Asset Allocation. The ultimate toolkit for long term investing success. TA/Indicators. Why Log Returns | Quantivity. A reader recently asked an important question, one which often puzzles those new to quantitative finance (especially those coming from technical analysis, which relies upon price pattern analysis): Why use the logarithm of returns, rather than price or raw returns? The answer is several fold, each of whose individual importance varies by problem domain. Begin by defining a return: at time , where is the price at time and Benefit of using returns, versus prices, is normalization: measuring all variables in a comparable metric, thus enabling evaluation of analytic relationships amongst two or more variables despite originating from price series of unequal values.
Several benefits of using log returns, both theoretic and algorithmic. First, log-normality: if we assume that prices are distributed log normally (which, in practice, may or may not be true for any given price series), then is conveniently normally distributed, because: This is handy given much of classic statistics presumes normality. Electronic Trading - Horizon Software - Trade Your Way. Investor Psychology Illustrated: One Year Later. It's funny how cycles work. Exactly one year ago we posted up a chart illustrating investor psychology. As we now look back, April of 2009 marked a time when the market had just bottomed and was in the nascent stage of a comeback.
Today, we find ourselves in a completely converse situation. Rather than watch the market decline and decimate, we're now faced with a seemingly never ending market rally that some would label an anomaly of an ascension. One year ago, for whatever reason, we were compelled to post up a chart illustrating investor psychology. (click to enlarge) As you can see, there are 19 stages in the cycle. While it's uncertain where exactly in the cycle we are, the point is that we're still in a cycle. Couple the above chart with this additional one from Prieur du Plessis, and you've covered the full spectrum of investor psychology: Complex adaptive systems.