Assessing the Efficiency and Persistence of African Stock Markets through DEA Score: Evidence from COVID-19 Pandemic

Abstract

The few studies on COVID-19’s impact on stock market efficiency have reached mixed conclusions. However, the findings lean towards a negative impact, no studies have assessed market efficiency when returns increase in the existing capacity of COVID-19 cases, exchange rates and inflation rates. This study uses data envelopment analysis (DEA) and the DEA-adjusted estimator. We finally adopt the cross and time product ratios to determine the persistence of stock market efficiency. We find that the COVID-19 pandemic severely impacted the efficiency of African stock markets in 2021 and that the efficiency of African stock markets persists only in the short run. These findings are relevant to investors seeking to diversify their portfolios during pandemics and to regulators of African stock markets. Global investors should diversify their portfolios with African stock markets to mitigate the impact of pandemics on their investments. To reap the benefits of diversification, investors should invest in efficient African markets during pandemics and sell stocks in inefficient markets in the short run. In addition, regulators of African stock markets should adopt technologies that aid in the flow of information among investors.

Keywords

COVID-19 Stock Market Efficiency Persistence Data Envelopment Analysis Cross Product Ratio

Introduction

Studies on the efficiency of African stock markets before the COVID-19 pandemic have found that most African stock markets were efficient (Abakah et al., 2018; Kelikume, 2016). However, on 11 March 2020 the World Health Organization (WHO) declared COVID-19 a pandemic. Since then, the increasing spread of the COVID-19 pandemic has prompted many governments to introduce unprecedented pandemic control measures. These measures led to the global shutdown of businesses. The pandemic has caused unprecedented damage to the global economy by disrupting the global supply chain (Hedwall, 2020). The economic impact of COVID-19 has increased market risk aversion in ways not observed since the global financial crisis (Baker et al., 2020a). Stock markets declined by over 30% and implied volatilities of equities and oil prices spiked to crisis levels. This heightened turmoil in global financial markets occurred despite the substantial and comprehensive financial reforms agreed upon by the G20 in the post-crisis era (OECD, 2020). Investors have lost considerable amounts of money because of the economic contractions caused by the disruption of economic activities during the pandemic (Zheng & Zhang, 2020). Empirically, it is established that COVID-19 cases negatively affected stock market returns (Iyke & Ho, 2021; Kumeka et al., 2021; Machmuddah et al., 2020; Rabhi, 2020; Takyi & Bentum-Ennin, 2021).

The pandemic has not only affected stock market returns, but also the efficiency of stock markets worldwide. It is a widely accepted concept in behavioural finance that instigates widespread panic, such as responses to wars, political crises, inflation rates, exchange rates and pandemics, often leading to the breakdown of the efficient market hypothesis (EMH) by causing asset prices to deviate from their fundamental values (Machmuddah et al., 2020). By investigating the impact of the COVID-19 pandemic on stock market efficiency for six countries, namely the US, Spain, the UK, Italy, France and Germany, Ozkan (2021) found that all stock markets deviated from market efficiency during some periods of the pandemic, especially in the US and UK stock markets. Similarly, Dias et al. (2020) argue that the stock prices of the Chinese and European stock markets do not fully reflect the information available and that changes in prices are not independent and identically distributed. Stock markets became more speculative during the COVID-19 pandemic, causing stock mispricing and increasing the likelihood of abnormal returns (i.e., gains).

Stock markets in Africa offer diverse options to international investors seeking to diversify their portfolios (Afego, 2015; Dias et al., 2022). Therefore, several questions arise: Are stock markets in African countries efficient during the pandemic? Does African stock market efficiency persist during the pandemic? Following Nkrumah-Boadu et al. (2022), this study compares the efficiency of African stock markets before and during the pandemic using monthly COVID-19 cases as a proxy for the pandemic.

This study contributes to the existing literature on COVID-19 in African stock markets in two ways. First, unlike previous studies that focused on the impact of COVID-19 on stock market returns in Africa (Iyke & Ho, 2021; Kumeka et al., 2021; Takyi & Bentum-Ennin, 2021), this study assesses the impact of COVID-19 on stock market efficiency in 15 selected African countries. In addition, this study contributes to the existing literature by applying data envelopment analysis (DEA) to study stock market efficiency. Although DEA has been applied extensively in studies on pensions, mutual funds and insurance, to the best of our knowledge, this study is the first to employ DEA to assess the efficiency of stock markets. This differs from the studies of Dias et al. (2022) and Dias Rui & Santos (2020) who assessed the impact of COVID-19 on the efficiency of African stock markets in their weak-form under the EMH assumption.¹ This study further determines the persistence efficiency of the African stock market by applying the cross product ratio (CPR) and time product ratio (TPR). Despite the significant number of studies on the efficiency and persistence of mutual and pension funds through nonparametric techniques, such as DEA and CPR, there are few studies on stock market efficiency using DEA. Yi et al. (2018) compared the valuation efficiency between the Mainland China and Hong Kong stock markets using the DEA-Malmquist model and price/earnings ratio. They concluded that the DEA model proposed by Charnes et al. (1978) is more suitable than the price/earnings ratio for measuring the relative valuation level and efficiency of stock markets.

In terms of structure, this study is organized into five sections. In addition to the current introduction, the second section is a literature review on the impact of COVID-19 on stock market returns and efficiency; the third section describes the methodology and data source used for the study; and the fourth section contains the results and discussion. Finally, the fifth section covers the general conclusions of the study.

