reactivate silenced cGAS, while silencing GAU1 long noncoding RNA (lncRNA) inhibited NF-κB p65 overactivation, resulting in efficient in vitro and in vivo antitumor efficacy in colorectal tumors. Intriguingly, we further demonstrated that oncolytic adenoviruses reactivated cGAS by promoting H3K4 trimethylation of the cGAS promoter. In addition, silencing GAU1 using antisense oligonucleotides significantly reduced H3K27 acetylation at the NF-κB p65 promoter and inhibited NF-κB p65 transcription. Our study revealed an aberrant therapeutic mechanism underlying two tumor defects, cGAS and NF-κB p65, and provided an alternative IDTR approach based on oncolytic adenovirus and antisense oligonucleotides for efficient therapeutic efficacy in tumors.

Impact of climate policy uncertainty on return spillover among green assets and portfolio implications

Green assets play a crucial role in addressing climate change, encompassing sustainable development, public health improvement, and climate risk mitigation. This study investigates the return spillover among green assets and examines the impact of climate policy uncertainty (CPU) on their interrelationship, using a quantile connectedness approach. Empirical results show that return connectedness among green assets is particularly strong during extreme events, with a surge in total connectedness attributed to increased spillover between the green bond market and other green assets. Additionally, CPU reduces the connectedness among green assets, favouring the idiosyncratic channel over investors' uncertainty channel. Based on these findings, we propose a CPU-driven portfolio rebalancing strategy for green investors to enhance diversification across green stock, green bond, and renewable energy markets. Simulation results demonstrate that the CPU-based portfolios outperform the buy-and-hold portfolio in terms of average monthly returns, standard deviation, and risk-adjusted returns. The research highlights the need for policymakers to acknowledge and address climate policy uncertainty, as it influences the interconnectedness of green assets, offering an opportunity to refine policy frameworks to better support stable and resilient investment environments conducive to sustainable development goals.

Optimizing Cryptocurrency Returns: A Quantitative Study on Factor-Based Investing

This study explores cryptocurrency investment strategies by adapting the robust framework of factor investing, traditionally applied in equity markets, to the distinctive landscape of cryptocurrency assets. It conducts an in-depth examination of 31 prominent cryptocurrencies from December 2017 to December 2023, employing the Fama–MacBeth regression method and portfolio regressions to assess the predictive capabilities of market, size, value, and momentum factors, adjusted for the unique characteristics of the cryptocurrency market. These characteristics include high volatility and continuous trading, which differ markedly from those of traditional financial markets. To address the challenges posed by the perpetual operation of cryptocurrency trading, this study introduces an innovative rebalancing strategy that involves weekly adjustments to accommodate the market’s constant fluctuations. Additionally, to mitigate issues like autocorrelation and heteroskedasticity in financial time series data, this research applies the Newey–West standard error approach, enhancing the robustness of regression analyses. The empirical results highlight the significant predictive power of momentum and value factors in forecasting cryptocurrency returns, underscoring the importance of tailoring conventional investment frameworks to the cryptocurrency context. This study not only investigates the applicability of factor investing in the rapidly evolving cryptocurrency market, but also enriches the financial literature by demonstrating the effectiveness of combining Fama–MacBeth cross-sectional analysis with portfolio regressions, supported by Newey–West standard errors, in mastering the complexities of digital asset investments.

Optimizing Cryptocurrency Portfolios: A Comparative Study of Rebalancing Strategies

