Asymmetric responses of the sectoral ETFs to market extremes: evidence from the left and right tails Open Access

Exchange traded funds (ETFs) represent a significant innovation in modern finance, having transformed the stock market since their inception in the early 1990s. First introduced in Canada and the USA, ETFs have experienced consistent growth over the years. By September 2020, global ETF assets under management had exceeded $7tn, despite the economic disruptions caused by the coronavirus pandemic (Nunkoo et al., 2022). This upward trend continued, and by 2021, ETF assets had reached $7.7tn, accounting for 16% of US stock market capitalization – surpassing the 14% share held by mutual funds (Magner et al., 2022). According to Henriques et al. (2022), U.S. ETF assets grew from $2.1tn in 2015 to $4.4tn by 2019, with Bank of America projecting a rise to $50tn by 2050. This rapid expansion highlights ETFs’ growing importance in financial markets. Amid ongoing market volatility, particularly during periods of boom and bust, passive investors must carefully select sectors for investment. The COVID-19 pandemic underscored the need for effective risk management, especially regarding tail risks (Gobbi and Mulinacci, 2023). Understanding how sectoral ETFs perform under extreme conditions is therefore essential for identifying defensive versus aggressive sectors, enhancing portfolio strategies and managing downside risk during times of heightened uncertainty.

Despite extensive research on downside risk, prior studies have primarily concentrated on estimating conditional downside betas when portfolio returns fall below a benchmark – often zero or a target return (Atilgan et al., 2020; Bawa and Lindenberg, 1977; Durand et al., 2011; Estrada, 2002, 2007; Fisher and D’Alessandro, 2021; Pettengill et al., 1995; Valadkhani, 2023). However, this focus on downside risk has largely overlooked the behavior of sectoral ETFs under extreme market conditions, especially with respect to both downside and upside betas analyzed across multiple threshold cut-off points. Additionally, most existing literature investigates individual stocks rather than ETFs, which represent diversified sector portfolios and thereby reduce firm-specific idiosyncratic effects such as mergers and acquisitions (Valadkhani, 2023). These gaps limit a comprehensive understanding of how sectoral ETFs respond to extreme market fluctuations and restrict investors’ ability to optimize portfolios amid volatile conditions.

Our study evaluates how sectoral ETFs respond to extreme market fluctuations by using both predetermined and optimal boundary points. Specifically, we estimate two types of betas for each industry-specific ETF. The first beta measures how sectoral ETFs react during the most severe market downturns, capturing their downside risk. The second beta assesses their responsiveness to the most significant market upturns, highlighting their upside potential. As investors vigilantly monitor the erratic oscillations of the market (Huang et al., 2012), their primary concern often revolves around the declines in asset prices, commonly referred to as downside risk (Menezes et al., 1980). In particular, investors tend to gravitate towards financial assets that exhibit resilience to negative market shocks while delivering robust returns during favourable market conditions.

To identify the worst and best market downturns and upturns from the longest available daily return data set, our study applies a 10% threshold (capturing 365 days out of 6,345 total days in the sample) to the left and right tails of the return distribution. This is followed by a more stringent 5% threshold (317 days out of 6,345 total days). We also estimate an optimal cutoff point for each ETF, which is likely to fall between these two predetermined thresholds. This study addresses three key research questions that are critical for informing investment strategies. First, which sectoral ETFs respond most strongly to extreme market downturns? Second, which sectoral ETFs respond most strongly to extreme market upturns? Third, which sectoral ETFs exhibit a higher upside beta than downside beta and demonstrate greater stability?

The study makes three important contributions to the existing literature. First, it extends beyond the traditional focus on downside risk by simultaneously analyzing downside and upside potentials of sectoral ETFs using a comprehensive data set over an extended period, thereby providing a richer understanding of sectoral risk-return dynamics. Second, unlike previous work centered on individual stocks, this research examines nine Standard and Poor’s Depositary Receipt (SPDR) sectoral ETFs, which aggregate the returns of multiple stocks – such as the XLE ETF, which represents 23 energy companies including ExxonMobil, Chevron, ConocoPhillips and EOG Resources – thus mitigating idiosyncratic firm-level noise. Third, by exploring sector-specific responses to both severe market declines and rallies, the study offers valuable insights for investors seeking to manage risk and optimize sector allocation, particularly during periods of heightened volatility. This nuanced understanding supports more effective portfolio diversification strategies that balance downside protection with upside opportunity, ultimately helping investors make more informed decisions to enhance portfolio performance under challenging market environments.

