1. Introduction
In financial markets, investors are most interested in returns and risk and the relationship between the two. Risk-return analysis plays a central role in financial decision-making. The underlying assumption is that risk-averse investors seek compensation for higher risk in the form of a risk premium on risky assets. However, historical risk-return analysis has limitations.
One important area of financial planning and risk management is to balance the risk and return of an investment with the appropriate allocation of portfolio weights. The _target investment ratio (i.e., the optimal proportion of the value of each asset in a portfolio that maximizes the owner’s utility) and its estimation have been widely studied (
De Prado 2016;
Csesznik et al. 2021;
Anelli 2023).
Bkhit and Ali (
2019), in their studies on the Khartoum Stock Exchange, found a link between portfolio management and return.
Liu et al. (
2022) addressed the design of portfolio weights in their study. They demonstrated that portfolio decisions are affected by the volatility of financial markets and the risk tolerance of investors. Regularly adjusting the portfolio of long-term investors is an essential aspect. As portfolios “age”, investors experience a reduction in the dispersion of returns, while the risk differentials between different portfolios increase. This implies that to maintain a fixed risk-return ratio in a portfolio as the time horizon increases, the investor needs to increase the proportion of lower risk financial assets in the asset allocation process (
Hanif et al. 2021). According to
Dai et al. (
2024), investors use sophisticated, predetermined ratios to allocate the asset weight of a portfolio to achieve a good trade-off between profitability and trading risk. In their view, rebalancing these weights due to market volatility without excessive transaction costs and tracking errors is a crucial financial planning problem. To this end,
Raffinot (
2017) proposed an asset allocation method based on hierarchical clustering using graph theory and machine learning techniques.
Abramov et al. (
2015) investigated the impact of increasing investment time horizons on the comparative advantage of fund asset classes and the principles of investment strategy design. In their view, the traditional approach of portfolio management theory, which argues that investing in equities is preferable to bonds in terms of long-term risk-return trade-offs, is in no way consistent with the empirical evidence.
Based on all this, the aim of our research is to investigate the effectiveness of the rebalancing strategies of the diversified portfolio of exchange-traded funds (ETFs). We selected five ETF types, including short-term U.S. Treasury bonds, U.S. equities, global commodities, U.S. real estate investment trusts (REITs), and a multi-strategy hedge fund, to create a portfolio covering various asset classes and economic sectors. Using a 10-year historical period from 28 March 2014 to 28 March 2024, a unique simulation model was applied to generate random portfolios with varying asset weights and rebalancing tolerance bands, assessing the impact of premium rebalancing on portfolio performance. Our research hypothesis is that if there is a significant relationship between the rebalanced yield and the Sharpe ratio, then rebalancing does not always have a positive effect on the performance of the portfolio, and its effectiveness may vary by ETF type. The results of our study contribute to the improvement of portfolio performance.
2. Portfolio Theory and Portfolio Management
The starting point for our study is the portfolio theory of
Markowitz (
1952,
1991). Modern portfolio theory has paved the way in the field of risk measurement. Modern portfolio theory is a normative theory that shows how investors should behave to achieve optimal investment. Diversification is the fundamental issue of the theory. The efficiency of diversification can be captured by covariances or correlations between returns (
Fabozzi et al. 2002).
The expected portfolio return and its standard deviation can be estimated as follows:
where
E(
rP) is the expected return on the portfolio;
n is the number of shares;
ai is the proportion of share
i in the portfolio; and
E(
ri) is the expected value of the return on share
i.
Here,
σ(
rP) is the standard deviation of the portfolio returns;
n is the number of shares in the portfolio;
ai is the proportion of share
i in the portfolio;
ρij is the correlation coefficient between the returns on stocks
i; and
j,
σ(
ri) is the standard deviation of the return on equity
i.
The return on a portfolio depends on the return of the shares and the proportion of the shares in it. The standard deviation of the portfolio depends on the weight of the stocks, their individual standard deviation, and the correlation between the returns.
Tobin (
1958) extended the theory by including a risk-free instrument.
Lintner (
1965),
Mossin (
1966), and
Sharpe (
1964) sought to extend the model to other instruments. The theories pointed to the possibility of reducing risk through diversification. They have also sought answers to optimize the allocation of assets in a portfolio and to calculate the relationship between risk and expected returns. The range of products that can be included in portfolios is constantly expanding (
Bányai et al. 2024).
