Concave-convex effect of financial resilience on corporate financial performance: quantile regression approach

The paper examines whether and how financial resilience (FR) relates to corporate financial performance (CFP) during the turbulent COVID-19 period. FR encompasses a firm’s capacity to withstand and recover from financial shocks through robustness, flexibility, foresight, and liquidity. Prior studies have separately linked financial flexibility (FF) and working capital management (WCM, proxied by the cash conversion cycle, CCC) to performance with mixed results, suggesting potential nonlinearity. Motivated by Taiwan’s manufacturing sector importance (≈30% of GDP) and conflicting findings on FF/CCC with CFP, the study asks: (i) Is FR associated with CFP? (ii) Is the relationship nonlinear (concave or convex) and does it vary across the performance distribution and by environmental sensitivity of industries? Using a quantile regression (QR) framework and tests for U-shaped relationships, the paper proposes that both TMGT (inverted U) and TLGT (U-shape) effects may govern the FR–CFP nexus, with managerial implications for optimizing FR investment.

The review defines FR as the capability to access internal and external resources to cope with financial adversity and to recover quickly from shocks. Traditional measures often focus on households via surveys, lacking objective firm-level metrics. From corporate finance and auditing perspectives, viability hinges on liquidity and solvency; thus, FR can be proxied by combining stock-based financial flexibility (FF) and flow-based liquidity via the cash conversion cycle (CCC). Prior evidence on FF–CFP is mixed: positive (e.g., Chun and Yanbo, 2016), negative (Agha and Faff, 2014), and nonlinear concave effects (Yi, 2020; Gu and Yuan, 2020; Chang and Wu, 2022a; Zhang et al., 2022). Similarly, WCM (CCC)–CFP links are variously negative, positive, or nonlinear, with several studies evidencing inverted U-shapes. No prior work synthesizes stock (FF) and flow (CCC) into a firm-level FR construct to assess its link with CFP. The review also motivates QR as robust to non-normality and outliers, capturing heterogeneity across the outcome distribution, and references methodological guidance (Haans et al., 2016; Lind and Mehlum, 2010) on testing U- and inverted U-shaped relations.

Sample: Publicly listed manufacturing firms on the Taiwan Stock Exchange (TSE) during the early COVID-19 phase, Q1 2020–Q3 2021; 6,051 firm-quarters initially, with 5,918 observations used in regressions after cleaning. Measures: - Dependent variable (CFP): Tobin’s Q = (book value of total assets − book value of common equity + market value of common equity) / book value of total assets. - Explanatory variable (FR): FR = FF + 1/CCC, where FF = Cash flexibility + Debt flexibility = (cash + cash equivalents)/total assets + (1 − total liabilities/total assets). CCC = INV + AR − AP, with INV = (Inventory/Cost of Sales)×365; AR = (Accounts Receivable/Sales)×365; AP = (Accounts Payable/Purchases)×365. If CCC is negative, 1/CCC is set to 1 (reflecting excellent liquidity). - Control variables: ARD = 365 / accounts receivable turnover; BNIG = (current − prior net profit before tax) / prior net profit before tax; OEG = % change in owners’ equity; RDG = R&D expenditures / sales; REVG = quarterly revenue growth (%); SIZE = ln(total assets); LEV = total liabilities / total assets. Model and estimation: Panel quantile regression (Koenker and Bassett, 1978) with firm fixed effects and seasonal (quarter) fixed effects to estimate effects at the 10th, 25th, 50th, 75th, and 90th quantiles of Tobin’s Q. Both FR and FR^2 are included to capture curvature. U-/inverted U-shapes are validated using the Lind and Mehlum (2010) U-test, reporting slopes at bounds, Fieller’s confidence intervals for turning points, and whether inflection points lie within data ranges. Inter-quantile tests assess coefficient heterogeneity across quantiles using bootstrap F-tests. Multicollinearity was checked via VIF (1.07–1.88 < 5). Robustness: (i) Alternative CFP measure price-to-book ratio (PBR); (ii) industry-adjusted FR (FR_ind). Industry heterogeneity: Subsamples for environmentally sensitive (ES: e.g., oil, gas, paper, metals, chemicals; 975 firm-quarters) and non-ES firms (4,943 firm-quarters).

