• Average Rate of Return
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Rate of return - Arithmetic average rate of return
1
The arithmetic average rate of return over
time periods of equal length is defined as:
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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.
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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:
1
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Rate of return - Geometric average rate of return
1
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.
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Rate of return - Comparing geometric with arithmetic average rates of return
1
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]
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Rate of return - Comparing geometric with arithmetic average rates of return
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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.
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Rate of return - Average returns and overall returns
1
The geometric average rate of return was
5%. Over 4 years, this translates into an
overall return of:
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Resource-based view
1
If these conditions hold, the bundle of
resources can sustain the firm's above
average Rate of return|returns
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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.)
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Perfect competition - Criticisms
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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
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Rate of return on a portfolio - Indirect calculation
1
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.
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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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