Maier-Paape and Zhu (
2018) have pointed out that a framework can be linked to the Markowitz portfolio theory, capital asset pricing model, the growth optimal portfolio theory, and the leverage portfolio theory. It can be deduced that if there are no arbitrage opportunities in the market, i.e., asset pricing is correct. This provides a basis for passive portfolio management strategies. However, due to changes in the perception of individual instruments, it may be appropriate to rebalance the portfolio from time to time due to changes in the market weight of the instruments.
While the primary aim of rebalancing is to maintain the desired asset allocation and minimize risk, there are scenarios where it can also enhance portfolio returns. For instance, rebalancing can lead to a disciplined buy low, sell high strategy by selling overperforming assets and buying underperforming ones, potentially capturing gains from market inefficiencies. Additionally, in volatile markets, frequent rebalancing can take advantage of short-term fluctuations, potentially boosting returns. Moreover, rebalancing during periods of market dislocation can position the portfolio to benefit from subsequent recoveries. Thus, while risk management remains the core objective, strategic rebalancing can indeed contribute to maximizing gains under certain market conditions.
The tolerance band approach is preferred over frequency-based rebalancing due to its responsiveness to significant market fluctuations, leading to potentially fewer transactions and reduced costs. This method initiates rebalancing only when asset allocations deviate substantially from their _target levels, thereby enhancing cost and tax efficiency while maintaining the desired risk profile with greater precision. Additionally, the tolerance band approach offers superior flexibility and customization, aligning with the unique volatility and correlation characteristics of different asset classes. It mitigates behavioral biases by adhering to predefined rebalancing triggers, contrasting with the potentially inefficient fixed-interval rebalancing, which may result in unnecessary trades and suboptimal risk management.
The Sharpe Indicator
More than 50 years ago,
Roy (
1952) introduced the risk-return ratio for ranking risky investments, originally called profit volatility. Subsequently,
Sharpe (
1966) first applied this ratio to the valuation of portfolios (investment funds), and it has become one of the most popular indicators in the world of both academics and practitioners, known as the Sharpe ratio (
Farinelli and Tibiletti 2008;
Basile and Ferrari 2016).
The Sharpe ratio can be easily applied to any return series without the need for additional information on the source of volatility and/or profitability. It is commonly used to compare the risk-adjusted returns of different types of investments such as equities, ETFs, mutual funds, and investment portfolios.
Traditionally, the Sharpe, Sortino, Treynor, and Jensen ratios have been most commonly used to measure the performance of different financial portfolios (
Mistry and Shah 2013).
The simple Sharpe portfolio optimization model allows the investor to find the portfolio that best matches the investor’s objectives and risk tolerance. The method helps to select an asset mix that provides the highest rate of return with the lowest risk (
Dileep and Rao 2013). From the investor’s perspective, the Sharpe ratio describes the extent to which the return on an investment portfolio compensates the investor for the risk taken.
The indicator is calculated as follows:
where
ri is the return of instrument;
rf is the risk-free rate of return; and σ(
ri) is the standard deviation of return of instrument
i.
Since the standard deviation of the portfolio return is a measure of the risk of the portfolio, the Sharpe ratio looks at the risk-adjusted return. If its value is positive, then the portfolio has been able to generate excess returns relative to the risk assumed. The Sharpe ratio can therefore indicate whether the higher return achieved by a portfolio was due to good investment decisions or simply the result of a riskier investment strategy.
According to the capital market pricing model, the market portfolio is also part of the risk-return equation, which represents the optimal portfolio of all fairly priced portfolios in the market. This means that all portfolios in the capital market equation to the left of the market portfolio have a lower risk-return combination than the market portfolio, and all portfolios to the right have a higher risk-return combination than the market portfolio. However, the Sharpe single index model helps the investor to identify the portfolio that has a higher return than the market portfolio with a lower risk than the market portfolio over the same period (
Mistry and Khatwani 2023).
The Sharpe ratio solves most of the technical difficulties of previous portfolio models and is very useful for individual investors and portfolio managers worldwide to build optimal portfolios and to compare and benchmark portfolio performance.
