1. Average Rate of Return

2. Rate of return - Arithmetic average rate of return
The arithmetic average rate of return over time periods of equal length is defined as:

3. Rate of return - Arithmetic average rate of return
If you have a sequence of logarithmic rates of return over equal successive periods, the appropriate method of finding their average is the arithmetic average rate of return.

4. Rate of return - Geometric average rate of return
With reinvestment of all gains and losses however, the appropriate average rate of return is the geometric average rate of return over n periods, which is:

5. Rate of return - Geometric average rate of return
In the case where the periods are each a year long, and there is no reinvestment of returns, the annualized cumulative return is the arithmetic average return. Where the individual sub-periods are each a year, and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.

6. Rate of return - Comparing geometric with arithmetic average rates of return
The geometric average rate of return is in general less than the arithmetic average return. The two averages are equal if (and only if) all the sub-period returns are equal. This is a consequence of the AM–GM inequality. The difference between the annualized return and average annual return increases with the variance of the returns – the more volatile the performance, the greater the difference.[note 1]

7. Rate of return - Comparing geometric with arithmetic average rates of return
This pattern is not followed in the case of logarithmic returns, due to their symmetry, as noted above. A logarithmic return of +10%, followed by −10%, gives an overall return of 10% - 10% = 0%, and an average rate of return of zero also.

8. Rate of return - Average returns and overall returns
The geometric average rate of return was 5%. Over 4 years, this translates into an overall return of:

9. Resource-based view
If these conditions hold, the bundle of resources can sustain the firm's above average Rate of return|returns

10. Tendency of the rate of profit to fall - Criticisms
# It may be that in the heyday of a technological breakthrough, profits do indeed initially increase, but as the new technologies are widely applied by all enterprises, the overall end result is that average rate of return on capital falls for all of them. (This, however neglecting #4, is exactly what Okishio's equilibrium model seeks to refute.)

11. Perfect competition - Criticisms
In particular, the rejection of perfect competition does not generally entail the rejection of free competition as characterizing most product markets; indeed it has been arguedClifton (1977) that competition is stronger nowadays than in 19th century capitalism, owing to the increasing capacity of big conglomerate firms to enter any industry: therefore the classical idea of a tendency toward a uniform rate of return on investment in all industries owing to free entry is even more valid today; and the reason why General Motors, Texon or Nestle do not enter the computers or pharmaceutical industries is not insurmountable barriers to entry but rather that the rate of return in the latter industries is already sufficiently in line with the average rate of return elsewhere as not to justify entry

12. Rate of return on a portfolio - Indirect calculation
The rate of return on a portfolio can be calculated indirectly as the 'Weighted mean|weighted average rate of return' on the various assets within the portfolio.Levy, A 2009, ECON331 'Uncertainty, risky assets (activities) and portfolio choice', lecture notes accessed 22 May 2009 elearning.uow.edu.au 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.

13. Accounting rate of return
'Accounting rate of return', also known as the 'Average rate of return', or 'ARR' is a financial ratio used in capital budgeting

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