COVID-19 and adaptive behavior of returns: evidence from commodity markets

The COVID-19 pandemic caused unprecedented swings in financial market returns, with rapid global spread leading WHO to declare a global emergency on February 20, 2020, and a pandemic on March 11, 2020. Major stock markets experienced sharp declines (e.g., S&P 500 fell 30% within 16 trading days), and volatility reached levels comparable to 2008, 1987, and the early 1930s. These conditions question the Efficient Market Hypothesis (EMH), which posits that past trading information cannot be used to forecast prices. The Adaptive Market Hypothesis (AMH) of Lo (2004) reconciles EMH with behavioral finance, proposing that market efficiency and predictability evolve over time due to changing market conditions, investor behavior, technology, and policy. COVID-19 developments, including distinct phases (incubation, outbreak, fever) in investor attention and behavior, provide a natural setting to test AMH. This study investigates whether commodity returns exhibit time-varying predictability during COVID-19, using popular commodities traded on the Chicago Board Options Exchange (CBOE). The analysis proceeds in two steps: (1) applying the Generalized Spectral (GS) test to detect evolving (linear and non-linear) dependencies indicative of adaptive behavior; and (2) applying linear and non-linear econometric tests to assess predictability and profitable opportunities across COVID-19 sub-periods (epidemic, pandemic, endemic, and fatality phases). The study contributes by focusing on commodity markets during COVID-19, examining return behavior under different COVID-19 conditions, and providing evidence on the engagement of commodity returns with COVID-19 shocks under AMH.

Prior work shows infectious disease outbreaks can disrupt economies and financial markets. COVID-19’s epidemic and pandemic phases generated large economic swings affecting billions (e.g., Gates, 2020), with prior outbreaks (SARS, Ebola, Zika) also linked to market underperformance and volatility (Lee and McKibbin, 2004; Chen et al., 2007; Macciocchi et al., 2016; Del-Giudice and Paltrinieri, 2017; Chen et al., 2018; Goodell, 2020). Studies during COVID-19 document negative relationships between deaths/cases and stock returns (Al-Awadhi et al., 2020; Ashraf, 2020; Liu et al., 2020; Zhang et al., 2020), varying impacts across countries and sectors, and heightened global risk and volatility (Baker et al., 2020; Alfaro et al., 2020; Papadamou et al., 2020). Others analyze volatility dynamics and spillovers (Onali, 2020; Ali et al., 2020; Gunay, 2021), effects of government interventions on liquidity (Zaremba et al., 2021), and contagion effects (Okorie and Lin, 2021). Research on commodities suggests substantial changes during the pandemic (Lin and Su, 2021) and supports AMH with periods of predictability and unpredictability (Shahid et al., 2020a). The literature motivates examining how COVID-19 phases affect commodity return predictability through the lens of AMH.

Data consist of popular commodity indices from three sectors—Agriculture, Energy, and Precious Metals—traded on the CBOE (data sourced via DataStream; sample from December 2, 2019, to December 31, 2020). Log returns are computed as r_t = [ln(P_t) − ln(P_{t−1})] × 100. The COVID-19 period is partitioned into: (i) epidemic (emergence to March 10, 2020), (ii) pandemic (around March 10, 2020 to August 2020), and (iii) endemic (post-August 2020). Additionally, fatalities-based sub-periods are defined as Fatal1 (Jan 1–Feb 14, 2020; primarily China), Fatal2 (Feb 15–Feb 28, 2020; Europe), and Fatal3 (post-Feb 28, 2020; USA and global). Methodologically, the study first applies the non-parametric Generalized Spectral (GS) test (Escanciano and Velasco, 2006) with a one-month rolling window to detect evolving linear and non-linear dependencies consistent with departures from the martingale difference hypothesis. The GS test statistic D_n^2 uses a Cramér–von Mises norm with the standard normal CDF as weighting; large values indicate rejection of efficiency. Second, to quantify predictability, linear dependence is tested using: (a) Autocorrelation (AC) at lag 5, (b) Runs test for independence, and (c) Variance Ratio (VR) tests (Lo and MacKinlay, 1988) under heteroskedasticity-robust M2(k) for holding periods k = 2, 4, 8, 16 (reported focus on k = 4). For non-linear dependence, after pre-whitening via AR models to remove linear structure, the BDS test (Brock et al., 1996) is applied to residuals using embedding dimensions m = 2–5 and ε proportional to the standard deviation (commonly ε = 0.5σ, 1σ, 1.5σ, 2σ; results highlighted for BDS 5(20)). Descriptive statistics summarize return behavior across full sample and sub-periods, and figures display rolling GS p-values to visualize evolving inefficiency.