Kuhle and Lin (
2018) used the indicator to measure the performance of real estate investment funds over a 10-year period from 2007 to 2016. They found that the reliability of Sharpe’s index outperforms the previously mentioned Treynor index, which can also be used to measure risk-adjusted returns, and the Sortino index in determining the performance of real estate investment funds.
Nuzula and Darmawan (
2019) investigated which of the aforementioned indicators is the most appropriate to measure portfolio performance in the Indonesian stock market. Their regression analysis showed that Sharpe’s method is the most suitable to measure portfolio performance.
Dileep and Rao (
2013) concluded from their studies on Indian firms that the Sharpe ratio is sustainable and applicable in the Indian market. In the Indian market,
Patel (
2017) also tested the applicability of the Sharpe index in optimal portfolio construction.
Using the Sharpe ratio,
Coates and Page (
2009) have shown that the Sharpe ratio values of financial market traders increase significantly with the number of years of trading, suggesting that learning plays a role in increasing traders’ returns. Errors in the covariance matrix can have a large impact on portfolio performance, especially when the forecast length is small relative to the number of assets. Thus, ignoring these errors when estimating the Sharpe ratio of an efficient portfolio leads to inaccurate results (
Chopra and Ziemba 1993;
Benjlijel and Mansali 2021).
The above examples illustrate why we considered it appropriate to use the Sharpe index in our study. Of course, none of the indicators that can be used to show the performance of portfolios is perfect.
3. Data and Methods
We built our portfolio in this research using just exchange-traded funds (ETFs), taking advantage of their many benefits. In comparison to alternative investment options such as individual stocks or traditional funds, exchange-traded funds (ETFs) are more affordable due to their lower expenses and vast diversification across regions or sectors. ETFs provide for easy comparisons between various investment products and reliable risk-return assessments because they are transparent and highly liquid and offer a representative sample of market performance. In order to analyze the interconnected effects of rebalancing premium, we have chosen the following EFTs:
Bond ETF: iShares 1–3 Year Treasury Bond ETF (SHY)—Focuses on short-term U.S. Treasury bonds, offering stability and lower risk for conservative income generation.
Equity ETF: SPDR® S&P 500 (SPY)—Tracks the S&P 500 Index, providing broad U.S. equity market exposure and serving as a core investment due to its market representation and historical returns.
Commodity ETF: First Trust Global Tactical Commodity Strategy Fund (FTGC)—Offers exposure to a diversified commodity portfolio, including energy, agriculture, and metals, acting as an inflation hedge and potential for returns uncorrelated with traditional assets.
REIT ETF: iShares Core U.S. REIT ETF (USRT)—Invests in U.S. real estate investment trusts, providing exposure to commercial, residential, and industrial properties for potential capital appreciation and dividend income.
Multi-Strategy ETF: NYLI Hedge Multi-Strategy Tracker ETF (QAI)—Replicates a broad hedge fund index with strategies like long/short equity and global macro, aiming for diversified alternative investment exposure to enhance returns and manage risk.
To conduct a comprehensive analysis of the characteristics of each asset, we selected a 10-year period from 28 March 2014, to 28 March 2024. This timeframe covers a wide range of macroeconomic conditions, including periods of economic growth, recession, market volatility, and various interest rate environments. By analyzing this extended timeframe, we aim to capture how each asset performs under different market conditions, providing a robust assessment of their risk-return profiles and the effects of rebalancing premiums (
Supplementary File).
With these assets selected, the portfolio comprises a diversified mix providing exposure to a wide range of regions and activities. This diversified approach ensures that the portfolio is not overly reliant on any single asset class, sector, or geographic region, thereby reducing risk through diversification. The inclusion of different asset classes such as bonds, equities, commodities, real estate, and multi-strategy investments also helps in optimizing the balance between risk and return. By regularly rebalancing this portfolio, we aim to capture the rebalancing premium, which can enhance overall returns and maintain the desired risk profile over time. This methodology ensures that our portfolio remains aligned with our investment objectives, while taking advantage of the unique benefits offered by ETFs.
