Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia

Indro, Daniel C.; Lee, Wayne

doi:10.2307/3666130

Cited by 45 publications

(23 citation statements)

References 15 publications

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“…Summing up, geometric average always understates the consistent value; most severely, if the forecasting horizon is short. These theoretical conclusions comply with Indro, Lee (1997).…”

supporting

confidence: 72%

“…It looks like arithmetic, and not geometric, average is the right way to calculate average yields, irrespectively of the forecasting horizon N. This would counter the conclusions of Indro, Lee (1997) and recommendations in Damodaran (2013b).…”

Section: Inconsistent Forecast For More-than-one Period (N ≥ 2)mentioning

confidence: 86%

“…5/2014 Finanční a hospodářský cyklus (Financial and Business Cycle). DOI: 10.18267/j.pep.563 the conclusions by Indro, Lee (1997). Nevertheless, the conclusions lack sound theoretical backing.…”

Section: Introductionmentioning

confidence: 97%

“…Indro, Lee (1997). It behaves more like arithmetic average when the forecasting horizon is small relative to the number of observation.…”

Section: Application To Sp500mentioning

confidence: 99%

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Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average

Dvořák¹

2016

Prague Economic Papers

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The choice of averaging method has considerable impact on the average yield of a financial variable. Usually, geometric average is preferred, though dissenting opinions exist. Here it is shown that the problem has a consistent solution, which is called the horizon-consistent average. It is shown why geometric and arithmetic average calculations are almost always biased. When using company valuation's most common SP500 dataset by Ibbotson Associates for 1928-2012 and the recommended 10-year forecasting horizon, consistent with the 10-year government securities in a CAPM model, the arithmetic average is severely flawed. On the other hand, the geometric average for similar horizons does not deviate much from the horizon-consistent average.

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“…Summing up, geometric average always understates the consistent value; most severely, if the forecasting horizon is short. These theoretical conclusions comply with Indro, Lee (1997).…”

supporting

confidence: 72%

Section: Inconsistent Forecast For More-than-one Period (N ≥ 2)mentioning

confidence: 86%

Section: Introductionmentioning

confidence: 97%

“…Indro, Lee (1997). It behaves more like arithmetic average when the forecasting horizon is small relative to the number of observation.…”

Section: Application To Sp500mentioning

confidence: 99%

See 2 more Smart Citations

Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average

Dvořák¹

2016

Prague Economic Papers

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show abstract

“…It is well known, however, that both these mean returns produce biased estimates when the investment horizon is greater than the unit-time (Indro and Lee, 1997). The arithmetic mean return of past returns will overestimate the expected terminal return, whereas, the geometric will underestimate it (Blume, 1974;Indro and Lee, 1997;Mayo, 2006).…”

Section: Introductionmentioning

confidence: 99%

Arithmetic mean: a bellwether for unbiased forecasting of portfolio performance

2010

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Estimates of terminal value of long-tern investment horizons are biased. Unbiased estimates exist only for investment horizon of one time-period. The purpose of our paper is to suggest a method based on the arithmetic mean in order to obtain unbiased estimates for the terminal value of long-tern investment horizons. We suggest equating the time-period of our observed data to the time-period of the investment horizons. The performance of the suggested method is statistically investigated with the help of loss functions or error statistics. It produced the closest values to the actual ones than any other suggested averaging method when we examined a ten-year investment horizons for Standard & Poor's 500 index and on Dow Jones Industrial index.

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2014

Cost of Capital

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Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia

Cited by 45 publications

References 15 publications

Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average

Measuring Yields: Arithmetic, Geometric and Horizon-Consistent Average

Arithmetic mean: a bellwether for unbiased forecasting of portfolio performance

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