- OLS versus QR: OLS finds FR and FR^2 insignificant. QR reveals significant nonlinearities and heterogeneity across Tobin’s Q quantiles. - Overall QR (full sample): - 10th, 25th, 50th quantiles: Inverted U-shaped (concave) FR–CFP relationship. Turning points and 95% Fieller CIs lie within data ranges: 10th: 1.159 [1.09, 1.24]; 25th: 1.324 [1.21, 1.49]; 50th: 1.527 [1.32, 2.02]. Slopes at lower bounds positive and significant; at upper bounds negative and significant. - 90th quantile: U-shaped (convex). Turning point 0.719 [0.46, 0.84], with negative significant slope at lower bound and positive significant slope at upper bound. - 75th quantile: Evidence consistent with curvature (FR^2 > 0 and significant), but FR linear term not significant; main narrative emphasizes concave at lower/median and convex at highest quantile. - Control variables: REVG, OEG, RDG, and LEV generally positive and significant. BNIG significant (mostly negative) except at the 10th quantile. ARD positive at lower quantiles but negative at upper quantiles. SIZE consistently negative and significant. - Inter-quantile differences: Bootstrap F-tests show significant coefficient heterogeneity between 90th vs 10th and 75th vs 25th quantiles for FR and FR^2 (and for most controls), confirming distributional heterogeneity. - Robustness: Using PBR as CFP yields consistent inverted U-shaped patterns in lower and median quantiles. Using FR_ind (industry-adjusted FR) reproduces baseline curvature and significance patterns. - Industry heterogeneity: - ES firms: Inverted U-shaped FR–CFP at 10th, 25th, 50th, and 75th quantiles. Turning points within data ranges: 10th: 1.078 [1.06, 1.09]; 25th: 1.072 [1.00, 1.14]; 50th: 1.098 [1.03, 1.18]; 75th: 1.076 [0.95, 1.22]. At the 90th quantile, curvature not supported (FR^2 not significant). - Non-ES firms: Inverted U-shaped at 10th (1.192 [1.14, 1.25]) and 25th (1.412 [1.25, 1.69]); median quantile exhibits monotone increase (no inverted U despite a numerical turning point 1.912). U-shaped at upper quantiles with turning points 75th: 0.511 [−0.14, 0.69]; 90th: 0.803 [0.34, 0.96]. - Descriptive context: Mean FR ≈ 0.791; many firms lie to the left of concave turning points in lower/median quantiles (benefits of increasing FR) and to the right of convex turning points at the top quantile (benefits of higher FR for high performers).

The findings address the central question by demonstrating that the FR–CFP relationship is nonlinear and heterogeneous across performance quantiles and industries. Concave effects at low/median quantiles indicate diminishing marginal returns in line with the TMGT perspective: investing in FR boosts CFP up to an optimal point beyond which benefits wane. Convex effects at the highest quantiles align with TLGT: insufficient FR harms performance until a minimum threshold is surpassed, after which additional FR strengthens CFP. The QR approach captures distributional nuances missed by OLS, resolving mixed prior results on FF- and WCM–CFP by showing where along the CFP distribution over- or under-investment in FR is most likely. Industry splits highlight that ES firms predominantly face TMGT-driven concavity across most quantiles, implying careful calibration of FR to avoid over-investment. Non-ES firms show concavity at lower quantiles but convexity at upper quantiles, suggesting high-performing non-ES firms benefit from elevating FR above minimal thresholds. Managerially, firms should estimate and target optimal FR levels (combining FF and CCC) contingent on their market-based performance and industry profile. For policymakers and investors, FR can be a salient criterion for resilience and valuation during crises, but optimality and heterogeneity are key.

The study contributes by (i) proposing and testing a synthesized firm-level FR metric (FF + 1/CCC) and showing a curvilinear FR–CFP nexus in Taiwan’s manufacturing sector during COVID-19; (ii) applying QR with formal U-tests to uncover heterogeneous concave and convex patterns across Tobin’s Q quantiles; and (iii) evidencing industry heterogeneity: ES firms mainly exhibit concave relations, whereas non-ES firms show concave at lower and convex at upper quantiles. Overall, too much or too little FR is detrimental; optimal FR depends on firm performance tier and industry context. Practical implications include maintaining adequate liquidity and working capital efficiency to position around the quantified thresholds. Future work should extend to multi-country settings, longer horizons, and explore channels (capital, labor, technology) and external supports affecting FR and CFP.

- Short observation window confined to early COVID-19 (Q1 2020–Q3 2021) and a single economy/sector (Taiwanese listed manufacturing), limiting generalizability. - Potential omitted external factors (e.g., government support, labor policies) affecting CFP during the pandemic were not fully incorporated. - FR mechanisms/channels (capital, labor, technology) were not decomposed; future research should examine these pathways. - Data sourced from a proprietary database; replication may require access to the same subscription data.