For our analysis, we created a unique model that simulates random portfolios comprised of listed ETFs (SHY, SPY, FTGC, USRT, and QAI) and measure how rebalancing premiums affect the risk-adjusted return, both at the portfolio and asset levels. When generating random portfolios, random weights were applied for each asset ranging from 0 to 1, which were then normalized.
These random weights followed a uniform distribution, ensuring each asset had an equal probability of being included in the portfolio. This approach helps mitigate extreme asset weight allocations, which are often observed in traditional Markowitz models. In these models, the optimal solution may lead to controversial outcomes, where certain assets are either extremely underweighted or overweighted as a result of the inherent characteristics of mean-variance optimization.
Table 1 and
Table 2 show the input and output parameters.
The overall volume of rebalancing returns in our model is based on daily rebalancing returns, where we take the trading fee into account as a reduction on a daily basis. This approach allows us to account for transaction costs at the time they are incurred, making the model more reflective of real-world trading platforms. The daily net rebalancing return is calculated as follows.
Daily Rebalancing Premium:
During the simulation, two possible outcomes occur based on daily portfolio performance. In the first scenario, if the absolute difference between the actual portfolio weights, driven by daily price movements, and the _target weights is within the tolerance band for all assets in the portfolio, no rebalancing is triggered. In the second scenario, if the weight of any asset deviates from the _target by more than the tolerance band, the algorithm initiates rebalancing to restore the portfolio to its _target allocations. Each time a rebalancing event occurs, the excess daily return is calculated by deducting trading fees and then aggregated as the average annualized return over the entire simulation period, similar to the annualized average daily net portfolio return. This approach allows each simulation outcome to reflect a specific number of rebalancings with corresponding rebalancing return and rebalancing-weighted return, along with other key performance indicators, such as standard deviation and Sharpe ratio. This variability may lead to situations where the rebalancing premium is negative, thus reducing the net return of the portfolio; however, the Sharpe ratio might be higher due to the complex dynamics of rebalancing and the various combinations of dependent sequences within the iteration.
By adopting a dynamic rebalancing approach, we can explore both asset-level and portfolio-level effects. This method reveals that the portfolio-level premium can differ from the sum of individual asset premiums due to interactions such as diversification benefits or correlations between assets. For instance, if rebalancing results in a significant increase in the weights of assets with negative premiums, the overall portfolio-level premium might become negative, even if the individual asset premiums are positive when weighted by their initial allocations. This discrepancy occurs because the portfolio-level rebalancing premium captures the combined impact of asset interactions, which can affect the premium differently than simply summing the individual premiums. Additionally, the timing of rebalancing plays a crucial role; rebalancing assets with higher volatility or differing performance patterns at suboptimal times can result in a negative overall rebalancing effect. Therefore, if rebalancing results in a negative premium when comparing the overall portfolio returns before and after the adjustment, it indicates that the rebalancing has led to a reduction in the net return of the portfolio. This negative outcome reflects the combined effect of asset interactions and the timing of rebalancing, even if individual asset premiums are positive when assessed in isolation.
The algorithm is executed for 10,000 iterations, in accordance with the maximum iteration setting, while the tolerance band increases linearly until a rebalancing event occurs. If the tolerance band reaches a level where no rebalancing is needed, the algorithm resets it to zero and restarts the process. Essentially, the algorithm begins with daily rebalancing and continues until only a single rebalancing event takes place. This mechanism introduces greater randomness into the simulation, as each reset occurs at varying tolerance band levels. Consequently, the simulation avoids being constrained by fixed upper or lower limits, dynamically adjusting while continuously monitoring the portfolio’s attributes. By capturing all 10,000 scenarios along with their associated attributes, we can analyze underlying trends and correlations in greater detail compared to conventional methods, such as mean-variance optimization and the capital asset pricing model, which often rely on static inputs. Unlike approaches that assume fixed historical returns and risks, this simulation adapts dynamically to changing portfolio conditions. The stochastic approach used in the simulation enhances its reliability and real-world applicability by incorporating random fluctuations and dynamic adjustments, making the results more representative of actual market conditions.
