In Data We Trust: Proving Market Manipulation on the Tehran Stock Exchange

The Iranian financial markets play an essential role in the country's economic development. In 2019 and 2020, ordinary traders were encouraged by the political authorities to invest in state-owned enterprises. Citizens who invested in Tehran Stock Exchange (TSE) indices routinely complain that the volatile market performance has wiped out their capital and savings. In this study, the reliability of intraday transaction data for 341 stocks listed on the TSE was examined. Our critical objective is to identify fraud on the TSE. The authors applied Benford's first and second digit laws to detect irregularities in financial data based on three goodness of fit tests. The authors found overwhelming evidence of the presence of market manipulation on the TSE. We found that 46 percent of the companies listed on the TSE did not adhere to the law of the first digit. A thorough analysis of compliance with the second digit revealed a similar pattern. Given the severe impact of trade restrictions imposed by the 2018 US sanctions and the substantial increase in Iran's public debt burden, the TSE has become a major source for offsetting the government's deficit by conducting IPOs of state-owned companies. Market manipulation in Iran appears to be motivated by the government's urgent need for fresh capital and its waste. It would be a common misconception to trust the TSE's data.


Introduction
Financial markets are a captivating example of complexity in action: a complex, multi-layered system that evolves around decisions made by a multitude of individual traders who ceaselessly try to win in a global game. Middle Eastern traders are no exception. Every day, millions of transactions are executed in the region, helping both ordinary and institutional investors to succeed.

Financial Market Manipulation
It is generally agreed that financial markets facilitate efficient allocation of funds, maturity transformation, risk transfer, fair pricing, and selling of financial instruments. Investors seek to both maximize returns and minimize risks (Markowitz, 1952). Eugene Fama was the first who introduced the concept of "efficient markets" in his groundbreaking work, according to which information determines the price of assets (Fama, 1963(Fama, , 1965a(Fama, , 1965b(Fama, , 1970. When investors buy (demand) and sell (supply) stocks, asset prices are generally set. The prevailing notion of efficient markets is founded on trust. As securities are claims on future distributions, investors participate in buy-side and sell-side transactions to the extent that they enjoy access to reliable data and are confident in future trades. Trust is the most important prerequisite for participation in trades.
It is noteworthy that the political leadership in Iran has repeatedly encouraged households to invest in the primary stock market (see for example https://www.leader.ir/en/content/24901/The-Leader%E2%80%99s-message-onthe-occasion-of-Nowruz, last accessed: 19/9/2021). Simultaneously, the Iranian government contributed to the millionaire boom by flooding the TSE with an influx of taxpayers' money. The government poured 1% of the state fund (National Development Fund) into the index, followed by an additional tranche of 25 trillion rials, approximately $595.2 million (Williams 2021). In the fall of 2020, the index exceeded two million points when the government began to sell its assets in the stock market and encouraged households to engage in investments. The higher the market rose, the more people saw the TSE as a common way to make money. However, the market soon fell by approximately half its value. After recouping some of its losses, it stands at around 1.3 million points (Iran International News, 2021). The 13-fold increase over the four years did not mean that people made much profit, as many entered the market too late. Figure 1 shows the TSE trend between 2010 and 2021 (TSE, 2021b). It is noteworthy that the number of millionaires in Iran has skyrocketed in recent years, contrary to general economic trends. In 2020, the total number of High-Net-Worth Individuals (or HNWI) grew by 21.6% in Iran, far above the global average of 6.3% (Khaasteh, 2021). In 2021 alone, the total wealth of these U.S. dollar millionaires increased by 24.3%.
The central question of this study is: Did the Iranian government fill its empty coffers by manipulating the financial market?

