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The geometric average return is equivalent to the cumulative return over the whole n periods, converted into a rate of return per period. Where the individual sub-periods are each equal (say, 1 year), and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.
The rate of return on a portfolio can be calculated indirectly as the weighted average rate of return on the various assets within the portfolio. [3] The weights are proportional to the value of the assets within the portfolio, to take into account what portion of the portfolio each individual return represents in calculating the contribution of that asset to the return on the portfolio.
Bacon (2002) proposed geometric excess return, as part of a geometric attribution, as a solution to this problem, and suggested that geometric attributions are preferable because they are compoundable, they are convertible among currencies, and they are proportionate (between different asset bases from period to period). [13]
Return on equity (ROE) and return on assets (ROA) determine how efficient a company can be at generating profits. Both formulas that can help investors determine how good a company is at turning a ...
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant ...
The phrase return on average assets (ROAA) is also used, to emphasize that average assets are used in the above formula. [2] This number tells you what the company can do with what it has, i.e. how many dollars of earnings they derive from each dollar of assets they control. It's a useful number for comparing competing companies in the same ...
Return on investment (ROI) or return on costs (ROC) is the ratio between net income (over a period) and investment (costs resulting from an investment of some resources at a point in time). A high ROI means the investment's gains compare favorably to its cost.
The change in a Fisher index from one period to the next is the geometric mean of the changes in Laspeyres' and Paasche's indices between those periods, and these are chained together to make comparisons over many periods: = This is also called Fisher's "ideal" price index.