Amid heightened volatility, particularly during crises such as the Global Financial Crisis (GFC) and the COVID-19 pandemic, passive and institutional investors have become increasingly concerned with managing downside risk while seeking exposure to upside potential. Although prior literature has extensively examined conditional downside risk, most studies focus on individual stocks or employ a single-threshold approach, offering limited insight into how sectoral ETFs behave in the tails of the return distribution. This study addresses this gap by examining the asymmetric responses of sectoral ETFs to both negative and positive extremes in the market, thereby enhancing our understanding of risk-return dynamics across sectors during turbulent periods. Rather than relying solely on conventional beta estimates, the study uses a threshold regression framework to estimate sector-specific upside and downside betas at both fixed (5% and 10%) and optimally derived cut-off points. The predetermined thresholds capture the most extreme deciles of return shocks. In contrast, the optimal thresholds, estimated via Bai and Perron’s structural break methodology, allow for ETF-specific sensitivity to market conditions, providing the best fitting data-driven boundary points that reflect the true asymmetry in each sector’s response to market extremes. This dual-threshold approach is essential for distinguishing between truly defensive and aggressive sectors across varying degrees of market stress. By adopting this framework, the study offers a more granular and context-sensitive understanding of sectoral risk asymmetry, yielding findings with significant implications for portfolio diversification and risk management.

The structure of the paper is as follows. Section 2 reviews the relevant literature and identifies gaps motivating this study. Section 3 outlines the methodology, and Section 4 describes the data. Section 5 presents and discusses the empirical findings. Section 6 concludes with key implications and directions for future research.

Extreme positive returns (upside reward) and negative returns (downside risk) are worthy of close attention because substantial gains and losses occur more frequently than expected based on traditional return distribution assumptions (Huang et al., 2012). Tail analysis is a commonly used approach particularly in fields like finance, risk management and insurance, where rare events can have significant impacts (e.g. Valadkhani, 2024; Yaghoubi and Yaghoubi, 2024; Mwamba et al., 2017). Institutional investors, passive investors and fund managers all benefit from analyzing upside reward and downside risk in making investment decisions. The importance of such analyses has been acknowledged since the inception of theoretical asset pricing models.

According to Bawa and Lindenberg (1977), more emphasis should be placed on downside risk compared to upside reward, especially in situations where the distribution is positively skewed. This is because a positively skewed distribution tends to increase the standard deviation of excess return, which results in a decrease in the Sharpe ratio, penalizing fund managers who seek higher returns. In instances of a negatively skewed distribution, where downside risk surpasses upside deviation, assets with low co-skewness demonstrate higher average returns. Conversely, in positively skewed distributions, investors are willing to pay a premium for positive co-skewness (Galagedera and Brooks, 2007).

Stevenson (2001) argues that lower partial moments offer a superior alternative to variance as risk measures because they are not contingent upon the normality assumption. He suggests that metrics like lower partial moments, which concentrate on losses, might be more intuitively graspable for investors. His study demonstrates that incorporating lower partial moments can significantly enhance return performance of risk-averse investors. Valadkhani (2023) discussed the advantages of traditional risk-adjusted performance measures such as Sharpe ratio, Treynor ratio, Sortino ratio and Calmar ratio, which account for both downside and upside risk. He also examined the performance of sectoral ETFs during significant market downturns from December 23, 1998, to November 2, 2022.

Ding and Uryasev (2022) introduced Expected Regret of Drawdown (ERoD) and ERoD Beta to measure market drawdowns beyond a set threshold, offering a dynamic, asymmetric alternative to traditional beta. ERoD Beta captures asset behavior under market stress, identifying securities that outperform during declines. Their findings show ERoD and CDaR (Conditional Drawdown-at-Risk) Betas are more sensitive to drawdown risk and persistent over time, making them useful for portfolio construction. In contrast, Wang (2023) argues downside risk is not priced in equity markets. His decomposition of bear beta, based on option-implied crash probabilities, reveals the negative beta–return link stems from a high-risk, low-return anomaly similar to the betting-against-beta puzzle. He attributes this to investor disagreement and speculative overpricing, concluding that downside risk does not drive stock returns, supporting skepticism from Levi and Welch (2020) and Barahona et al. (2021).

