Statistics for Returns (Geometric mean)

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 GEOMETRIC MEAN:

The arithmetic mean return is an appropriate measure of the central tendency of a distribution consisting of returns calculated for a particular time period, such as 10 years. However, when an ending value is the result of compounding over time, the geometric mean, is needed to describe accurately the “true” average rate of return over multiple periods. 


The geometric mean is defined as the nth root of the product resulting from multiplying a series of return relatives together, as in :

where TR is a series of total returns in decimal form. Note that adding 1.0 to each total return produces a return relative. Return relatives are used in calculating geometric mean returns, because TRs, which can be negative or zero, cannot be used in the calculation.
The geometric mean return measures the compound rate of growth over time. It is important to note that the geometric mean assumes that all cash flows are reinvested in the asset and that those reinvested funds earn the subsequent rates of return available on that asset for some specified period. It reflects the steady growth rate of invested funds over some past period; that is, the uniform rate at which money actually grew over time per period, taking into account all gains and losses.

Advantages And Disadvantages Of Geometric Mean:

Main advantages and disadvantages of geometric mean can be expressed as follows:

Advantages Of Geometric Mean:

1. Rigidly Defined

As geometric mean is rigidly defined, its value will be always fixed.

2. Based Upon Items

Geometric mean is based on all the items of the series.

3. Suitable For Percentage And Ratio

Geometric mean can determine most correct average while dealing with percentages and ratios.

4. Less Affect

Geometric mean is less affected by sampling fluctuations.

5. Useful For Further Calculation

It is useful for algebraic calculation and other mathematical treatments.

Disadvantages/Demerits Of Geometric Mean

1. Complex Method

It requires different mathematical knowledge ( logarithm, ratio, roots etc.) to determine geometric mean. So, it is complex to compute and difficult to understand.

2. Less Popular

Because if difficulty in calculation and complex to understand, it is not commonly used method.

3. Not Applicable

Geometric mean cannot be calculated in the case of negative or zero value of any variable in the series.

4. In case of open end distribution, geometric mean cannot be obtained


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