Literature Review

Theoretical Background

Among studies on efficiency and persistence, there is a large focus on stock markets and mutual and pension funds. Studies have focused on the efficiency of stock markets and mutual and pension funds, because they are catalysts for wealth building (Gopalakrishnan & Ramakrishna, 2018). Investors consider the past efficiency of these assets before making their investment decisions. The past efficiency provides useful information for predicting the future efficiency of an asset. Non-financial factors, such as pandemics, affect the efficiency and persistence of financial markets (Machmuddah et al., 2020; Ozkan, 2021). The COVID-19 pandemic has caused a surge in the number of empirical studies on stock market returns and their efficiency in relation to the pandemic. COVID-19 is concluded to be the most severe outbreak of an infectious disease to have affected stock markets (Baker et al., 2020a; Baker et al., 2020b;, Cox et al., 2020; Maretno Agus & Fabrizio, 2023).

COVID-19 Pandemic on Global Stock Markets Returns

By investigating the effect of the COVID-19 pandemic on emerging Asian stock markets, Rabhi (2020) argues that COVID-19 cases and deaths negatively affected stock market returns. The negative effect is attributed to behavioural factors, such as fear of death and a surge in new cases (Vasileiou, 2021). In Africa, several empirical studies document a negative effect of COVID-19 on stock returns. Kumeka et al. (2021) find that the COVID-19 cases and deaths in Nigeria negatively affected stock market returns. Also, Takyi and Bentum-Ennin (2021) estimating the relative effects of the COVID-19 on stock market returns in 13 African countries, concluded that, stock markets returns have significantly reduced during and after the occurrence of the COVID-19, usually between −2.7% and −21%. This confirms the findings of Cedric (2022) that stock market returns are reduced in five stock markets (Nigeria, Morocco, Tunisia, Cameroon and Zambia) out of eight markets employed in the study.

COVID-19 has not only affected stock market returns, but also the global efficiency of stock markets. Various studies conclude that the negative impact of the COVID-19 pandemic on stock market returns and trade volume also reduces the efficiency of stock markets around the globe (Dias et al., 2022; Lee, 2022; Ozkan, 2021; Souza de Souza & Tibúrcio Silva, 2020; Vasileiou, 2021).

COVID-19 Pandemic on Non-African Stock Markets Efficiency

Dias et al. (2020) conducted random walks and market efficiency tests in the US, Chinese, and European capital markets during the COVID-19 pandemic. They found that 8 of the 10 stock markets are inefficient. This finding confirms the argument of Dias et al. (2022) that stock prices are predictable in both developing and developed economies. Contrary to the random-walk hypothesis, the inefficiency of stock markets offers an opportunity for arbitrage and abnormal returns. Vasileiou (2021) examined behavioural finance and market efficiency during the COVID-19 pandemic and discovered that the US stock market was inefficient. According to Lee (2022), the inefficiency of stock markets in European equity markets was due to the ban on short sales during the pandemic in France, Spain and Italy. The ban on the two-month short sale offered price predictability opportunities in the market, and hence arbitrage opportunities for speculative investors. Ozkan (2021) realizes that stock markets deviated from their average efficiency during the pandemic in developed economies such as the US and the UK. The study also reveals that the pandemic has facilitated the prediction of stock prices and abnormal returns. Thus, stock markets were inefficient during the pandemic, and stock prices did not reflect all available information, leading to arbitrage trading and abnormal returns.

On the contrary, Aikins Abakah et al. (2021) analysed the effects of containment measures and monetary and fiscal responses on US financial markets during the COVID-19 pandemic and stipulated that, except for S&P500, the US stock markets were mainly efficient and highly persistent. They documented that monetary announcements by the government uplifted the markets. While studying the effects of the COVID-19 pandemic on international capital markets, Souza de Souza and Tibúrcio Silva (2020) indicated that the efficiency of stock markets increased post-COVID-19, confirming the notion that stock markets returned to their means post-pandemic.

COVID-19 Pandemic on African Stock Markets Efficiency

Dias Rui & Santos (2020) tested the impact of the COVID-19 pandemic on the EMH in its weak form in Africa’s stock markets, concluding that African stock markets do not follow the random walk hypothesis theory. Dias et al. (2022) suggest no difference in the impact of COVID-19 on the efficiency of stock markets in developed countries (Japan, the UK and the US) and African ones (Botswana, Egypt, Kenya, Morocco, Nigeria and South Africa). The findings of the study reject the random walk hypothesis in Africa and develop stock markets. The rejection of the random walk hypothesis in these markets indicates that stock market prices can be predicted and, hence, the opportunity for abnormal earnings. The authors’ evidence is consistent with stock market yields in Africa and developing economies. Furthermore, Iyke and Ho (2021) suggest that an increase in investor attention consistently reduces stock returns in Botswana, Nigeria and Zambia. By contrast, it enhances stock returns in Ghana and Tanzania. They estimate that in uncertain times, such as pandemics, Ghana and Tanzania stock markets may offer potential diversification benefits to investors.

Use of DEA for Efficiency Studies

DEA was first used to assess efficiency in 1978 by Charnes et al. (1978), via constant return to scale (CRS). This was followed by Banker et al. (1984), who utilized it through variable returns to scale (VRS). Brown and Goetzmann (1995) were the first to use a 2×2 contingency table based on the CPR to check performance persistence. Since then, studies have begun to use DEA and CPR. Various scholars use DEA to assess the efficiency of pensions and mutual funds. Tuzcu and Ertugay (2020) and Zamuee (2015) used DEA CRS output and input orientation to assess the efficiency of Turkish mutual funds and Namibia pension funds respectively. According to Demirtaş and Keçeci (2020) and Paradi et al. (2018), DEA is the most valuable technique for measuring financial institutions’ efficiency. Yi et al. (2019) confirmed that DEA is appropriate for measuring stock market efficiency. Moreover, Ferruz et al. (2007) and Rao et al. (2019) used CPR based 2×2 contingency table to determine the performance persistence of the Spanish pension market and Chinese mutual funds, respectively.