Within the stochastic approach, the simulation leverages a historical method to provide more realistic scenarios, focusing primarily on varying asset weights and rebalancing tolerance bands while incorporating historical asset prices. We chose this historical method because it is well-suited when high-quality historical data are available and highly effective in analyzing complex or non-linear portfolios, as is the case in our simulation. Unlike other methods (e.g., parametric or quantile estimation-based Monte Carlo), which may rely on theoretical distributions or assumptions, the historical approach allows us to capture the actual behaviors and interactions of assets over time. This leads to more reliable and realistic results, particularly valuable for accurately capturing rebalancing returns based on real-life market conditions. To ensure the robustness of our model, we conducted extensive testing, including back-testing and sensitivity analyses, to validate the rebalancing effects observed in the simulation.
To understand the impact of rebalancing on a portfolio, we analyze two key metrics: the portfolio rebalancing return and the rebalancing-weighted return. The portfolio rebalancing return reflects the overall return generated by rebalancing activities at the portfolio level, which is equivalent to the sum of the individual asset rebalancing returns. In contrast, the rebalancing-weighted return represents the weighted sum of individual asset returns, adjusted according to _target allocations. By examining the relationship between these two metrics, we can gain insights into the efficiency of rebalancing by considering both the overall rebalancing performance and the asset-weighted performance. This analysis helps us understand how effectively rebalancing is executed. The following four scenarios illustrate the interplay between these metrics:
Positive Rebalancing Return and Positive Rebalancing-Weighted Return: In this scenario, both the overall rebalancing return and the individual rebalancing-weighted returns are positive. This indicates that the rebalancing strategy is effectively improving performance at both the asset and portfolio levels. The adjustments made during rebalancing are beneficial for both individual assets and the overall portfolio, likely due to favorable changes in asset weights and positive interaction effects.
Positive Rebalancing Return and Negative Rebalancing-Weighted Return: This scenario indicates that while the overall rebalancing return is positive, the individual rebalancing-weighted returns are negative. This suggests that although the overall rebalancing process is beneficial, the interaction effects or adjustments made during rebalancing are negatively impacting some individual assets. It could imply that the rebalancing strategy is having a mixed effect, where the portfolio benefits overall but specific assets suffer.
Negative Rebalancing Return and Positive Rebalancing-Weighted Return: This scenario suggests that despite the overall rebalancing return being negative, some individual assets show positive rebalancing-weighted returns. This indicates that the combined effect of rebalancing—through diversification benefits and interaction effects—has resulted in positive outcomes for specific assets, even if the overall portfolio is negatively affected.
Negative Rebalancing Return and Negative Rebalancing-Weighted Return: This scenario reveals that both the overall rebalancing return and the individual rebalancing-weighted returns are negative. It suggests that rebalancing has been ineffective or harmful, with negative impacts on both the individual assets and the portfolio as a whole. This may point to poor timing or execution of rebalancing, resulting in detrimental effects across all levels.
4. Results and Findings of the Research
In this section, we first analyze the relationship between portfolio performance, as measured by the Sharpe ratio, and rebalancing effectiveness, assessed through the rebalancing-weighted return. Second, we explore the connection between asset-level rebalancing returns and the portfolio’s Sharpe ratio, employing a support vector regression (SVR) model to reveal the unique characteristics of each ETF. Third, we identify the optimal rebalancing band based on the outcomes derived from our stochastic model. Finally, we evaluate the portfolio performance across key scenarios, emphasizing the relationship between portfolio-level rebalancing returns and rebalancing-weighted returns. This stochastic approach offers a novel perspective on portfolio management, providing deeper insights into the dynamics and effectiveness of rebalancing strategies.
Figure 1 demonstrates a significant linear relationship between the Sharpe ratio and rebalancing-weighted return, with a correlation coefficient of 0.6492 (
p < 0.001), indicating a positive association. As the rebalancing-weighted return increases, the Sharpe ratio tends to rise, highlighting the advantages of effective rebalancing strategies on portfolio performance. The R-squared value of 0.4215 suggests a moderate fit of the model to the data, accounting for 42.15% of the variation in the Sharpe ratio based on changes in the rebalancing-weighted return.
To gain a deeper understanding of how individual rebalancing returns correlate with the portfolio’s weighted return, we analyzed each asset individually.