Adding further depth to this debate, Schneider et al. (2020) argue that low-risk anomalies, such as the outperformance of low-beta or low-volatility stocks, stem from co-skewness risk rather than true pricing anomalies. They show that option-implied skewness predicts residual co-skewness and Capital Asset Pricing Model (CAPM) alphas, and controlling for skewness renders strategies like betting-against-beta and betting-against-volatility insignificant. Their results suggest these anomalies reflect compensation for negative co-skewness and that skew-aware pricing models better explain asset returns than traditional CAPM. Further refining the understanding of tail risk, Stoja et al. (2023) investigate whether systematic tail risk is priced in equity markets. They introduce two measures: the systematic tail coefficient, a generalization of Sibuya’s (1960) tail dependence and the systematic tail component, similar to Van Oordt and Zhou (2016) tail beta. Their analysis shows systematic tail coefficient carries a significant risk premium, indicating investors are compensated for joint market–asset tail events. In contrast, the systematic tail component does not earn a premium, which they attribute to common features that offset its predictive power.

Extending the analysis of tail risk into commodity markets, Yang et al. (2024) analyse tail risk spillovers and co-movement across INE (China), Brent (UK) and WTI (USA) crude oil futures. Using asymmetric slope CAViaR, transfer entropy and wavelet coherence, they find INE is a net receiver of tail risk, with Brent exerting more influence than WTI. Tail risk co-movement is asymmetric, stronger for upside risks and varies across time scales, with short-term links more volatile. Network analysis identifies a few dominant co-movement modes and rare but critical bridging modes. These findings highlight the need for multi-scale monitoring and early warning systems, particularly for emerging markets like INE.

Complementing these quantitative insights, Merkle and Ungeheuer (2025) provide behavioral evidence that investors systematically underestimate beta, particularly downside beta, and overestimate their ability to select portfolios that outperform the market. Their experiments reveal a common belief in “downside protection with upside participation,” especially among active investors. This cognitive bias distorts expectations and may limit the effectiveness of traditional risk metrics in guiding investment decisions. Overall, these contributions highlight the evolving understanding of downside and tail risk in finance, combining advanced quantitative tools with behavioral insights. They highlight the importance of integrating both perspectives in portfolio theory and practice.

The present study can be positioned alongside the works of Kinateder et al. (2024), Batten et al. (2024) and Aliu et al. (2021), as all explore asset behavior under stress or uncertainty, though across different asset classes and perspectives. Kinateder et al. (2024) examine the role of gold as a sector-specific safe haven during major crises, showing that some sectors, particularly financials, technology, health care and consumer discretionary, benefit from gold, while defensive sectors rely less on it. Similarly, Batten et al. (2024) compare gold mining stocks and gold ETCs (exchange-traded commodities), demonstrating the superior safe-haven properties and lower risk of ETCs, especially under heightened policy uncertainty, emphasizing external hedging mechanisms. By contrast, Aliu et al. (2021) highlight the elevated risk and limited diversification benefits of cryptocurrency portfolios relative to European equity portfolios, underscoring the challenges of risk management in emerging digital assets.

Collectively, all above studies complement the present work by illustrating that managing portfolio risk under extreme conditions involves both understanding intrinsic sectoral asymmetries and considering external hedges or alternative high-risk assets. While prior research often focuses on single-threshold models or individual stocks, the present study addresses a gap by employing threshold regression analysis across long-term, high-frequency data to provide nuanced insights into the dual nature of upside and downside risk in sectoral ETFs, offering practical implications for portfolio construction and risk management in volatile markets.

In empirical research, many scholars use equation (1) as a response function to estimate unconditional betas (Agrrawal and Waggle, 2010; Auer and Schuhmacher, 2015; Liang and John Wei, 2020). The underlying hypothesis of the proposed response model is that daily return fluctuations for a sectoral ETF are driven by two distinct components. The first component accounts for factors driving overall market changes, while the second component (⁠$εit$⁠) captures idiosyncratic factors specific to a particular ETF at time t, as illustrated below:

where $Rit$ measures i^th sectoral ETF daily return at time t, $Rmt$ is the total market daily return, β is the beta coefficient and $εit$ is the error term. As suggested by Valadkhani (2023), a higher $R2$indicates that the profitability of ETFs closely mirrors market performance. Consequently, the performance of sectoral ETFs is predominantly driven by broader market trends.

However, stock returns exhibit asymmetrical behavior in bullish and bearish markets (Li and Lam, 1995). Karolyi and Stulz (1996) and Hong et al. (2007) found that during market pullbacks, individual asset prices decline in unison, while during market rallies, they rise independently. They also argued that in bear markets, investors exhibit increased risk aversion, necessitating higher expected returns to compensate for the elevated risk. Furthermore, during bear markets, lower-risk investments tend to yield higher returns, whereas in bull markets, higher-risk investments generate greater returns.

