Geometric Versus Arithmetic Returns

Unbiased Estimators of Long-Run Expected Rates of Return

Author(s): Marshall E. Blume

Reviewed work(s):

Source: Journal of the American Statistical Association, Vol. 69, No. 347 (Sep., 1974), pp. 634638

Published by: American Statistical Association

Stable URL: http://www.jstor.org/stable/2285993 .

Accessed: 12/05/2012 13:43

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .

http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact support@jstor.org.

American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal

of the American Statistical Association.

http://www.jstor.org

of

E

UnbiasedEstimators Long-Runxpected

Ratesof Return

*

E

MARSHALL . BLUME

This article documents the biases in using sample arithmetic or

geometric means of one-period returnsto assess long-run xpected

e

rates ot return.The formulasdeveloped are applicable to othercompound growthprocesses. For types of distributions f one-period reo

turnslikelyto be encounteredforbonds and stocks, numericalvalues

for these biases are given. Four unbiased estimators of long-run

expected rates of returnare developed and their relative efficiency

examined.

The article develops formulasfor the magnitude of

these biases which,when evaluated at reasonable values

forthe stock market,show that the biases are sometimes

substantial. More generally, hese formulascan be used

t

to calculate their magnitudeforany compound process.

An unbiased estimateofthe expectedN-periodrelative

for N < T will thereforebe between the arithmetic

mean raised to the Nth power and...