Benford's Law
It is common knowledge that natural numbers follow expected frequencies. The so-called logarithmic law, or Benford's law (BL), was first invented by the Canadian American mathematician Newcomb (1881). BL distinguishes natural from fictitious figures and provides empirical evidence of data manipulation if any, (Ravenda, Valencia-Silva, Argiles-Bosch & Garcia-Blandon, 2018). In this context, BL is instrumental in detecting anomalies and fraud (Nigrini, 2000) and was previously operationalized to identify fraudulent financial data.
Several studies have addressed market manipulation and have applied statistical techniques to detect such attempts. These studies unanimously used the numerical frequency law of first digits, also known as Benford's law (BL). In addition to the order of the first digit, other frequencies can also be determined for the second digit. The core idea refers to the frequencies of the first and second digits in naturally generated datasets according to Equations 1 and 2 (Newcomb, 1981;Benford, 1938): (1) P(d) = ∑ log_10 [1 + 1 (10 + ) ⁄ ] , d ∈ {0, 1, 2, 3, … , 9}  Table 1 summarizes frequencies of the first and second digits. The first-and second-digit tests are high-level adequacy tests used in a complementary manner to assess whether the dataset is adequate. According to Benford's law for the first digit (1BL), the numbers one to nine follow a certain logarithmic distribution: 30.1% for one, 17.6% for two, 12.5% for three, 9.7% for four, 7.9% for five, 6.7% for six, 5.8% for seven, 5.1% for eight, and 4.6% for nine [20]; for Benford's law for two digits (2BL), the frequencies are distributed from zero to nine: 12% for zero, 11.4% for one, 10.9% for two, 10.4% for three, 10.0% for four, 9.7% for five, 9.3% for six, 9.0% for seven, 8.8% for eight, and 8.5% for nine (Nigrini, 1999, Newcomb, 1881. The observed frequencies are likely to deviate from the BL distributions in an artificially generated dataset. Benfordness -compliance with the law -can be measured by applying financial data with a geometric trend and is characterized by the absence of minima and maxima. BL is a common practice and has been widely used in various disciplines, such as financial markets (Karavardar, 2014), epidemiology (Sambridge & Jackson, 2020;Farhadi, 2020;Farhadi & Lahooti, 2021a, 2021b, finance, and accounting (see Durtschi, Hillison, & Pacini, 2004), political science (Roukema, 2014), and compliance (Deleanu, 2017). The body of knowledge provides several tests to assess such agreement. Three standard techniques are well-known and widely used: the Kuiper test, chisquare test, and mean average deviation (MAD) (see Farhadi & Lahooti, 2021a).
The Kuiper statistic is a nonparametric test of discrete data. It is a modification of the Kolmogorov-Smirnov test. It quantifies the distance between the empirical distribution of samples of observations and the cumulative distribution of first-and second-digit frequencies [9]. The two summed parts are and is calculated as where is the cumulative observed distribution and _0 is the cumulative Benford distribution. Nonparametric tests are distribution-free and more powerful when small sample size [25]. The Kuiper test is calculated as follows (see Equation 3): Another popular approach is Pearson's chi-square test (^2) with the confirmatory null hypothesis that the distribution of the first digit must match Benford's frequency curve [12]. The chi-square test is sensitive to the sample size and is not recommended for inference when the dataset exceeds 5,000 observations [22,26]. The chisquared statistic uses the expected number of observations. If the sample size is too large, the null hypothesis is rejected even if there is no significant difference between the actual and expected subsets. The chi-squared test was calculated as follows (see Equation 4): In this study, the mean absolute deviation (MAD) technique was used, less dependent on sample size. Equation 5 shows the MAD calculations for the observed and expected frequencies. k is the number of leading digit bins. O .I. and E .I. are the observed and expected frequencies, respectively. A MAD > 0.015 indicates a lack of agreement with the law (Nigrini, 2018).
Furthermore, we operationalized all goodness-of-fit tests based on a significance level of 0.05. We tested all shares of listed companies in Iran for the following hypotheses.
H0: The frequency of the volume of Ji adheres to BL, where Ji stands for a specific security listed on the Tehran Stock Exchange.

Sampling of Data
We collected data on the number of intraday transactions published by the TSE from 21/3/2019 to 8/9/2021. The original datasets used in this study were obtained from the TSE website. The sample consisted of 176,618 integers (n or the sample size). Intermediaries, who disseminate information on financial instruments, can centrally control and theoretically change the number of intraday transactions. As mentioned earlier, changes in the number of transactions may signal higher demand and improve the attractiveness of traded securities. For each security, we compiled a sample of more than 100 observations, that is, the minimum number of intraday transactions, which can be considered an acceptable size for the application of Benford's law, even though the minimum threshold is not specified in the literature. Measuring compliance with the BL law is only helpful if the sample size is not too small. Small datasets may erroneously deviate from the expected logarithmic law and affect the reliability of the results. It was assumed that BL compliance increase as the sample size gets larger.

Benfordness
To explore the BL agreement of data, six goodness-of-fit tests were conducted in this study: the Kuiper test, chisquare goodness-of-fit test, and MAD for the first and second digits of intraday transactions. Forty-one securities were included in the primary sample, with an average number of observations of n = 536, resulting in a subset of 330 stocks with over 100 records. This selection was necessary to perform reliable tests to assess the Benfordness. The MAD, Kuiper, and Chi-square tests quantified the distance between the reported and referenced Benford distributions. The results are summarized in Tables 3-5, including list of financial products that did not conform to BL at an 0.1 alpha level. These assets are marked and highlighted in red. One hundred forty-eight assets did not meet the BL compliance requirements based on at least two goodness-of-fit tests for the first and second digits; thus, we reject the null hypothesis, suggesting market manipulation of the TSE. Looking at the Kuiper statistics for first-and second-digit compliance, nine assets with a total market capitalization of IRR 998,270,000 do not meet BL compliance requirements. A similar analysis of the MAD statistics resulted in a subset of 63 assets that did not meet the Benfordness thresholds. One hundred thirty-three securities did not pass the first-digit chi-squared test for adequacy. Figure 2 shows the frequency of the first leading digits of the most significant violations.