Kim and Zumwalt (1979) observed that risk levels are higher during bear markets compared to bull markets in the US stock market. Similarly, Kim and Ismail (1998) found that risk, measured by earnings variability, is greater during bear markets for US firms. They argued that investors become more risk-averse in bear markets, demanding higher expected returns to compensate for the increased risk. Also, lower-risk investments tend to yield better returns in bear markets, whereas higher-risk investments are more profitable in bull markets. Valadkhani (2023) proposed a response model that distinguishes between upside beta (⁠$βu$⁠) and downside beta (⁠$βd$⁠), building upon the work of Kim and Ismail (1998) and Kim and Zumwalt (1979). This study adopts the response model proposed by Valadkhani (2023) as seen in the equations below:

Equation (2) and equation (3) can be estimated by sorting the data and considering the left and right tails of the SPY return distribution. Specifically, equation (2) estimates two beta coefficients that correspond to the 5% of observations located at the extreme left and right tails of the SPY return distribution. These coefficients are referred to as downside beta and upside beta, respectively. Similarly, equation (3) estimates two beta coefficients associated with the 10% of observations found at the extreme left and right tails of the SPY return distribution. These coefficients are also known as downside beta and upside beta, respectively.

Equation (4), however, estimates the downside and upside betas using an optimal threshold rather than the arbitrary 5% and 10% cut-off points. This is achieved by minimizing the sum of squared residuals through an iterative procedure developed by Bai and Perron (2003).

Equations (2), (3) and (4) have been widely used by scholars for estimating upside and downside betas (Estrada, 2002; Harlow and Rao, 1989; Rashid and Hamid, 2015; Valadkhani, 2023). In the equations above, beta can transition between $βu$ and $βd$ depending on the state of the market (i.e. positive vs negative). The term “trigger point,” denoted by $τ5%$ and $τ10%$of both tails in the parentheses of equations (2) and (3), respectively, serves as a switch causing a shift between the coefficients of beta. In equation (4), the “trigger point” or threshold parameter (τ) is not necessarily set at zero. This allows us to differentiate the β parameter that captures extreme negative and positive returns. The degree of these extreme negative and positive returns depends on how far the threshold parameter is positioned toward the right and left tail of the return distribution. The function I(.) is an indicator function, taking the value of one if the condition in the parentheses is true and zero otherwise. In this paper, we estimated the upside beta and downside beta for the extreme left and right tails of the return distribution using 5%, 10%, and optimal threshold cut-off points.

To demonstrate the boundary points, we use Figure 1 which shows the return distribution of SPY (a proxy for S&P 500 or total market) between January 1, 1999 and October 17, 2023, with daily observations. It can be ascended from Figure 1 that the return distribution is negatively skewed containing −0.241. To ensure our results are robust and not overly influenced by the most severe downside and upside deviations, we establish three threshold levels (τ) to capture the worst and best 5%, 10% and optimal of days with the highest negative and positive daily returns. The optimal sector-specific values for τ will be determined internally and can fall at any point on both tails. However, the daily negative return cut-offs (τ) for 5% and 10% are −1.9%, and −1.3%, respectively. On the other hand, the daily positive return cut-off (τ) for 5% and 10% are 1.7% and 1.2%. On the graph, the y-axis represents the frequency of returns, while the x-axis shows the daily return in percentages.

Informed by the growing body of literature on asymmetric risk responses and sectoral heterogeneity, this study develops and implicitly tests the hypothesis that sectoral ETFs exhibit significantly different upside and downside betas in the tails of the market return distribution. Building on earlier works that emphasize the importance of downside risk (Bawa and Lindenberg, 1977) and more recent empirical findings on asymmetry in asset behavior (Valadkhani, 2023; Ding and Uryasev, 2022), the hypothesis suggests that certain sectors, particularly those classified as defensive (e.g. consumer staples, utilities and health care), will have downside betas below unity, while aggressive sectors (e.g. energy, financials and technology) will display higher upside betas during market rallies. The discussion section systematically evaluates this hypothesis using threshold regression estimates across three boundary points – 5%, 10% and an optimally derived threshold – confirming that most sectoral ETFs exhibit significant asymmetries. The finding that XLK consistently shows a greater upside than downside beta contrasts with most prior studies that focus solely on downside risk, thereby extending the literature by explicitly addressing the dual nature of tail responses. This comparative analysis reinforces the relevance of testing asymmetry hypotheses when assessing sector-specific ETF behavior in extreme market conditions.

