Dangerous Measures: The Fine Art of Calculating Returns

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The following is an excerpt from Hello Harold, a book by Harold Evensky - click here for a free Kindle version!

The person responsible for translating the math chapter of my book, Wealth Management, into Japanese told me, “You give me much headache.” Welcome to the math chapter.

Okay, class, today we’re going to be discussing one of the most common activities for financial planners, namely, the calculation of investment returns. Accounting in some measurable way for changes in investment values is fundamental to the work of financial planners. It may come as a surprise to you that such a simple concept is fraught with danger. The danger lies in the potential misuse of valid measurements.

There wouldn’t be much room for confusion if there were only one valid measure of investment return. Unfortunately, the mathematics of finance offers many choices. Among the most common are:

  • Current return
  • Total return (holding period return)
  • Real return
  • Compounded return
  • Time-weighted return
  • Dollar-weighted return (internal rate of return (IRR) and modified IRR)
  • Arithmetic return
  • Risk-adjusted return
  • Sharp ratio

Let’s consider each and I’ll simplify the discussion by assuming that we’re referring to the income received for a full year.