Discussion
A thorough evaluation of intraday demand for public shares listed on the TSE revealed significant noncompliance with Benford's Law. There is overwhelming evidence that shares listed on the TSE are most likely to be affected by attempts to manipulate the market, most likely by a falsified number of intraday trades reported by the Iranian Financial Market Regulatory Authorities. The most common BL violations in this study were observed in various industries. Companies across the mining, financial services, banking, construction, pharmaceutical, energy, and manufacturing sectors were equally identified among the most frequent BL violators.
As mentioned, Iran's supreme leader, Ali Khamenei, repeatedly encouraged citizens and called for proactive engagement in investing in the country's primary and secondary equity markets. Analysts claim that these attempts were primarily associated with the desolate Iranian economy. Moreover, the persistent mismanagement, continuous incompetence, bribery in public administration, and international political and economic pressures on Iran have left deep scars on the Iranian economy (Bertelsmann Stiftung, 2020).
Iran is indeed a developing country that can barely sustain its economy on its own.
State-owned enterprises (SOEs) account for approximately 80% of the country's economic activity. According to the International Monetary Fund (IMF), as of December 2020, public sector debt exceeded IRR 500 trillion. More than 89% was held by the theocratic government and less than 11% by state-owned enterprises (IMF, 2020). Iran's national debt has increased by 41% annually over the past ten years. In terms of the soundness of its banking system, Iran ranks 131 out of 140 worldwide. These facts can explain Iran's political leadership motivation to encourage capital inflow through people's engagement in the TSE transactions. Figure 3 highlights Iran's national debt as forecasted by International Monetary Fund (IMF) until 2025. To plug budget holes, the clerical regime has repeatedly raised (latent) taxes, leading to widespread public unrest  Vol. 17, No. 4;2022 and scrutiny. With Initial Public Offerings (IPO) throughout semi-functioning equity markets, the Islamic regime was able to access the people's savings and capital that had less engagement in Iran's equity markets. The deficit is indeed an additional motive for the interventions of the government across the TSE. It can be a driver behind the questionable development of the securities. Despite the impact of the U.S. sanctions on the Iranian crude oil exports, the country is a paragon of profligacy. For example, the Islamic government's annual budget for 2020/21 included a substantial $40 million for the domestic travel expenses of the supreme leader, Ali Khamenei (Iran Budget, 2021). Comparing this amount to the $14 million travelling costs of the former U.S. President Barack Obama (Delikik, 2020) shows how wasteful and inefficient the government in Iran is. Accordingly, Khamenei received three times more taxpayer money for his national trips than the former U.S. president for his international presence. This is quite surprising, as the chief cleric has already banned "too many foreign trips" by Iranian officials to save foreign currency in 2018 (Radio Farda, 2018).
Like budgeting and planning practices in Iran, the TSE is opaque. The lack of data integrity in Iran is nothing new. One can assume that the efficient market hypothesis cannot function in Iran due to the low quality of data. Existing investors in Iran shall exercise extreme caution when trading on TSEs. Given the empirical evidence found in this study, it is imperative to perform due diligence on all securities listed on TSE, including financial statements, the number of intraday transactions, representing transaction value and volume. This way, Iranian investors would be better able to navigate through the inherent risks of untransparent transactions on TSE. Nonetheless, novice investors should refrain from making any new transactions on the TSE until the market data is proven to be conclusive and reliable.

Limitations
This study is based mainly on the Tehran State Stock Exchange data. Former studies on the financial market in Iran do not exist. The literature driven by Iranian scientists appears to be inconclusive and compliant with the political will of the Iranian government. Given the lack of prior knowledge in the literature in this context, we took due care to avoid cognitive biases such as naïve realism, conformation, and authority biases while studying the literature and collecting data.

Future Research
In view of our results, we suggest that the actual returns and risks of the best-performing stocks should be examined based on the portfolio selection theory. Although we recognize the overall issues with financial data in Iran, in a hypothetical investment scenario, one should determine the efficient frontier portfolio. This would greatly enhance the present understanding of the TSE indices as a multi-layered and diversified financial market and provide some guidance to investors who are quite inexperienced with the advanced techniques of portfolio management.