- GS test with one-month rolling window reveals evolving inefficiencies across commodities during COVID-19, with p-values indicating episodes of significant predictability and no predictability, consistent with AMH. - Full-sample (COVID-19) linear tests: AC indicates predictability for a subset (e.g., feeder cattle, live cattle, non-energy, crude oil; and silver, palladium, platinum at lag 5). Runs test suggests soybean is predictable in agriculture; no predictability for energy and precious metals by this test. VR test (k = 4) shows returns of nearly all commodities across agriculture, energy, and precious metals are predictable (significant VR statistics), evidencing linear dependencies. - Full-sample non-linear tests: BDS statistics are significant (often at 1%) for the majority of agriculture and precious metal indices, indicating strong non-linear dependence; energy indices exhibit strong predictability during COVID-19. - Phase analysis (epidemic, pandemic, endemic): Many indices show no AC-based predictability in the epidemic phase but become highly predictable in the pandemic, with predictability waning in the endemic phase (agriculture except agriculture-livestock and live cattle; most precious metals except copper; most energy indices except unleaded gasoline). Live cattle is predictable in pandemic and endemic but not epidemic; copper and unleaded gasoline are predictable in epidemic and pandemic but not endemic. - Runs tests across phases also show alternating episodes of predictability and no predictability, supporting AMH. - VR tests: majority of indices are predictable in pandemic and endemic conditions, but not in the epidemic phase. - Non-linear (BDS) across phases: commodities generally show significant non-linear predictability during the pandemic, with little to none in epidemic and endemic phases. Exceptions include palladium, reduced energy, and unleaded gasoline, which are not predictable in epidemic conditions but are predictable in pandemic and endemic conditions. - Descriptive performance patterns: during COVID-19, most agriculture indices generated positive returns except feeder cattle and live cattle; most energy indices had negative returns; all precious metals had positive returns. By sub-phase, agriculture was largely negative in epidemic and pandemic but positive in endemic (except feeder cattle); energy indices were negative in the epidemic but positive in pandemic and endemic; precious metals were negative in epidemic but positive thereafter (Table 1).

The findings show that commodity return predictability evolves with COVID-19 market conditions, directly addressing the study’s AMH-based research question. Periods of significant predictability emerge particularly during the pandemic phase, while predictability tends to dissipate in the epidemic and endemic phases. The coexistence of linear and non-linear dependencies, their rise and fall across sub-periods, and broad confirmation via GS, VR, and BDS tests support AMH’s premise that market efficiency is dynamic and contingent on environmental pressures such as crises. This adaptive behavior suggests that shocks, policy measures, and investors’ changing attention during COVID-19 temporarily altered market structure and trading behavior, creating and then removing profitable opportunities in commodity markets. The sectoral differences observed (e.g., energy vs. precious metals vs. agriculture) further underscore heterogeneous adaptive responses across commodities.

Commodity markets exhibited adaptive behavior during COVID-19, with return predictability varying over time and across epidemic, pandemic, endemic, and fatalities-based phases. Linear (AC, Runs, VR) and non-linear (BDS) tests, supported by rolling GS evidence, reveal alternating episodes of predictability and efficiency consistent with the Adaptive Market Hypothesis. The study contributes by documenting how COVID-19 phases engaged with commodity return dynamics, showing that predictability strengthened during the pandemic phase and weakened in epidemic and endemic periods. Future research is suggested for other asset classes—debt, equity, and currency markets—to assess whether similar adaptive patterns arise under COVID-19 or comparable crises.