This study uses the most comprehensive daily data set accessible for sectoral ETFs, spanning from January 1999 to October 2023. Data for 1998 was excluded due to its limited availability, consisting of only seven observations, and the absence of other sectoral ETFs before this year. These sectoral ETFs are denoted as Standard and Poor’s depository receipts (SPDRs), managed by State Street Global Advisors, designed to track the Standard and Poor’s 500 index (S&P 500). This ensures a consistent delineation of sectoral ETF constituents, avoiding any instances of overlap. Although the initial US ETF (SPY) was introduced on February 1, 1993, it was not until December 23, 1998, that sectoral ETFs were first issued. The ETFs encompassed in this investigation are as follows: SPY (representing the entire market or S&P 500), XLK (technology), XLV (healthcare), XLE (energy), XLF (financial), XLU (utility), XLP (consumer staples), XLY (consumer discretionary), XLI (industrial) and XLB (materials). Table 1 outlines the SPDR ETFs along with their top 10 holdings.

The 10% cut-off point comprises 365 days out of the total 6,345 in the sample, encompassing both the right tail and the left tail of the return distribution. Left tail observations occurred when SPY fell between −11.6% (March 16, 2020) and −0.18% (February 2, 2016). Conversely, right tail observations transpired when SPY rose between 1.25% (April 20, 1999) and 13.6% (October 13, 2008). To enhance the confidence and reliability of our findings, we also consider more stringent and optimal cut-off points. The more stringent cut-off point involves 5% (representing 317 days of the total 6,345 days in the sample) of the most extreme daily returns. Right tail observations occurred when SPY rose between 1.7% (February 18, 2003) and 13.6% (October 13, 2008), while left tail observations were observed when SPY fell between −11.6% (March 16, 2020) and −1.20% (July 16, 2002).

Our study also takes into account the GFC as an important event that prompted structural shifts in return series. Therefore, we assess the consistency and sensitivity of upside and downside betas at the extreme tails of the return distribution. We analyze the pre-GFC period (from 1999 to 2007) and the post-GFC period (from 2008 to 2023) separately to investigate whether the GFC impacted on downside and upside betas. The GFC stands out as a significant economic event that instigated substantial changes in financial markets, economic policies, regulatory frameworks and business environments worldwide. It marked a period of economic and regime transition, during which many economic and financial time series data were distorted. Various countries implemented diverse monetary and fiscal policies, which had differential impacts on financial variables between the post-GFC and pre-GFC periods.

Table 2 presents the descriptive statistics of our data set. According to Table 2, XLE exhibited the highest daily return (15.3%) on October 13, 2008, during GFC, while the lowest return (−22.5%) occurred on March 9, 2020, amid the COVID-19 outbreak. The kurtosis statistics for the return distributions are all greater than 3, indicating that they are leptokurtic. This suggests that investing in these ETFs involves a substantial level of financial risk due to the heightened likelihood of both extremely large positive and negative returns. Specifically, sectors with the highest kurtosis, such as XLF (17.39) and XLE (15.65), demonstrate significant risk.

In this section, we use threshold regression analysis to rigorously examine the behavior of sectoral ETFs under extreme market conditions. This method includes the estimation of downside and upside betas using predetermined and optimal threshold cut-off points to capture the response of ETFs during severe market downturns and upturns. We use high-frequency, long-term daily return data to ensure robust statistical inference and to accurately identify tail events. The analysis also incorporates comparative stability assessments across sectors to determine which ETFs exhibit resilience during volatile periods.

Before estimating the mean and standard deviation equations, it is essential to analyze the time series properties of our daily return data for the period January 1, 1999, to October 17, 2023. Table 2 also shows the outcomes of the Augmented Dickey–Fuller (ADF) test (Dickey and Fuller, 1979) and the Phillips and Peron (PP) test for all series in both their levels and logarithmic differences. The Schwarz criterion is used to determine the optimal lag length and bandwidth for these tests. The results in Table 2 reject the unit root null at the 1% level for all return series based on the PP tests and for most series under the ADF test. Hence, it can be concluded with confidence that all daily return series are I(0), consistent with expectations, implying that random shocks exert only transitory effects on returns,

As all return series are stationary, we can proceed to estimate equation (2), (3) and (4). Table 3 shows the estimated threshold mean and standard deviation equations for the nine SPDR sectoral ETFs over the same sample period, allowing for a direct comparison. Three sets of coefficients are calculated using boundary points for the threshold parameter (τ) at 5%, 10% and the optimal point. These coefficients include $βd$ for extreme negative returns (when the market is in the extreme left tail of the return distribution) and $βu$ for extreme positive returns (when the market is in the extreme right tail of the return distribution).