Gap and Contribution

The few studies on the COVID-19 pandemic on stock markets have mixed conclusions although the findings lean towards a negative impact. In Africa, it has been established that the pandemic has deteriorated market efficiency; however, there are no studies on market efficiency when returns are increased in the existing capacity for inflation, exchange rate and the number of COVID-19 cases. To achieve this, this study distinguishes itself from the two studies on stock market efficiency by utilizing DEA, robust to the DEA-adjusted estimator. This study further checks whether efficiency can be consistently achieved in African stock markets by employing CPR and TPR. Thus, the following hypotheses are developed:

H₁: African stock markets are efficient during the COVID-19 pandemic.

H₂: African stock markets’ efficiency persists during COVID-19 pandemic.

Data and Methods

Data

This study assesses the efficiency of stock markets in 15 African countries during the COVID-19 pandemic and compares the efficiency of markets to the pre-COVID-19 era. In addition, this study determines the efficiency persistence of these markets using monthly data from January 2019 to December 2021. The stock markets under study are Botswana, Egypt, Ghana, Ivory Coast, Kenya, Malawi, Mauritius, Morocco, Namibia, Nigeria, South Africa, Tanzania, Tunisia, Uganda and Zambia. Data on stock returns, inflation rates and exchange rates are obtained from the monthly reports of Databank.² We obtain total COVID-19 cases data from www.virusncov.com.³

To evaluate the efficiency of stock markets before and after the pandemic, 2019 is considered as the period before COVID-19 in Africa, while 2020 and 2021 are the pandemic years. This study considers returns as the output and inflation rates, exchange rates and total COVID-19 cases as the input variables using the DEA VRS output orientation. This study uses the total number of COVID-19 cases reported by countries as inputs in 2020 and 2021. COVID-19 cases were not included in the 2019 inputs because COVID-19 reached Africa in 2020. By doing so, we can compare the pre-COVID-19 efficiency of the stock markets with that of the COVID-19 period. We adopt reported COVID-19 cases as an input following the works of Baker et al. (2020a), Kumeka et al. (2021) and Rabhi (2020). The reported COVID-19 cases negatively affect stock market returns. Inflation and exchange rates are macroeconomic variables that stock market managers and regulators have an eye on because they can either depreciate or appreciate the stock market’s prices, thus affecting stock markets’ returns and efficiency (Rabhi, 2020). This study adopts inflation and exchange rates based on volatility during the pandemic in the region. Stock markets tend to be more volatile when inflation is high. Stock markets with a DEA score of 1 or more are efficient.

We further assess the efficiency scores based on their neighbours. We generate the output neighbours; that is, we decrease the returns by 0.05, and increase the input inflation rates, exchange rates and total COVID-19 cases by 0.05. Stock markets with an adjusted DEA score of 1 or more are efficient. Finally, we generate the medians for all stock markets based on their efficiency scores for each year, that is, for 2019, 2020 and 2021, on monthly and yearly bases. We then classify stock markets with DEA scores above the median as winners (W) and those with DEA scores below the median as losers (L). After categorizing the stock markets as WW, LL, WL and LW, we apply CPR and TPR, following the formula. Stock markets with a CPR and TPR of 1 and below lack persistence.

Method

Efficiency of Stock Markets

This study uses the DEA proposed by Charnes et al. (1978) to assess the efficiency of stock markets. DEA is the most valuable technique for measuring the efficiency of any financial institution (Demirtaş & Keçeci, 2020; Paradi et al., 2018). This entails the identification of inputs (resources) and outputs (transformation of resources) (Ali, 2016). An inefficient decision-making unit (DMU) in an output space can improve its output by increasing it (Ali, 2016; Demirtaş & Keçeci, 2020) to reach the efficiency frontier, which is called the best practice. In the same line of thought, the research objective to increase the return in existing inputs (inflation rate; exchange rate; total COVID-19 cases) capacities to gain efficiency justifies the choice of the DEA model as output orientation. DEA can be VRS (Banker et al., 1984) when outputs change by different proportions (increasing or decreasing) as inputs change (Ali, 2016). Thus, this study relies on the VRS as a model.

Vrs Output Orientation Dea Specification Equation

\begin{array}{l} \max φ_{t} \\ s . t \\ \begin{array}{l} \sum_{j = 1}^{n} λ_{j} x_{i j} \leq x_{i l}, i = 1, \dots ., m \\ \sum_{j = 1}^{n} λ_{j} y_{r j} \geq φ_{l} y_{r l}, r = 1, \dots, s \\ \sum_{j = 1}^{n} λ_{j} = 1 \\ λ_{j} \geq 0, j = 1, \dots, n \end{array} \end{array}

(1)

Here, φ_t is the efficiency score (φ_t = 1) in the output space. x_{ij, yrj} and are the inputs and output, respectively. λ_j represents the weights assigned to inputs and output. n, m, and s represent the number of DMU, inputs and output.

The study further uses the DEA-adjusted estimator method proposed by Khezrimotlagh et al. (2019) to improve the efficiency of all stock markets lying on the efficient frontier line from the DEA results. The DEA-adjusted estimator assesses the efficiency of DMUs lying on an efficient frontier line based on their neighbours (Khezrimotlagh et al., 2019). The DEA-adjusted estimator assesses the impact of a slight change in the input or output of a best-practice DMU and identifies which of them has a strong neighbour, which is less sensitive to a minimal change in input or output. Hence, the adjusted estimator relies on all feasible neighbours of a DMU to assess its efficiency (Khezrimotlagh et al., 2019). A DMU has the highest efficiency score compared with any other DMU if its corresponding feasible neighbours are more efficient than those of any other DMU; otherwise, all DMUs have the same strength in their inputs and outputs (Khezrimotlagh et al., 2019).