Objective – This study aims to contribute to the field of cryptocurrency portfolio management and rebalancing strategies by empirically investigating the impact of different allocation frequencies and threshold percentages on the risk-adjusted returns of cryptocurrency portfolios. Methodology/Technique – Utilizing a simulation of 10,000 cryptocurrency portfolios comprising seven assets, including Ethereum (ETH), Bitcoin (BTC), Tether (USDT), Litecoin (LTC), Solana (SOL), Dogecoin (DOGE), and Polygon (MATIC), this study examines and compares the effects of different allocation frequencies (daily, weekly, and monthly) in time-based rebalancing and various threshold percentages (5%, 10%, and 15%) in threshold-based strategies on the portfolios' risk-adjusted returns, using the Sharpe ratio. The performance of these strategies is also compared with a passive buy-and-hold strategy. Findings –The research reveals statistically significant differences in the risk-adjusted returns between the buy-and-hold strategy and the daily rebalancing and threshold-based strategies with 5% and 10% threshold percentages. The daily rebalancing strategy demonstrates a higher Sharpe ratio, while lower threshold percentages lead to better risk-adjusted returns. Novelty – These empirical findings, using a simulation of 10,000 cryptocurrency portfolios, provide valuable insights into optimizing cryptocurrency portfolio performance through rebalancing strategies. Additionally, they highlight the effectiveness of implementing rebalancing techniques in cryptocurrency portfolios, contributing to the understanding of rebalancing optimization in this domain. Type of Paper: Empirical JEL Classification: G11, G19. Keywords: Cryptocurrency; Mean-Variance Optimization; Portfolio Management; Rebalancing Strategies; Risk-Adjusted Returns Reference to this paper should be made as follows: Sornmayura, S; Sakolvieng, N; Numgaroonaroonroj, K. (2024). Optimizing Cryptocurrency Portfolios: A Comparative Study of Rebalancing Strategies, J. Fin. Bank. Review, 8(4), 01 – 16. https://doi.org/10.35609/jfbr.2024.8.4(1)

Optimal portfolio selection with volatility information for a high frequency rebalancing algorithm

We propose a high-frequency rebalancing algorithm (HFRA) and compare its performance with periodic rebalancing (PR) and threshold rebalancing (TR) strategies. PR refers to the process of adjusting the relative weight of assets within portfolios at regular time intervals, whereas TR is a process of setting allocation limits for portfolios and rebalancing when portfolios exceed a specific percentage of deviation from the target allocation. The HFRA is constructed as an integration of pairs trading and a threshold-based rebalancing strategy, and the profitability of the HFRA is examined to determine the optimal portfolio size. The HFRA is applied to a dataset of real price series from cryptocurrency exchange markets across various trends and volatility regimes. Using cointegrated price data, it is shown that increasing the number of assets in a portfolio supports the profitability of the HFRA in an up-trend and reduces the potential loss of the HFRA in a down-trend in a high-volatility environment. For low-volatility regimes, although increasing portfolio size marginally enhances the HFRA’s profitability, the profits of portfolios of varied sizes do not significantly differ. It is demonstrated that when volatility is relatively high and the trend is upward, the HFRA can yield a substantial return via portfolios of large sizes. Moreover, the profitability of the HFRA is compared with that of the PR and TR strategies for long-term application. The HFRA is more profitable than the PR and TR strategies. This achievement of the HFRA is also validated statistically using the Fisher–Pitman permutation test.

Optimizing bike rebalancing strategies in free-floating bike-sharing systems: An enhanced distributionally robust approach

Bike-sharing systems are important components of urban transportation systems that facilitate short-distance travel. In recent years, free-floating bike-sharing systems have become popular. However, a major problem in such systems is the increasing number of idle bikes due to their spatial dispersion, which leads to a loss of demand and difficulty in bike rebalancing. To overcome these drawbacks, operators reserve parking areas, and laborers are incorporated into the bike rebalancing operation. We propose a novel dynamic bike rebalancing strategy based on trucks and laborers for free-floating bike-sharing systems. This strategy combines bike collection by laborers and bike transportation by trucks for rebalancing operations. In addition, we consider broken bike detection by laborers and user dynamics in two extension models. Because of the demand uncertainty in bike-sharing systems, we employ an enhanced distributionally robust optimization (EDRO) approach to protect against uncertainty. A target-level constraint is added to the general distributionally robust optimization (DRO) model to further improve the out-of-sample performance. An adaptive robust strategy is also employed to avoid overly conservative solutions. Furthermore, a linear decision rule is adopted to reformulate the EDRO model into a mixed-integer programming model, which guarantees computational tractability. The results of numerical experiments show that the EDRO model outperforms other benchmark models on a series of measures. Moreover, we verify the value of laborers in dynamic rebalancing operations and explore the effect of different bike supply levels and several other parameters on the value of laborers. We also test how the target-level parameter affects the model performance.

