Return on assets (ROA) tells you how good a job a company did generating profit given the amount of assets it had, whereas return on equity (ROE) tells you how good a job a company did generating profit given the capital put up by equity holders to finance the firm.

ROA and ROE are related in that ROE is equal to ROA times financial leverage. You can see this relationship between ROA and ROE by performing a DuPont analysis:

ROA = (net income / net sales) (net sales / average assets)
ROE = (net income / net sales) (net sales / average assets) (average assets / average stockholders' equity)

where financial leverage is measured as average assets divided by average stockholders' equity.

We can thus show the relationship between ROE and ROA as follows:
ROE = ROA x financial leverage

Financial leverage thus amplifies the effects of ROA. In good times (when the company is making money) higher financial leverage makes ROE higher than ROA. But in bad times (when the company is losing money) higher financial leverage makes ROE more negative than ROA.

Companies can thus strategically increase the return on equity by relying more heavily on debt financing, but this increases the risk of default and the costs of financial distress.
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