Neighbour as an input (output) is defined as increasing (decreasing) a small input (output) value. For a DMU lying on the frontier line, increasing (decreasing) a small proportional amount of input (output) should not have a considerable effect on its efficiency score; that is, the efficiency score of the DMU should still be very close to 1 (Khezrimotlagh et al., 2019).

Vrs Output Orientation Dea Adjusted Estimator Specification Equation

\begin{array}{l} \max φ_{t} \\ s . t \\ \begin{array}{l} \sum_{j = 1}^{n} λ_{j} x_{i j} \leq (1 + δ t_{i}^{-}) x_{i l}, i = 1, \dots ., m \\ \sum_{j = 1}^{n} λ_{j} y_{r j} \geq (1 + δ t_{r}^{+}) φ_{l} y_{r l}, r = 1, \dots, s \\ \sum_{j = 1}^{n} λ_{j} = 1 \\ λ_{j} \geq 0, j = 1, \dots, n \end{array} \end{array}

(2)

Here, $1 + δ t_{i}^{-}, 1 - δ t_{r}^{+}$ denote the neighbours of the inputs and outputs, respectively.

DEA Adjusted Estimator Procedure

We define a feasible virtual set of neighbours for each DMU.

Compute the efficiency scores of the neighbours for each DMU.

If the efficiency score of neighbours for a DMU is constant throughout the neighbours’ stage, the efficiency score is maintained as the adjusted version of the DMU.

If the efficiency score of neighbours for a DMU varies throughout the neighbours’ stage, the efficiency score of neighbours who lie on the frontier line is excluded. We then obtain the average efficiency score for the remaining neighbours as the adjusted version of the efficiency score for the DMU.

Rank the DMUs according to their efficiency score-adjusted versions.

Neighbours’ Computation

Choose a real value α [0,1] such that 0 < α < 1, to add (subtract) an α percentage to (from) the input (output).

Get the number of neighbours required by applying 2^m+s.

The neighbours of a DMU (including the DMU) are evaluated.

Tables 1 and 2 display the neighbours’ computation in an output space for the years 2019, 2020, and 2021, respectively.

Table 1.

Neighbours’ Computation—Output Orientation for Year 2019.

Code	INF	EX	Return
000	x ₁	x ₂	y
001	x ₁	x ₂	y – ay
010	x ₁	x₂ + ax₂	y
011	x ₁	x₂ + ax₂	y – ay
100	x₁ + ax₁	x ₂	y
101	x₁ + ax₁	x ₂	y – ay
110	x₁ + ax₁	x₂ + ax₂	y
111	x₁ + ax₁	x₂ + ax₂	y – ay

Notes: With two inputs x_1, x₂ (inflation, exchange rate) and one output y (return), the formula 2^{m + s} is 2^{1 + 2} = 2^{3 = 8}. Thus 16 neighbours are illustrated from 000–111 (0 is the initial state and 1 is the neighbours’ state). m + s = 3 represents the number of figures for each neighbour code, and the code varies accordingly. 000 represents the DMU itself which dominates all other defined neighbours of the DM, and is therefore called best neighbour, whereas 111 is dominated by all other defined neighbours of the DMU; therefore, it represents the worst neighbour.

Table 2.

Neighbours’ Computation—Output Orientation for Years 2020 and 2021.

Code	INF	EX	TCC	Return
0000	x ₁	x ₂	x ₃	y
0001	x ₁	x ₂	x ₃	y – ay
0010	x ₁	x ₂	x₃ + ax₃	y
0011	x ₁	x ₂	x₃ + ax₃	y – ay
0100	x ₁	x₂ + ax₂	x ₃	y
0101	x ₁	x₂ + ax₂	x ₃	y – ay
0110	x ₁	x₂ + ax₂	x₃ + ax₃	y
0111	x ₁	x₂ + ax₂	x₃ + ax₃	y – ay
1000	x₁ + ax₁	x ₂	x ₃	y
1001	x₁ + ax₁	x ₂	x ₃	y – ay
1010	x₁ + ax₁	x ₂	x₃ + ax₃	y
1011	x₁ + ax₁	x ₂	x₃ + ax₃	y – ay
1100	x₁ + ax₁	x₂ + ax₂	x ₃	y
1101	x₁ + ax₁	x₂ + ax₂	x ₃	y – ay
1110	x₁ + ax₁	x₂ + ax₂	x₃ + ax₃	y
1111	x₁ + ax₁	x₂ + ax₂	x₃ + ax₃	y – ay

Notes: With three inputs x₁, x₂, x₃ (inflation, exchange rate, total COVID cases) and one output y (return), the formula 2^m+s is 2³⁺¹. Thus, 16 neighbours are illustrated from 0000–1111 (0 is the initial state and 1 is the neighbours’ state). m + s = 4 represents the number of figures for each neighbour code, which varies accordingly. 0000 represents the DMU itself which dominates all other neighbours of the DMU, and is therefore called the best neighbour. In contrast, 1111 is dominated by all other neighbours of the DMU, therefore representing the worst neighbour.

Persistence of Stock Markets Efficiency

In addition, we use the CPR-based 2×2 contingency table approach (Brown & Goetzmann, 1995; De Souza & Gokcan, 2004; Rao et al., 2019) and TPR-based CPR to check the efficiency persistence of stock markets. 2×2 contingency table under CPR summarizes the number of stocks into two successive sub-periods (both current and the following period, respectively) as ‘winner’ ‘winner’ (WW), ‘loser’ ‘loser’ (LL), ‘winner’ ‘loser’ (WL) and ‘loser’ ‘winner’ (LW). The 2×2 contingency table under TPR summarizes a stock in two successive subperiods over a defined period. We assert a stock winner (W) if its DEA score is equal or above 1; equally, a stock is a loser (L) if its DEA score is less than 1.

