Risk and Return Measures - Measures of Investment Return


  1. Geometric Average/Arithmetic Average - These are both measures of central tendency.
    1. Geometric Average: the average compounded return. The formula is expressed as follows:
Formula

GM=n((1.R1)(1+R2)...(1+Rn)-1
    1. Arithmetic Average
: division of the sum of the returns for each period by the number of periods under evaluation. The formula is expressed as follows:
Formula
n
AM = ?HPRt/n
t=1

2001 2002 2003 2004 2005
17.9% 8.73% 9.01% 11.96% 14.32%

Geometric Average - Geometric average is always less than the arithmetic mean, except when returns are equal for each period. Then, the geometric and arithmetic averages would be equal. This average is the same as the internal rate of return (IRR).

1/5(1.179)(1.0873)(1.0901)(1.1196)(1.1432)-1= 12.33%

Arithmetic Average - does not take into account the compounding effects of returns. It is good for approximating the earning rate over time, but will tend to be less accurate if returns fluctuate widely from year to year.

17.9%+8.73%+9.01%+11.96%+14.32%/5=12.38%

  1. Time-Weighted Return/Dollar - Weighted Return:
    1. Time-Weighted Return: a measure of the performance of an investment over time without regard to cash flows in either direction. This is the preferred return measure that planners use, as it strips out the bias that cash flows create with a dollar-weighted return.
    2. Dollar-Weighted Return: a measure of performance of an investment over time, only here cash flows figure into the return calculation, giving effect to inflows and outflows of money.
Measures of Investment Return (Contd.)


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