Is Log Ratio a Good Value for Measuring Return in Stock Investments?

Measuring the rate of return is an important issue for theory and practice of investments in the stock market. A common measure for rate of return is the logarithm of the ratio of successive prices (LogRatio). In this paper it is shown that LogRatio as well as arithmetic return rate (Ratio) have several disadvantages. As an alternative relative differences (RelDiff) are proposed to measure return. The stability against numerical and rounding errors of RelDiff is much better than for LogRatios and Ratio). RelDiff values are identical to LogRatios and Return for small absolutes. The usage of RelDiff maps returns to a finite range. For most subsequent analyses this is a big advantage. The usefulness of the approach is demonstrated on daily return rates of a large set of actual stocks. It is shown that returns can be modeled with a very simple mixture of distributions in great precision using Relative differences.