Calculating and Comparing Security Returns is Harder than you Think: A Comparison between Logarithmic and Simple Returns

33 Pages Posted: 7 Feb 2010 Last revised: 25 Feb 2013

Robert Hudson

Hull University Business School (HUBS)

Andros Gregoriou

University of Brighton

Date Written: February 7, 2010

Abstract

We show that there are some troubling differences between mean returns calculated using logarithmic returns and those calculated using simple returns. The mean of a set of returns calculated using logarithmic returns is less than the mean calculated using simple returns by an amount related to the variance of the set of returns. This implies that there is not a one-to-one relationship between mean logarithmic and mean simple returns. In addition, when logarithmic returns are used, ceteris paribus, higher variance will automatically reduce expected returns. We illustrate when these effects are important drawing on examples from the extant literature.

Keywords: Stocks, Logarithmic Returns, Simple Returns, Risk, Return

JEL Classification: G10

Suggested Citation

Hudson, Robert and Gregoriou, Andros, Calculating and Comparing Security Returns is Harder than you Think: A Comparison between Logarithmic and Simple Returns (February 7, 2010). Available at SSRN: https://ssrn.com/abstract=1549328 or http://dx.doi.org/10.2139/ssrn.1549328

Robert Hudson (Contact Author)

Hull University Business School (HUBS) ( email )

Hull, HU6 7RX
United Kingdom

Andros Gregoriou

University of Brighton ( email )

Brighton
Brighton, BN2 4AT
United Kingdom

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