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When the amount of debt in a capital structure is decreased, the expected rate of return on equity tends to decrease as well. This relationship is primarily due to the fact that the levels of debt influence the overall risk profile of the firm.

Debt financing typically increases the financial leverage of a company, allowing it to potentially earn higher returns on equity during profitable periods. However, this added leverage comes with increased risk, as the company is obligated to meet its debt repayments regardless of its financial performance. When debt levels are reduced, the company relies more on equity financing, which generally entails lower risk.

With lower financial leverage, the potential returns for equity holders are reduced as there is less risk-premium attached to their investment. Consequently, the expected rate of return on equity decreases because the firm is perceived as being less risky with lower debt in its capital structure.

This relationship highlights fundamental concepts in corporate finance where the risk-return tradeoff plays a crucial role in determining expected returns. Thus, the decrease in debt leads to a decrease in expected rates of return for equity investors, reflecting a lower risk profile of the firm.