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A highly leveraged firm's earnings per share can indeed be characterized by more volatile earnings. Leverage involves the use of debt to finance the firm's operations, which can amplify both the firm's gains and losses. When a company has a significant amount of fixed debt obligations, any changes in revenue can lead to more pronounced changes in earnings per share.

When a firm experiences an increase in sales, the additional revenue contributes more significantly to earnings due to the fixed nature of interest expenses, resulting in a disproportionate increase in earnings per share. Conversely, if the firm's sales decline, the fixed debt obligations remain, leading to a sharper decline in earnings per share. This relationship creates a situation where the earnings per share fluctuate more dramatically compared to a firm with little to no debt, making them more volatile overall.

In summary, the high level of fixed costs due to leverage causes the earnings per share of a firm to react more sensitively to changes in business performance, which confirms that they experience more volatility in their earnings.