<p>This article studies the tail behavior of stock returns as a result of the interplay between a firm’s innovation search strategy and the environment in which the firm operates. Using a sample of 848 innovation-intensive firms trading in 13 countries over the 1995–2019 period, we provide evidence of time-varying exploration–exploitation choices by the sample firms. Our main analysis reveals that exploration-focused firms are more prone to stock price crash risk, but these firms are also more likely to experience large right tails. In addition, the positive relation between exploration and extreme changes in stock prices in either direction is non-linear (inverted U-shaped) in the intensity of competition in the external environment of the firm. Interestingly, ambidexterity appears to play an insulation role against crash risk, but the insulation effect only prevails in concentrated market settings and among financially constrained firms, which makes of ambidexterity a ‘hedge’ innovation search strategy when compared with one-sided exploration or one-sided exploitation. Furthermore, while we corroborate the evidence in prior studies that exploitation-oriented firms are undervalued, we add that the risk-adjusted returns and the exploration–exploitation choices share a complex non-monotonic relationship. Finally, we document that long-term orientation and uncertainty avoidance shape investor perceptions of stock price crash risk. Collectively, our results have important implications for investor portfolio choice and the financing of innovation.</p>