CPR is the ratio of the number of stocks that repeat efficiency to those that do not for two successive sub-periods. Similarly, TPR is the ratio of the number of successive sub-periods to the number of non-repeating sub-periods for a stock market. CPR and TPR are calculated as follows:

CPR / TPR = \frac{(WW \times LL)}{(WL \times LW)}

(3)

Z-statistics are calculated as described by Ferruz et al. (2007) to determine the statistical significance of persistence scores as follows:

Z = \frac{Ln CPR or LnTPR}{σ ln CPR or σ LnTPR}

(4)

where σ InCPR or σ LnTPR is

\sqrt{\frac{1}{WW} + \frac{1}{LL} + \frac{1}{WL} + \frac{1}{LW}}

(5)

Results

Descriptive Statistics

Table 3 presents the descriptive statistics of the variables.

Table 3.

Descriptive Statistics.

	Variable	All			Before		During		Difference
	Variable	Obs	Mean	Std Dev	Mean	Std Dev	Mean	Std Dev	Mean	\|t\|
Output	Returns	540	−0.22	15.48	−0.81	7.60	0.07	18.18	−0.88	−0.62
Input	Inflation	540	5.90	4.70	5.29	3.74	6.21	5.09	−0.91	−2.13**
	Exchange rate	540	570.44	1236.69	656.41	1584.77	527.45	1019.03	128.96	1.14
	COVID-19	540	120,938	374,249	0	0	181,407	446,418	−181,407	−5.45***

Note: ***p < 0%, ** p < 5%.

In any case, from Table 3, the mean assessments do not consider the confounding dynamics of the COVID-19 pandemic, inflation and exchange rates on the efficiency of stock markets, despite the pandemic significantly affecting financial systems. However, evidence from the fundamental descriptive analysis indicates a negative systematic difference in the exchange rate between the pre-COVID-19 and COVID-19 periods. This means that the local currencies of various countries appreciated during the pandemic period. In contrast, there is no significant systematic difference in stock market returns and inflation during COVID-19. The means show that the average returns on African stock markets were positive during the COVID-19 pandemic and negative before. Takyi and Bentum-Ennin (2021) argue that, although COVID-19 has significantly impacted stock market returns in African countries, the impact was only in the early days of the pandemic.

Therefore, we use DEA to evaluate the efficiency of stock markets in Africa before and during the pandemic. We use a DEA-adjusted estimator as a robust econometric technique to address the unbiased effects of the pandemic on stock market efficiency. In the envelopment model, the number of degrees of freedom increased with the number of DMUs. It decreases with the input and output because of its orientation towards the relative efficiency. Cooper et al. (2007) suggest that the number of DMUs must be equal to or greater than max {m * s, 3 * (m + s)}. In this study, three inputs and one output are used during the COVID-19, and two inputs and one output before the pandemic. The number of stock markets is equal to 15; therefore, the number of DMUs rule given by Cooper et al. (2007) is satisfied.

Efficiency

Table 4 displays the results for stock market efficiency.

Table 4.

The Efficiency of Stocks Markets Under DEA, VRS Output Orientation.

Periods	2019			2020				2021
Countries	Score	Islack: INF	Islack: EX	Score	Islack: INF	Islack: EX	Islack: TCC	Score	Islack: INF	Islack: EX	Islack: TCC
Botswana	1 (1)	–	–	1 (1)	–	–	–	0.05 (15)	–	–	3821.26
Egypt	0.84 (10)	–	–	1 (1)	–	–	–	0.31 (11)	–	–	74839
Ghana	1 (1)	–	–	1 (1)	–	–	–	1 (1)	–	–	–
Ivory Coast	1 (1)	–	–	0.71 (13)	–	–	–	1 (1)	–	–	–
Kenya	1 (1)	–	–	0.38 (14)	–	–	–	0.27 (12)	–	–	43554
Malawi	0.10 (13)	0.50	65.57	1 (1)	–	–	–	0.99 (8)	4.77	252.05	–
Mauritius	1 (1)	–	–	1 (1)	–	–	–	1 (1)	–	–	–
Morocco	1 (1)	–	–	1 (11)	–	–	–	1 (1)	–	–	–
Namibia	0.01 (15)	–	–	0.95 (12)	–	–	–	1 (1)	–	–	–
Nigeria	0.87 (9)	1.45	–	1 (1)	–	–	–	0.10 (14)	–	28.21	3020.93
South Africa	1 (1)	–	–	1 (1)	–	–	–	0.80 (9)	–	–	2646493
Tanzania	0.05 (14)	–	101.68	0.00 (15)	–	–	–	0.23 (13)	–	491.21	–
Tunisia	0.33 (12)	0.71	–	1 (1)	–	–	–	1 (1)	–	–	–
Uganda	0.37 (11)	–	1346	1 (1)	–	–	–	0.54 (10)	–	1793	–
Zambia	1 (1)	–	–	1 (1)	–	–	–	1 (1)	–	–	–

Note: Inputs slacks (Islack) are inflation rate (INF), exchange rate (EX) and total COVID-19 cases (TCC).