As
Figure 2 shows, the relationship between the risk-adjusted return and rebalancing premium at the asset level suggests a complex, non-linear relationship. To model this complexity, we employed support vector machines (SVMs) with support vector regression (SVR). SVR is particularly well-suited for capturing non-linear patterns in financial data, which traditional linear regression models might fail to represent adequately. Using a radial basis function (RBF) kernel, SVR maps the data into a higher-dimensional space where non-linear relationships can be more effectively modeled. This approach allows us to uncover intricate dynamics between rebalancing returns and the Sharpe ratio that simple linear models could miss.
Additionally, SVR is effective in handling the inherent noise and outliers in financial datasets, such as those caused by extreme market events, by employing an epsilon-insensitive loss function that emphasizes the overall trend rather than being skewed by individual anomalies. Overall, SVR provides a robust framework for analyzing how rebalancing strategies affect portfolio performance, offering deeper insights into risk-adjusted returns and enabling more refined investment decisions (
Table 3).
The SVR models reveal diverse impacts of rebalancing returns on the Sharpe ratio across different assets, with the number of support vectors providing insight into the complexity of the relationships modeled. For SHY and USRT, the models exhibit a negative relationship between rebalancing returns and the Sharpe ratio. The model for SHY, which used 9060 support vectors, indicates that increasing rebalancing returns is associated with a lower Sharpe ratio. This high number of support vectors reflects a complex model that captures significant data variations, potentially due to extreme market conditions or intricate market dynamics. Similarly, the SVR model for USRT, with 8499 support vectors, shows a negative relationship, suggesting that more aggressive rebalancing might adversely affect USRT’s risk-adjusted performance. The considerable number of support vectors here also suggests a complex and potentially noisy relationship.
In contrast, the SVR models for SPY and FTGC display a positive relationship between rebalancing returns and the Sharpe ratio. The SPY model, which used 8889 support vectors, reveals that higher rebalancing returns are associated with a higher Sharpe ratio, indicating that effective rebalancing strategies can enhance SPY’s risk-adjusted performance. Likewise, the FTGC model, with 9172 support vectors, shows that increased rebalancing returns lead to an improved Sharpe ratio, suggesting that FTGC benefits from effective rebalancing strategies. The high number of support vectors for both assets reflects complex relationships where effective rebalancing has a positive impact on performance. On the other hand, the model for HDG, which involved 9076 support vectors, also reveals a negative relationship, showing that higher rebalancing returns are linked to a lower Sharpe ratio. This finding suggests that rebalancing strategies might be less effective or even detrimental for HDG’s performance, with the high number of support vectors indicating a complex model where rebalancing efforts do not yield better risk-adjusted returns (
Figure 3).
The other main objective of this research is to build a model that identifies the optimal rebalancing band for maximizing risk-adjusted returns. After analyzing asset-level attributes, we optimized the tolerance band to maximize the average Sharpe ratio. We computed the average of all simulated Sharpe ratios for various tolerance bands. Our findings indicate that an 18% tolerance band yields the best results, with an average Sharpe ratio of 0.4529. Increasing the tolerance band beyond this point significantly lowers the Sharpe ratio. Conversely, a 0% tolerance band, which implies daily rebalancing, results in the lowest average Sharpe ratio and is generally not an optimal strategy due to the high trading costs associated with frequent rebalancing. Maximum Sharpe ratios remain relatively high up to 18%, suggesting that the range of best performances expands; however, the minimum Sharpe ratios become more volatile, reflecting increased risk or variability. Additionally, we highlight that the best-performing scenario occurred at a tolerance band of 8.5%, with a Sharpe ratio of 0.6299, though this band exhibited higher fluctuations. The asset weights for this scenario are noted as follows (
Table 4).
If we take a look at how the average asset weights impact the overall performance of the portfolio at given rebalance bands, we can see that SHY, a short-term Treasury bond ETF, offers stability and acts as a defensive asset, with its allocation ranging from 17% to 35%. This variability in weight reflects its role in maintaining stability across all tolerance bands, with a notable increase in weight in higher tolerance bands to enhance risk mitigation. SPY, representing the S&P 500, provides significant growth potential, with its allocation varying from 18% to 28%. This higher weight supports the portfolio’s growth, especially as the tolerance bands increase, enabling more significant equity exposure. FTGC, focusing on global markets, is allocated between 15% and 24%, contributing to diversification with a steady weight that remains relatively stable across tolerance bands; however, its impact is less pronounced compared to SPY. USRT, a U.S. real estate ETF, is weighted between 15% and 21%, offering exposure to real estate and helping to balance the portfolio’s risk; its weight increases slightly in higher tolerance bands to capture more real estate growth. HDG, a hedge fund ETF, ranges from 15% to 23% in allocation, playing a crucial role in risk mitigation. Its weight rises in higher tolerance bands, reflecting its stabilizing effect on the portfolio and helping manage risk effectively.