Table 3 shows the estimated betas for the 10%, 5% and optimal boundary points. Our analysis reveals that the 10% downside betas for XLP, XLV and XLU are below unity, suggesting the defensive response when the market is in turmoils. To ensure the reliability of our findings, we apply the more stringent 5% and optimal boundary points, respectively. It can be confirmed from Table 3 that both the 5% and optimal downside betas for XLP, XLV and XLU remain once again less than unity. This confirms the assertion by Valadkhani (2023) that XLP, XLV and XLU are defensive or antirecessionary ETFs. Since their downside beta is less than unity, investors may choose XLU, XLP and XLV during market downturn, especially XLP. These findings are consistent with the expectation that utilities, consumer staples and health-care sectors are more stable during extreme market downturns. As Cowan (2020) noted, many investors favor these sectors due to their greater resilience compared to other sectors. Both Valadkhani (2023) and Cowan (2020) argue that utilities, consumer staples and health-care sectors are defensive during crises.

According to Table 3, the results for the 5%, 10% and optimal cut-offs are consistent for XLB, XLE, XLF, XLI, XLV and XLY, as their downside beta is greater than their upside beta. This confirms that that these ETFs tend to experience larger declines during market downturns. In contrast, XLK consistently shows the opposite pattern, regardless of the cut-off used. However, the results for XLP are less conclusive as the other ones due to its defensive nature. Interestingly, XLK stands out as the only sectoral ETF with its downside beta less than its upside beta irrespective of the boundary point. This suggests that it rises more than the market during bull markets and falls less than the market during bear markets, reminiscent of the rockets and feathers hypothesis in energy economics: XLK shoots up like rockets and falls like feathers.

Our findings are in line with previous research (Cowan, 2020; Valadkhani, 2023). Berman and Pfleeger (1997) investigated the role of sectoral ETFs in the business cycle. The existing literature suggests that defensive sectors (XLP, XLV and XLU) comprise essential goods with inelastic demand throughout different economic cycles. Conversely, aggressive sectors such as consumer durables, industrial and financial sectors are more vulnerable to macroeconomic fluctuations in the business cycle (Ngene, 2021).

In their study, Bhardwaj and Dunsby (2014) discovered that in the stock market, the energy and industrial metals sectors exhibit high responsiveness to the business cycle and tend to provide higher returns during periods of increasing and unexpected inflation. Murphy (2012) suggests that economically sensitive cyclical groups and the technology sector typically lead the stock market. As economic expansion progresses, leadership transitions to the basic materials and energy sectors. However, the dominance of the energy sector often signals the conclusion of the economic expansion and the bull market in stocks. Rising energy prices prompt the Federal Reserve to raise short-term rates to curb inflation, potentially dampening the equity market.

Table 3 further reveals that XLB, XLE, XLF and XLY consistently exhibit downside betas greater than unity. This signifies that during bear markets, these high-beta ETFs are highly susceptible to generating poorer returns compared to the three defensive ETFs (XLP, XLV and XLU). Conversely, during market rallies, XLE, XLF and XLK showcase upturn betas greater than unity. These sector-specific ETFs are prone to delivering higher returns compared to other sectoral ETFs, particularly the defensive ones. According to Novy-Marx (2014), defensive sectors comprise companies involved in utilities, staples and health care, which are considered low-beta, low-volatility assets with earnings and resilience against economic downturns. In contrast, aggressive sectors such as consumer durables, information technology, industrial and financial sectors exhibit high betas and tend to generate greater returns than defensive stocks during periods of economic expansion (Ngene, 2021).