As shown in Table 4, in 2019, the stock markets of eight countries (Botswana, Ghana, Ivory Coast, Kenya, Mauritius, Morocco, South Africa and Zambia) are efficient, whereas seven (Egypt, Malawi, Namibia, Nigeria, Tanzania, Tunisia and Uganda) are inefficient with the Namibian Stock Exchange being the most inefficient followed by Tanzania with efficiency scores of 0.01 and 0.05. To reach the efficiency line, Malawi, Nigeria and Tunisia must reduce their inflation rates by 0.50, 1.45 and 0.71. In addition to reducing Malawi’s inflation rate, the exchange rate must also be reduced by 65.57. In contrast, Tanzania and Uganda must reduce their exchange rate by 101.68 and 1346, respectively, to reach the efficiency line. For the stock markets in Egypt, Malawi, Namibian, Nigeria, Tanzania, Tunisia and Uganda to reach the efficiency line, returns must increase by 0.16, 0.90, 0.99, 0.13, 0.95, 0.67 and 0.63, respectively, in the same year. The stock market returns for these markets were negative in 2019. The efficiency of most stock markets in Africa before the pandemic confirms the works of Abakah et al. (2018) and Kelikume (2016), who argue in studies before the pandemic on the efficiency of some stock markets in Africa.

By 2020, Africa’s efficient stock markets had increased from 8 to 11. Stock markets in Egypt, Malawi, Nigeria, Tunisia and Uganda, which were inefficient in 2019, became more efficient in 2020. By contrast, the Ivory Coast and Kenya stock markets, which were efficient in 2019, became inefficient in 2020. In 2020, Africa’s least efficient stock market is the Dar Es Salam Stock Exchange of Tanzania, followed by the Nairobi Securities Exchange of Kenya, with efficiency scores of 0.00 and 0.38. In 2020, COVID-19 has no significant impact on the efficiency of African stock markets. While these two markets became inefficient in 2020, five inefficient markets became efficient in 2020 during the pandemic. This contradicts Ozkan’s (2021) findings in their analysis of the impact of COVID-19 on stock market efficiency in developed countries. This contradiction in the impact of the pandemic on stock market efficiency in developed and African countries is because of the number of daily confirmed cases in these two regions. While Europe had a growing number of daily confirmed cases in 2020, most African countries had low COVID-19 cases on average. Stock markets in Ivory Coast, Kenya, Namibia and Tanzania must increase their returns by 0.29, 0.62, 0.05 and 1, respectively. The significant improvement in the efficiency of African stock markets can be attributed to the increase in trade volume in 2020. During the pandemic, most global investors diversified their investments by trading in African stock markets when COVID-19 took a toll on the stock markets of developed economies (Dias Rui & Santos, 2020; Kumeka et al., 2021).

In 2021, when African countries had a growing number of COVID-19 cases, primarily because of the Omicron variant, only seven countries’ stock markets (Ghana, the Ivory Coast, Mauritius, Morocco, Namibia, Tunisia and Zambia) were efficient, whereas eight (Botswana, Egypt, Kenya, Malawi, Nigeria, South Africa, Tanzania and Uganda) were inefficient. The least efficient stock market in 2021 was Botswana, followed by Nigeria, with efficiency scores of 0.05 and 0.1, respectively. Botswana, Egypt, Kenya, Malawi, Nigeria, South Africa, Tanzania and Uganda must increase their returns by 0.95,0.69, 0.73, 0.01, 0.90, 0.20, 0.77 and 0.46, respectively, to reach the efficiency line. To reach efficiency, Malawi must reduce the inflation rate by 4.77 and the exchange rate by 252.05. To attain efficiency, Nigeria, Tanzania, and Uganda had to reduce their exchange rates by 28.21, 491.21 and 1793, respectively

The impact of COVID-19 is evident because the efficiency of the stock markets in Botswana, Egypt, Kenya, Nigeria and South Africa was affected by COVID-19 in 2021. To attain efficiency, these five countries must reduce their COVID-19 infection rates by 3821.26, 74,839, 43,554, 3020.93 and 2,646,493, respectively. The South African stock markets were the most affected by COVID-19 during the study period. Overall, when COVID-19 cases soared in Africa in 2021, 7 of the 15 under-studied stock markets were efficient, with 8 being inefficient. Six markets that were efficient in 2020 had become inefficient by 2021, with the Botswana stock market being the most affected. Stock markets in Botswana, the Ivory Coast, Kenya and South Africa have stock market efficiency affected by COVID-19. The stock markets in Ivory Coast and Kenya became inefficient in 2020, whereas the stock markets in Botswana and South Africa were inefficient by 2021. This confirms the findings of Ozkan (2021) and Takyi and Bentum-Ennin (2021). However, in 2020, COVID-19 had no significant impact on the efficiency of African stock markets. Ghana, Mauritius, Morocco and Zambia maintained their efficiency throughout the pandemic.

Table 5 shows the robustness check of the stock markets that lie on the efficient frontier line from 2019 to 2021.

Table 5.

The Efficiency of Stocks Markets under DEA-Adjusted Estimator with a = 0.05, VRS Output Orientation.

Periods	Year 2019	Year 2020	Year 2021
Countries	Adjusted Score	Adjusted Score	Adjusted Score
Botswana	1	1	–
Egypt	–	1	–
Ghana	1	1	1
Ivory Coast	1	–	1
Kenya	1	–	–
Malawi	–	1	–
Mauritius	1	1	1
Morocco	1	1	1
Namibia	–	–	1
Nigeria	–	1	–
South Africa	1	1	–
Tunisia	–	1	1
Uganda	–	1	–
Zambia	1	1	1

To check the findings on the efficiency of stock markets in Africa before COVID-19 and during COVID-19, we adopt an adjusted estimator through neighbour computation. The neighbour’s computation assesses whether efficient stock markets would still be efficient if their outputs decrease and their inputs increase. Table 5 shows that increasing inputs and decreasing outputs have no significant impact on the efficiency scores, indicating that efficient stock markets have the same strength in their inputs and outputs.

Persistence Efficiency Score

Table 6 shows the persistence of the efficiency scores of the stock markets from month to month in 2019.

Table 6.

Cross and Time Product Ratios for Efficiency Persistence of Stocks Markets for Year 2019.

