The capital market's stability is crucial for economic development, yet the risk of stock price crashes poses a significant threat. Customer concentration, the extent to which a company relies on a few key customers for revenue, is a critical factor influencing cash flow generation and, potentially, crash risk. Existing literature presents mixed findings regarding the relationship between customer concentration and stock price crash risk. This study addresses this inconsistency by focusing on the Iranian market, a developing economy with unique characteristics, and by introducing three novel measures of customer concentration: the proportion of significant customer sales, the Herfindahl-Hirschman Index (HHI), and a Ranking Index. The study analyzes 82 companies listed on the Tehran Stock Exchange (TSE) between 2013 and 2020, using a robust methodological framework, including panel data and multiple regression analysis, to investigate the relationship between customer concentration, both corporate and government, and stock price crash risk, also examining the moderating role of institutional investors.

The study's theoretical framework is grounded in agency theory, which explains how conflicts of interest between shareholders (principals) and management (agents) can affect decision-making, including those concerning customer relationships. The literature review examines existing research on the relationship between customer concentration and stock price crash risk, noting inconsistent findings. Some studies suggest that high customer concentration increases risk due to factors like the potential financial distress of major customers, relationship-specific investments, and reduced profitability due to bargaining power. Other studies argue that high customer concentration can improve firm performance through reduced operational costs and increased asset utilization. The existing literature also offers conflicting views on the role of institutional investors in mitigating this risk. The study builds upon previous work, especially Lee et al. (2020), but addresses the limitations of prior research by focusing on a developing market and introducing new metrics to measure customer concentration.

The study uses panel data from 82 companies listed on the TSE from 2013 to 2020, meeting specific criteria: at least three years on the exchange, identified major customers (contributing 10% or more to revenue), and exclusion of financial institutions. Data were collected from audited financial statements and board reports. Three indicators measure customer concentration: 1) Sales-based Index (proportion of revenue from significant customers); 2) HHI (incorporating both number and size of significant customers); and 3) a Ranking Index (ranking customers into quintiles based on revenue contribution). Stock price crash risk was measured using negative conditional return skewness (NCSKEW), following Chen et al. (2001) and Kim et al. (2011). The study employs panel data regression analysis using the "R" software. The models test four hypotheses: 1) the relationship between corporate customer concentration and crash risk; 2) the relationship between government customer concentration and crash risk; 3) the moderating effect of institutional investors on the corporate customer concentration-crash risk relationship; and 4) the moderating effect of institutional investors on the government customer concentration-crash risk relationship. Control variables include firm size, ROA, leverage, turnover difference, standard deviation of abnormal returns, average monthly returns, market-to-book ratio, percentage of floating shares, and a dummy variable for crash risk above the industry average. Chow and Hausman tests were used to select the appropriate model (pooled or fixed effects).

Descriptive statistics provide means, medians, and standard deviations for key variables. Inferential statistics are presented via regression analysis. The results vary based on the customer concentration measure used. Using the Sales-based Index and HHI, neither corporate nor government customer concentration significantly impacts crash risk. However, using the Ranking Index, a significant negative relationship emerges between the *highest* level of both corporate and government customer concentration and stock price crash risk. This indicates that companies with the highest concentration of significant customers, according to the ranking index, experience lower crash risk. Regarding the moderating role of institutional investors, the presence of institutional investors significantly and positively moderates the relationship between corporate customer concentration (Sales-based Index and HHI) and crash risk, but it does not significantly moderate the relationship between government customer concentration and crash risk. Additional analysis considering all significant customers together revealed no significant overall effect of customer concentration on crash risk, except when using the Ranking Index, where high concentration was significantly and negatively related to crash risk. This effect was also moderated by institutional investment.

The findings challenge some existing literature, particularly Lee et al. (2020), by demonstrating a negative relationship between high customer concentration and crash risk in the Iranian context. This suggests that the relationship may be context-specific, affected by factors like economic development, regulatory frameworks, and cultural norms. The negative relationship found with the Ranking Index likely reflects the stabilizing effects of high customer concentration in reducing operational costs and enhancing firm performance, particularly when dealing with a smaller number of stable, high-value customers. The moderating role of institutional investors on the corporate customer concentration relationship aligns with the efficient monitoring hypothesis, suggesting that they can improve corporate governance and reduce information asymmetry. The lack of a moderating effect for government customer concentration might reflect the specific nature of government contracts and interactions in Iran.

This study provides novel insights into the relationship between customer concentration and stock price crash risk in a developing economy. The findings highlight the importance of using diverse measures of customer concentration and considering the context-specific factors that influence the relationship. The study's contribution lies in its use of a novel Ranking Index and its examination of the moderating role of institutional investors in a developing market context. Future research could investigate the role of information disclosure practices, corporate governance, and communication between institutional investors and management to further refine the understanding of this complex relationship.

The study is limited to companies listed on the TSE in Iran, which might not be generalizable to other markets. The specific measures of customer concentration may influence the results. The timeframe of the study (2013-2020) might not capture longer-term trends. Future research could examine a broader range of countries and industries and investigate the impact of additional relevant factors.