Calculating and comparing security returns is harder than you think: A comparison between logarithmic and simple returns

• Published in: International review of financial analysis 2015-03, Vol.38, p.151-162
• Main Authors: Hudson, Robert S., Gregoriou, Andros
• Format: Article
• Language: English
• Subjects: Comparative analysis; Intraday data; Logarithmic returns; Observation periods; Rates of return; Return; Risk; Risk assessment; Securities; Simple returns; Stocks; Studies
• ISSN: 1057-5219; 1873-8079
• DOI: 10.1016/j.irfa.2014.10.008

We analyse the relationships between return calculation methods, risk and observation periods. We show that the mean of a return set calculated using logarithmic returns is less than the mean calculated using simple returns by an amount related to the variance of the set. This implies that there is not a one-to-one relationship between mean logarithmic and mean simple returns and also that risk and return calculations are not independent as the measure of risk is part of the measure of return. Finally we draw on examples from the extant literature to illustrate that these effects can be very important particularly when dealing with short observation periods. •We analyse the relationship between logarithmic and simple return calculations.•The difference between logarithmic and simple means depends on population variance.•There is not a one-to-one relationship between mean logarithmic and simple returns.•The measure of risk is part of the measure of return.•These effects are very important when dealing with short observation periods.