Geometric_Versus_Arithmetic_Means

Geometric_Versus_Arithmetic_Means - Geometric-Mean Returns...

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Geometric Versus Arithmetic Means 1 Arithmetic-Mean Returns These returns are simple averages of the returns experienced through time. Their virtue is that they are statistically correct estimates of expected returns. For instance, suppose you contemplate a two-year investment, and, in each of the two years, two outcomes are equally possible: up 50 percent or down 25 percent. You will, therefore, contemplate four possible scenarios of returns across two years: Return Value Probability Weighted Year 2 Year 2 of Outcome Outcomes 50% $2.2500 0.25 $0.562500 -25% $1.1250 0.25 $0.281250 50% $1.1250 0.25 $0.281250 -25% $0,5625 0.25 $0.140625 $1.265625 Expected Future Value The internal rate of return between $1.00 invested today and $1.266 expected to be received in two years is 12.5 percent, which is equal to the simply arithmetic average of +50 percent and -25%. In short, the arithmetic return describes expected returns well.
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Unformatted text preview: Geometric-Mean Returns The geometric-mean return is the internal rate of return between one outlay and future returns. It measures actual investment experienced better than the arithmetic mean. For instance, suppose you realize the following returns: Value of Investment--$1.00 1 100% $2.00 2-50% $1.00 Time Return The arithmetic-mean return is 25 percent. The geometric-mean return is 0 percent, which is exactly consistent with the fact that you have no more money at the end of the investment holding period than you invested at the beginning. In short, the geometric mean measures historical investment experience accurately. 1 I believe that the material above is based on a note published by Brunner (Darden) in conjunction with the Grand Metropolitan Case....
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This note was uploaded on 07/13/2011 for the course FIN 4414 taught by Professor Staff during the Spring '08 term at University of Florida.

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