To understand why a business's return on assets may be a different than its return on equity, it is important to understand exactly what assets and equity are, and why they are different. It is also important to understand the role of leverage, and how it affects both assets and equity.
Equity is another word for ownership. It is the total amount of capital the owners of the company have invested in it, including the appreciation or depreciation of any assets. If share prices decline, or if real estate or other assets the company owns declines, so does its equity. You cannot increase equity by borrowing money by itself. But you can increase equity by borrowing money, and then using those proceeds to purchase assets which then increase in value.
Assets are anything of value that the company owns, and comprise half of a company's balance sheet. The other half is a listing of the company's liabilities, and the difference between the two is the company's net worth, or book value. This is also an approximation of the company's shareholder equity. The act of borrowing money, or leveraging, does not directly affect equity by itself because each loan increases the liability and asset columns by the same amount. If a company borrows $100,000, its assets go up by that amount. However, so do its liabilities. But shareholder equity does not change.
When a company borrows money to invest or expand, it can increase its potential profits. For example, a company with $1 million in the bank -- and nothing else of value - can borrow $5 million to purchase property, leveraging 5 to 1, and then rent that property for a profit of $600,000 per year. The return on assets is 10 percent. The company owns $6 million in assets, and generates $600,000 in rental income, net of expenses. But the return on assets, on the other hand, is 60 percent. The owners have used leverage to generate $600,000 of profit per year on $1 million in equity - assuming the property can be liquidated, if necessary, to pay off the debt.
While leverage can potentially increase return on equity by boosting assets, this practice is a double-edged sword. If a company uses leverage to purchase assets, and then the assets decline in value, the company can lose money much more rapidly than if it didn't leverage at all -- and in some cases, shareholders' equity can get wiped out.