Why would you want to calculate average shareholder equity?
Average shareholder equity is a common baseline for measuring a company's returns over time. Using average shareholder equity makes particular sense if a company's shareholder equity changed from one period to another. That number can change because of retained earnings, new capital issues, share buybacks, or even dividends.
For example, a company may have shareholder equity of $1 million as of the first quarter and then issue new shares during the second quarter, raising shareholder equity to $1.5 million. Their average shareholder equity then for the first and second quarters is $1.25 million.
If you were to calculate their return on equity for the period using just the second quarter's $1.5 million number, ROE would appear lower than the company's actual performance. That's because the return on equity calculation places shareholder equity in the denominator of the equation; therefore, a higher level of shareholder equity results in a lower return on equity, all things being equal.
In this example, that lower ROE calculation isn't necessarily a fair performance metric because the new capital hasn't had a chance to be invested in profitable opportunities. Over time, that new capital will be deployed and should drive higher profits and ROE. It just takes a little time to work.
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