2019	WW	LL	WL	LW	CPR
Jan–Feb	5	3	3	4	1.25
Feb–Mar	7	4	2	2	7
Mar–Apr	6	2	3	4	1
Apr–May	9	4	1	1	36**
May–Jun	6	4	4	1	6
Jun–Jul	7	6	N/A	2	21***
Jul–Aug	7	3	2	3	3.50
Aug–Sep	7	5	3	N/A	11.67***
Sep–Oct	6	6	1	2	18**
Oct–Nov	7	5	1	2	17.50**
Nov–Dec	6	4	3	2	4
Total	73	46	23	23	6.35***
Countries	WW	LL	WL	LW	TPR
Botswana	2	6	1	2	6
Egypt	7	1	2	1	3.50
Ghana	9	N/A	1	1	9
Ivory Coast	9	N/A	1	1	9
Kenya	6	3	1	1	18*
Malawi	1	8	1	1	8
Mauritius	9	1	N/A	1	9
Morocco	8	N/A	1	2	4
Namibia	N/A	8	2	1	4
Nigeria	N/A	4	4	3	0.33
South Africa	5	3	1	2	7.50
Tanzania	4	5	1	1	20*
Tunisia	3	4	2	2	3
Uganda	2	2	4	3	0.33
Zambia	8	1	1	1	8
Total	73	46	23	23	6.35***

Notes: WW: Winner–winner, LL: Loser–loser, WL: Winner–loser and LW: Loser–winner.

CPR: Cross product ratio; TPR: Time product ratio.

N/A represents non-applicable.

***p < .01, **p < .05, *p < .1.

This study uses monthly and yearly efficiency scores to assess the persistence of the 15 understudied stock markets for 3 years. From Table 6, under the CPR, most of the persistence in the efficiency of stock markets in Africa is seen in 11 subperiods. There is no persistence in one subperiod (March–April). However, only 5 of the 11 sub-periods of stock markets are statistically significant in their persistence. A TPR analysis is used to assess the persistence efficiency of each stock market. From the TPR analysis, the Nigerian and Ugandan stock markets reverse at ratio of 0.33 each. In 2019, only the Kenyan and Tanzanian stock markets showed significant persistence in efficiency. While the Kenyan stock market continues to be efficient, the Tanzanian one continues to be inefficient. These findings regarding the persistence of efficiency in most African markets indicate that they remain efficient. In contrast, unlike Nigeria and Uganda, inefficient stock markets continue to be inefficient and their efficiency fluctuates monthly.

Table 7 displays the persistence of stock market efficiency in 2019.

Table 7 under the CPR analysis presents the persistence in the efficiency of African stock markets in 2020. These findings are similar to those reported in 2019. Over this period, the efficiency of stock markets in Africa persisted throughout the sub-periods. However, only seven sub- periods are statistically significant. The TPR shows that in 2020 during COVID-19, the two stock markets did not persist in their efficiency. Apart from South Africa and Tanzania, all the stocks are consistent in their efficiency scores. However, Mauritius, Morocco, South Africa and Tunisia are statistically significant in their persistence of efficiency. This implies that efficient stock markets will maintain their efficiency by 2020, whereas inefficient stocks will remain inefficient.

Table 7.

Cross and Time Product Ratios for Efficiency Persistence of Stocks Markets for the Year 2020.

2020	WW	LL	WL	LW	CPR
Jan–Feb	4	4	4	3	1.33
Feb–Mar	4	4	3	4	1.33
Mar–Apr	5	6	3	1	10*
Apr–May	6	7	N/A	2	21***
May–Jun	7	6	1	1	42**
Jun–Jul	7	6	1	1	42**
Jul–Aug	6	6	2	1	18**
Aug–Sep	6	6	1	2	18**
Sep–Oct	8	4	N/A	3	10.67***
Oct–Nov	8	2	3	2	2.67
Nov–Dec	9	3	1	2	13.50
Total	70	54	19	22	9.04***
Countries	WW	LL	WL	LW	TPR
Botswana	1	7	1	2	3.50
Egypt	7	1	1	2	3.50
Ghana	9	N/A	1	1	9
Ivory Coast	N/A	8	2	1	4
Kenya	N/A	9	1	1	9
Malawi	4	3	2	2	3
Mauritius	8	2	N/A	1	16**
Morocco	11	N/A	N/A	N/A	11***
Namibia	9	1	1	N/A	9
Nigeria	2	7	1	1	14
South Africa	N/A	2	4	5	0.10**
Tanzania	1	4	3	3	0.44
Tunisia	11	N/A	N/A	N/A	11***
Uganda	7	1	1	2	3.50
Zambia	N/A	9	1	1	9
Total	70	54	19	22	9.04***

Note: ***p < .01, **p < .05, *p < .1.

Table 8 displays the persistence of stock market efficiency in the years 2020 and 2021.

Table 8.

Cross and Time Product Ratios for Efficiency Persistence of Stocks Markets for the Year 2021.

2021	WW	LL	WL	LW	CPR
Jan–Feb	7	4	2	2	7*
Feb–Mar	7	5	2	1	17.50**
Mar–Apr	6	5	2	2	7.50*
Apr–May	8	6	N/A	1	48***
May–Jun	8	6	1	N/A	48***
Jun–Jul	8	5	N/A	2	20***
Jul–Aug	9	5	1	N/A	45***
Aug–Sep	7	4	2	2	7*
Sep–Oct	6	6	3	N/A	12***
Oct–Nov	4	8	2	1	16**
Nov–Dec	5	8	N/A	2	20***
Total	75	62	15	13	23.85***
Countries	WW	LL	WL	LW	TPR
Botswana	7	3	1	N/A	21**
Egypt	3	3	3	2	1.50
Ghana	11	N/A	N/A	N/A	11***
Ivory Coast	6	3	1	1	18*
Kenya	N/A	11	N/A	N/A	11***
Malawi	N/A	8	2	1	4
Mauritius	11	N/A	N/A	N/A	11***
Morocco	11	N/A	N/A	N/A	11***
Namibia	6	N/A	2	3	1
Nigeria	4	3	2	2	3
South Africa	N/A	9	1	1	9
Tanzania	8	2	1	N/A	16**
Tunisia	1	8	1	1	8
Uganda	6	3	1	1	18*
Zambia	1	9	N/A	1	9
Total	75	62	15	13	23.85***

Note: ***p < .01, **p < .05, *p < .1.