To address the last research question, we calculated the difference between the upside and downside deviations at the optimal boundary points in Figure 2. This figure compares upside betas (performance during market upturns) and downside betas (performance during market downturns) for various sectors, each represented by a three-bar cluster: the blue bar represents the difference between upside and downside betas, the orange bar indicates the upside beta, and the green bar corresponds to the downside beta. XLK and XLP stand out as the only sectors with a higher beta during market upturns than during downturns, suggesting that the technology and consumer staples sectors tend to perform better when the overall market is bullish at the optimum. XLY and XLE exhibit downside betas noticeably higher than their upside betas, indicating higher volatility during market downturns. As can be seen from Figure 2, XLK and XLP emerge as the top-performing ETFs in terms of upside performance exceeding downside fall, showing relatively better performance during market upswings at the optimum. Investors can leverage this information to make informed decisions. They may consider overweighting XLK and XLP during bullish phases while being cautious with XLY and XLE due to their higher downside betas. Exploring investment opportunities in XLK, XLP, XLI and XLV sectors could potentially yield favourable results during market rallies. It is crucial to remember that beta measures a stock or sector’s volatility relative to the overall market, so other factors should be considered, and consulting financial experts is advisable when making investment choices.

Having compared the downside beta to the upside beta in Table 3, we now need to analyze whether there are significant differences between them at various cut-off points. We use the Wald test to compare the upside and downside beta at the 5%, 10% and optimal boundary points, with the null hypothesis $H0: βd$= $βu$⁠. Table 4 provides the Wald test results, showing that the differences for XLB, XLE, XLF, XLI, XLK, XLP and XLY are significant for at least one cut-off point. This suggests that asymmetries in the behavior of US equity returns vary depending on the specific thresholds used to define extreme returns. Table 4 also shows that, among all the sectoral ETFs irrespective of the boundary point, XLK is the only sectoral ETF that has its upside beta greater than the downside beta at the optimum. This confirms the initial assertion that XLK performs better in bullish market condition than bearish market condition. Therefore, our results are robust.

To further assess the consistency and reliability of our results, we examine pre- and post-GFC sample observations. The pre-GFC period spans from January 1, 1999, to December 31, 2007. We use 10% of the pre-GFC sample period, representing 235 out of 2,346 observations, and further explore a more stringent 5% sample, representing 117 observations, as well as the optimal cut-off point. Table 5 confirms that the defensiveness of XLP, XLU and XLV for at least one boundary point. Considering all the cut-off points, our results in Table 5 are similar to those in Table 4. Most of the sectoral ETFs (XLB, XLE, XLF, XLI, XLP, XLU, XLV and XLY) exhibit greater downside beta than upside beta in at least two of the boundary points. XLK remains the only sectoral ETF with an upside beta that exceeds its downside beta, regardless of the boundary points. Hence, our results are consistent with previous results in Table 3.

Also, XLF, XLI and XLY continue to exhibit greater downside beta regardless of the boundary point considered. This implies that once again, XLF, XLI and XLY are less desirable during market downturns. On the other hand, the upside beta for XLF and XLK remains greater than unity. These results confirm that during market rallies, XLK and XLF are likely to yield higher returns and, therefore, perform better during market upturns.

To check the robustness of the pre-GFC results, we consider Wald test of the upside and downside betas at the various boundary points. It can be confirmed from Table 6 that the null hypothesis $H0: βd$= $βu$ can be rejected for XLE, XLI, XLK and XLV in at least one of the boundary points. This confirms the consensus of the results in Table 4 and Table 6 as most of the differences are significant for at least one cut of point. In conclusion, the asymmetry behavior of US equity returns varies depending on the specific thresholds used to define extreme returns. However, our model is robust in estimating the upside and downside betas. The post-GFC sample observation spans from January 1, 2008, to October 17, 2023. The study uses a 10% boundary point, representing 412 out of the total 4,121 observations, followed by the stringent 5% cut-off, representing 206 observations, and the optimal boundary point.

Table 7 reveals that XLP, XLU and XLV consistently have downside betas less than unity across all boundary points, confirming their defensive nature. This confirms our initial finding that XLP, XLU and XLV are defensive sectors. Consistently, irrespective of the boundary points most of the sectoral ETFs (XLB, XLE, XLF, XLP and XLY) have their downside betas greater than their upside betas. XLK on the other hand, remain the only ETF that has its upside betas greater than its downside betas irrespective of the cut-off. XLV and XLU are not conclusive as other ones, this is because of their defensive nature.

Conversely, XLB, XLE and XLF exhibit downside betas greater than unity, indicating a higher likelihood of yielding poorer returns during market downturns. This supports our finding that XLB, XLE, XLF and XLY are risky during market downturns. Furthermore, Table 7 indicates that XLE, XLF and XLK have upside betas greater than unity. This suggests that these sectors are highly prone to higher returns during market upswings, consistent with our earlier findings. Interestingly, XLI is now considered defensive in our new sample. The post-GFC results demonstrate that our initial findings remain generally consistent and robust even after the GFC, a period characterized by various fiscal and monetary policies affecting the financial market.