This balanced mix of assets (results can find in
Appendix A), while maintaining an average weight close to 20% for each of the five assets, varies significantly across different tolerance bands, leveraging their unique characteristics. SHY, with its weight adjusted for stability, and SPY, emphasizing growth potential, illustrate how variations in tolerance bands allow the portfolio to exploit each asset’s strengths. FTGC, USRT, and HDG also adapt their allocations to enhance diversification, real estate exposure, and risk management, respectively.
The trend analysis supports the findings of the SVR models, indicating that SHY and USRT demonstrate a negative relationship between rebalancing returns and Sharpe ratios. This suggests that while these assets provide stability, their performance tends to suffer with excessive rebalancing, likely due to their defensive nature. On the other hand, SPY and FTGC show a positive relationship with rebalancing, highlighting their potential for improved Sharpe ratios through more active management, given their growth-oriented characteristics. HDG also shows a negative relationship with rebalancing, indicating that frequent adjustments can reduce its effectiveness as a risk management tool. Overall, the statistical trends confirm that rebalancing strategies must be tailored carefully, as growth assets benefit from rebalancing, while defensive assets may experience diminishing returns with frequent shifts.
In addition to previous analyses, we specifically examined the connection between rebalancing premium returns and rebalancing-weighted premium returns. This was assessed using the average Sharpe ratio, which measures the overall risk-adjusted return for each scenario. This detailed evaluation not only assesses the overall performance of each scenario but also measures the effectiveness of the rebalancing approach in optimizing returns relative to risk. Understanding the interplay between rebalancing premium returns and weighted premium returns provides valuable insights into how individual asset-level impacts and dynamics affect portfolio performance. This evaluation helps determine which outcomes achieve a more favorable risk-return profile and how well the integration of rebalancing premiums influences overall performance (
Figure 4).
The first scenario, with a positive rebalancing return and a positive rebalancing-weighted return (iteration count: 1498), offers a Sharpe ratio of 0.3824, which is higher than the second scenario but not as strong as the third. The connection between rebalancing premiums is reasonably effective, but the lower iteration count may limit the potential for capturing more diverse market conditions, reducing its broader applicability.
The second scenario, with a positive rebalancing return and a negative rebalancing-weighted return (iteration count: 1906), has the lowest average Sharpe ratio of 0.2756, indicating the least favorable risk-adjusted return. The disconnect between rebalancing premiums and weighted returns makes this scenario the least optimal.
The third scenario, featuring a negative rebalancing return and a positive rebalancing-weighted return (iteration count: 3175), demonstrates the highest Sharpe ratio of 0.4328, reflecting the best risk-adjusted performance. This scenario also shows the most effective connection between rebalancing premium returns and weighted returns, making it the top performer.
The fourth scenario, with a negative rebalancing return and a negative rebalancing-weighted return (iteration count: 3421), has a Sharpe ratio of 0.3055, with the highest iteration count. While this suggests a robust sample size, its risk-adjusted return is lower than the third scenario, and the relationship between rebalancing premiums is less effective.
Results suggest that effective rebalancing is not primarily determined by the absolute value of rebalancing premiums, contrary to initial expectations. While we might have anticipated that scenarios with both a positive rebalancing return and a positive weighted return would yield the best performance, the findings indicate otherwise. Instead, the combined overall effect of rebalancing—whether the returns are positive or negative—plays a more critical role. This challenges the assumption that simply having higher rebalancing premium is sufficient for optimal performance, highlighting the importance of understanding how different rebalancing returns interact to affect overall portfolio performance.