In 2021, under the CPR, the African stock markets in Table 8 exhibit statistically significant persistence in their efficiency throughout the year. This means that stock markets remain efficient throughout the year, while inefficient markets remain inefficient. The Time-product ratio shows that 14 of the stock markets are persistent in their efficiency scores in 2021, while the stock markets in Namibia are not persistent in their efficiency scores. The study further reveals that eight persistent markets are statistically significant, while six are not. Overall, the efficiency of the African stock markets is statistically significant in 2021. This implies that Ghana and the Ivory Coast remain efficient, whereas Botswana, Kenya, Mauritius, Tanzania and Uganda remain inefficient.

Table 9 displays the persistence of stock market efficiency from 2019 to 2021.

Table 9.

Cross and Time Product Ratios for Efficiency Persistence of Stocks Markets for Years 2019, 2020 and 2021.

Period	WW	LL	WL	LW	CPR
2019–2020	6	2	2	5	1.20
2020–2021	5	2	6	2	0.83
Total	11	4	8	7	0.79
Countries	WW	LL	WL	LW	TPR
Botswana	1	N/A	1	N/A	1
Egypt	N/A	N/A	1	1	1
Ghana	2	N/A	N/A	N/A	2
Ivory Coast	N/A	N/A	1	1	1
Kenya	N/A	1	1	N/A	1
Malawi	N/A	N/A	1	1	1
Mauritius	2	N/A	N/A	N/A	2
Morocco	2	N/A	N/A	N/A	2
Namibia	N/A	1	N/A	1	1
Nigeria	N/A	N/A	1	1	1
South Africa	1	N/A	1	N/A	1
Tanzania	N/A	2	N/A	N/A	2
Tunisia	1	N/A	N/A	1	1
Uganda	N/A	N/A	1	1	1
Zambia	2	N/A	N/A	N/A	2
Total	11	4	8	7	0.79

From the CPR in Table 9, the study shows persistence in efficiency scores for year-on-year persistence from 2019 to 2020 and no persistence from 2020 to 2021. The TPR reveals that only five stock markets persist in their efficiency scores, with the exception of Ghana, Mauritius, Morocco, Tanzania and Zambia. This indicates that for most stock markets, being efficient in a subyear is not a guarantee of efficiency in the subsequent subyear. Inefficiency for one year does not guarantee that the stock market will become inefficient the following year. Tanzania is inefficient in terms of efficiency during the two sub-period studies of the five persistent stock markets. In contrast, Ghana, Mauritius, Morocco and Zambia are efficient throughout these periods.

Conclusion

The few studies on the COVID-19 pandemic on stock markets have mixed conclusions, although the findings leaned towards a negative impact. In Africa, it has been established that the pandemic has deteriorated market returns; however, no studies have assessed market efficiency when returns are increased in the existing capacity of inflation, exchange rate and the number of COVID-19 cases. To achieve this, the present study distinguished itself from the two studies on COVID-19 on stock market efficiency in Africa by utilizing DEA and DEA-adjusted estimator. The study found that the efficiency of African stock markets improved in 2020 when COVID-19 spread to Africa; however, it worsened in 2021 when the number of active COVID-19 cases soared, owing to the Omicron variant of the virus. Stock markets in southern Africa suffered the most. The findings of this study imply that regulators of stock markets in Africa should be proactive during pandemics, periods of rising inflation and exchange rates. Despite the pandemic’s negative impact on stock market efficiency, Ghana, Mauritius, Morocco and Zambia maintained their efficiency throughout the study period. The findings of this study suggest that authorities in some countries should strengthen their price-forming information structure. Technologies should be adopted in these markets to accelerate the dissemination of information both in the market and among investors. Investors should adjust their investment strategies during pandemics to minimize potential losses by examining dynamic, tactical, risky, active, diversified and managed risk strategies. Central Banks should adopt measures to stabilize exchange and inflation rates during pandemics by injecting sufficient reserve assets and encouraging production at full capacity to reduce the impact of the pandemic on stock market efficiency.

This study went further and checked whether efficiency can be consistently achieved by stock markets in Africa and employed CPR and TPR. It is evident from the findings that stock markets that are efficient in one month continue to be efficient in the subsequent months. This indicates that the past efficiency is related to the future efficiency. However, markets lose persistence in terms of efficiency on a yearly basis. The lack of persistence in yearly efficiency scores indicates that most stock markets persist in the short run and not in the long run. For most African stock markets, efficiency in one year does not guarantee efficiency in the subsequent years. These findings are useful for fund managers and regulators who forecast future winners in terms of efficiency and investors seeking to diversify their investments. Investors should invest in efficient markets during pandemics and sell stocks in inefficient markets in the short run. Investors must participate in share trading to allow information to be disseminated freely and on time. Authorities must also introduce hedging instruments and allowances for short sales. Considering the number of stock markets in Africa, this study is limited to half of the sample. Thus, further research should include more African stock markets to extend the sample and explore their efficiency and persistence.

Supplemental Material

Supplemental material for this article is available online.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Notes

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