U.S. Economic Policy Towards China under the Biden Administration

Since the inception of the open-door policy in 1978, China has progressively become more integrated into the global economy through trade, foreign direct investment, and, more recently, outward direct investment. This economic integration has gained momentum with initiatives like the ‘Go Global’ strategy, China’s entry into the World Trade Organization (WTO) in 2001, and the launch of the Belt and Road Initiative in 2013. China’s economic ascent, coupled with its increasing political influence and military power, prompted the United States (US) to initiate a strategy of rebalancing in the Asia Pacific region, starting with the Bush administration and continuing through the Obama, Trump, and Biden administrations. During the Trump administration, this rebalancing strategy was supported by decoupling strategy, ultimately leading to a trade war with China. Despite its intention to avoid the initiation of a new Cold War and to adopt a more moderate stance towards China, the US-China trade war has evolved further into a tech war under the Biden administration. Given this context, this article aims to outline the primary characteristics of the US economic policy towards China during the Biden administration, comparing it to the Trump administration and assessing its impact on both nations. The central argument of this article is that the primary characteristics of the US economic policy towards China under Biden administration are rebalancing and decoupling, carried over from the policies of the preceding Trump administration, and there are clear signs that these characteristics are deepening. Furthermore, the article demonstrates that the extensive decoupling measures enacted by the US have proven effective in diminishing China’s role in global industrial and supply chains, particularly in industries related to semiconductors and chipmaking equipment.

Residual Shrinkage ViT with Discriminative Rebalancing Strategy for Small and Imbalanced Fault Diagnosis

In response to the challenge of small and imbalanced Datasets, where the total Sample size is limited and healthy Samples significantly outweigh faulty ones, we propose a diagnostic framework designed to tackle Class imbalance, denoted as the Dual-Stream Adaptive Deep Residual Shrinkage Vision Transformer with Interclass–Intraclass Rebalancing Loss (DSADRSViT-IIRL). Firstly, to address the issue of limited Sample quantity, we incorporated the Dual-Stream Adaptive Deep Residual Shrinkage Block (DSA-DRSB) into the Vision Transformer (ViT) architecture, creating a DSA-DRSB that adaptively removes redundant signal information based on the input data characteristics. This enhancement enables the model to focus on the Global receptive field while capturing crucial local fault discrimination features from the extremely limited Samples. Furthermore, to tackle the problem of a significant Class imbalance in long-tailed Datasets, we designed an Interclass–Intraclass Rebalancing Loss (IIRL), which decouples the contributions of the Intraclass and Interclass Samples during training, thus promoting the stable convergence of the model. Finally, we conducted experiments on the Laboratory and CWRU bearing Datasets, validating the superiority of the DSADRSViT-IIRL algorithm in handling Class imbalance within mixed-load Datasets.

BWLM: A Balanced Weight Learning Mechanism for Long-Tailed Image Recognition

With the growth of data in the real world, datasets often encounter the problem of long-tailed distribution of class sample sizes. In long-tailed image recognition, existing solutions usually adopt a class rebalancing strategy, such as reweighting based on the effective sample size of each class, which leans towards common classes in terms of higher accuracy. However, increasing the accuracy of rare classes while maintaining the accuracy of common classes is the key to solving the problem of long-tailed image recognition. This research explores a direction that balances the accuracy of both common and rare classes simultaneously. Firstly, a two-stage training is adopted, motivated by the use of transfer learning to balance features of common and rare classes. Secondly, a balanced weight function called Balanced Focal Softmax (BFS) loss is proposed, which combines balanced softmax loss focusing on common classes with balanced focal loss focusing on rare classes to achieve dual balance in long-tailed image recognition. Subsequently, a Balanced Weight Learning Mechanism (BWLM) to further utilize the feature of weight decay is proposed, where the weight decay as the weight balancing technique for the BFS loss tends to make the model learn smaller balanced weights by punishing the larger weights. Through extensive experiments on five long-tailed image datasets, it proves that transferring the weights from the first stage to the second stage can alleviate the bias of the naive models toward common classes. The proposed BWLM not only balances the weights of common and rare classes, but also greatly improves the accuracy of long-tailed image recognition and outperforms many state-of-the-art algorithms.