To eliminate potential biasing factors in the model, particularly the possible distorting effects of model parameters, we first examined the impact of transaction costs by conducting the simulation with a 0% trading fee, as this might directly impact the results. We measured a 99.97% correlation (r = 0.9997,
p < 0.001) between the initial results from the 1% trading fee scenario and the results from the 0% trading fee scenario across the population. This analysis allows us to confidently exclude the possibility that the observed effect between rebalancing return and the Sharpe ratio is significantly driven by the 1% trading fee used in the initial simulation, especially given that trading fees are incorporated into the Sharpe ratio calculation as part of the net return (
Table 5).
To further support this, we applied the percentile method to analyze the distribution of the Sharpe ratio and rebalancing-weighted returns at the 99.9% confidence interval. The results indicate that with a 0% trading fee, both the Sharpe ratio and rebalancing-weighted return shift in a positive direction, which aligns with our expectations. A reduction in transactional costs will always result in an increase in returns, which consequently leads to an improvement in the Sharpe ratio. A shift in the opposite direction would have signaled a potential issue or inconsistency in our model, which is clearly not the case. Furthermore, we conducted similar tests on other parameters of the simulation (e.g., risk-free rate, trading days) and concluded that they did not impact the observed rebalancing effects, as they acted as static variables throughout the simulation without introducing any significant bias, thereby reinforcing the reliability of our results.
5. Conclusions
Based on our research results, it can be stated that we were able to verify our hypothesis. Our study reveals a positive correlation between the rebalancing-weighted return and the Sharpe ratio (correlation coefficient of 0.6492, p < 0.001). This indicates that effective rebalancing strategies can improve the risk-adjusted returns of a portfolio. The analysis identified an inflection point at around 1% of the rebalancing premium, beyond which the Sharpe ratio starts to decline. This finding suggests that while rebalancing generally enhances portfolio performance, excessive rebalancing can be counterproductive.
The study confirms that rebalancing strategies can significantly impact portfolio performance, and their effectiveness varies by ETF type. For example, equity ETFs like SPY and commodity ETFs such as FTGC benefit from frequent, strategic rebalancing, which can enhance risk-adjusted returns due to their inherent volatility and market dynamics. Conversely, bond ETFs like SHY, REIT ETFs like USRT, and multi-strategy ETFs such as QAI showed that rebalancing can have a negative impact, suggesting that a more conservative or less frequent rebalancing approach may be more suitable for these asset classes. This indicates that while frequent rebalancing is advantageous for some ETFs, a tailored approach is necessary for others to optimize performance and manage costs.
Our findings underscore the importance of selecting an appropriate tolerance band that balances transaction costs with portfolio performance. For the simulated portfolio, the best-performing scenario occurred at an 8.5% tolerance band, achieving a Sharpe ratio of 0.6299; however, the 8.5% tolerance band exhibited higher fluctuations. Therefore, the 18% tolerance band was optimal for balancing risk-adjusted returns with rebalancing frequency and costs, resulting in an average Sharpe ratio of 0.4529. This highlights that the relationship between rebalancing premium and the Sharpe ratio is non-linear and dependent on portfolio characteristics. Portfolio managers and investors should prioritize a balanced rebalancing strategy that considers the compound effect of rebalancing, rather than solely maximizing excess returns as measured using the rebalancing premium. While there are scenarios where rebalancing may significantly enhance excess returns without proportionally increasing risk, our results confirm that this is not always the case.
Additionally, the analysis revealed a complex relationship between rebalancing returns and weighted rebalancing returns. The top-performing scenario featured negative rebalancing returns but positive rebalancing-weighted returns, achieving the highest average Sharpe ratio of 0.4328. This underscores the importance of a nuanced approach to rebalancing, considering asset-specific dynamics rather than relying solely on broad measures. Our quantitative analysis confirms that rebalancing is a double-edged sword, with its effectiveness largely dependent on the nature of the assets, market conditions, and the investor’s risk tolerance. Key findings highlight that understanding the relationship between rebalancing returns and weighted rebalancing returns is crucial for evaluating rebalancing effectiveness. While short-term buy-sell rebalancing may offer immediate benefits, it can adversely affect the risk profile over the long term. Thus, a balanced approach is essential, prioritizing long-term stability over short-term gains, even when the rebalancing premium appears negative.