To check the robustness of the post-GFC results, we consider Wald test of the upside and downside betas at the various boundary points. It can be confirmed from Table 8 that the null hypothesis $H0: βd$= $βu$ can be rejected for most sector specific ETFs (XLE, XLF, XLK, XLP and XLY) indicating a significant difference between $βd$ and $βu$⁠, suggesting the asymmetrical behavior of sectoral ETFs irrespective of the boundary point. This results in consistent with previous results. Our results remain consistent even at post-GFC.

The empirical analysis conducted in this study examines how sectoral ETFs respond to extreme market downturns and upturns from January 1, 1999, to October 17, 2023. By considering various cut-off points at the extreme tails of return distributions, we estimate the downside and upside betas for all SPDR sectoral ETFs. Our findings shed light on the behavior of sectoral ETFs in different market conditions. Specifically, we observe that consumer staples (XLP), health care (XLV) and utility (XLU) ETFs exhibit lower downside betas during market downturns, indicating their defensive nature. This aligns with expectations and suggests these sectors may serve as safer investment options during turbulent market periods. Conversely, technology (XLK), materials (XLB), energy (XLE), financial (XLF), industrial (XLI) and consumer discretionary (XLY) ETFs demonstrate higher upside betas during market upturns. Notably, XLP, XLV and XLU maintain lower upside betas during market upturns, implying they may not perform as strongly as other sectors during bullish market phases. Our results hold consistent across different boundary points in the full sample and in pre- and post-GFC sub-periods, indicating the robustness of our findings. Our analysis highlights practical implications for investors navigating volatile market environments. During market downturns, defensive sectors such as XLP, XLV and XLU may offer stability and lower downside risk. Conversely, during market upswings, sectors like XLK, XLE and XLF may present opportunities for higher returns.

Our analysis consistently shows that the sectoral ETFs XLP, XLV and XLU have both upside and downside betas below unity, confirming their defensive characteristics. Investors holding these ETFs may not achieve outsized gains during strong market rallies, but they are generally protected from severe losses during downturns. In contrast, XLB, XLE, XLF and XLY exhibit downside betas exceeding unity, indicating higher susceptibility to large losses in extreme market declines, suggesting caution when investing heavily in these sectors during turbulent periods.

Across all boundary points and sample periods (full, pre-GFC and post-GFC), XLK uniquely displays an upside beta greater than its downside beta, highlighting its stronger performance in market upswings. Most other ETFs, including XLB, XLE, XLF, XLI and XLY, consistently have higher downside than upside betas. Defensive sectors like XLU, XLP and XLV show more mixed results due to their stable nature. Notably, XLE, XLF and XLK exhibit upside betas greater than one, signaling their potential to outperform in market rallies. XLK and XLU particularly stand out by having higher upside than downside betas, reinforcing their reputation for stability and strong performance. Meanwhile, XLE and XLY show stronger downside risk than upside potential. Overall, XLK, XLU, XLP and XLV emerge as top-performing sectors where upside gains exceed downside losses.

While XLU, XLP and XLV are widely regarded as defensive due to their historical resilience during downturns, the inclusion of XLK among stable sectors is noteworthy. This is largely driven by the presence of mega-cap technology companies like Apple, Microsoft and Nvidia within XLK. These firms’ diverse product portfolios, spanning hardware, software, cloud and digital services, allow them to generate revenues from multiple sources, reducing reliance on any single market. Their strong financial health, substantial cash reserves and share buyback programs further buffer them against economic shocks.

In financial terms, stocks or ETFs with higher upside than downside risk, such as XLK, present an asymmetric risk profile that is attractive to investors willing to accept volatility for greater returns. This asymmetry often leads to higher valuation multiples as markets price in expected future growth and profitability. Consequently, these stocks draw significant capital, benefiting companies through increased valuations and supporting growth initiatives.

A key limitation of this study lies in its exclusive focus on US sectoral ETFs, which may limit the generalizability of the findings to other markets or asset classes. While the threshold regression framework captures asymmetries effectively, it does not account for time-varying dynamics or macroeconomic drivers that may influence beta estimates. Future research could extend this analysis by incorporating international sectoral ETFs, exploring regime-switching models or integrating macro-financial variables to better understand the drivers of asymmetric responses under varying economic conditions.