The statement that adjusting the debt-to-equity ratio does not change the overall expected rate of return is correct because the overall expected rate of return is determined by the fundamental characteristics of the investment, rather than the specific financing mix. While the proportions of debt and equity may shift, impacting risk, the overall expected return on the investment remains anchored in its cash flow and growth potential. When debt is introduced into the capital structure, it typically serves to boost returns for equity holders due to the leverage effect. However, the total risk-adjusted return from the investment does not inherently change just because the ratios of debt and equity fluctuate. Instead, the risk profile might alter, which can lead to different required rates of return for investors, but the foundational expected return based on the asset's performance remains unchanged. For the other statements, decreasing the amount of debt can result in a lower overall rate of return because equity holders may now have a larger share of the risk without the benefits of leverage; similarly, increasing the equity can dilute returns for existing equity holders. Thus, while these statements reflect potential consequences of changing capital structure, they do not assert the invariance of the expected return, which is the key aspect highlighted in the correct option.