When analyzing investment performance, it is important to understand the differences between the various calculations. Especially as the preparer will undoubtably choose the ones most favourable to his/her perspective, not yours.
In my last post we looked at median and arithmetic mean investment returns.
Today we review and differentiate two additional investment return calculations: geometric mean or time weighted return and the dollar weighted or internal rate of return.
A tad more complicated. But much more helpful with your performance analysis.
Geometric Mean (Time Weighted) Return
The geometric mean is also known as the time weighted rate of return.
It measures the compound growth rate of the portfolio’s beginning market value over the evaluation period. The geometric mean return assumes that all cash flows are reinvested in the portfolio.
To calculate the geometric mean you need to add 1 to each period’s return. Then, multiply the results together for each period. Next, take the root value using a root equal to the number of periods. Finally, subtract 1 and you get the result.
Not as easy a calculation as the arithmetic mean return, but not too complex.
In my prior post’s arithmetic mean example, we had three year returns of 10%, 20%, 5%. The arithmetic mean is 5%.
The geometric mean return though is = [(1-0.1)(1+.20)(1+0.05)]1/3-1.0 = 4.3%
Note that the geometric mean is always less than the arithmetic mean. Good to know for quick calculation checks.
In our second arithmetic example, we had two periods with results of 100% and -50%. Year one we went from $1000 to 2000. Year two, we fell from the $2000 back to our original $1000. Ended up right back where we began, so our actual return was $0 and 0%. Yet our arithmetic return is 25% ((100-50)/2).
This makes no sense. Enter geometric or (hint hint) time weighted mean returns.
In looking at the geometric return, we see that this is addresses the illogical arithmetic result.
The geometric mean return = [(1+1.00)(1-0.50)]1/2-1.0 = 0%
This calculation reflects the reality of how returns are impacted by prior periods’ accumulated results.
Unless you need to know the calculations for exams, I suggest you not worry too much about them.
The key is to know that arithmetic mean returns are useful for independent data, whereas geometric mean returns are best used for investment results where the data is interdependent to some degree.
Also, when comparing arithmetic to geometric returns, arithmetic results will always be higher for identical data.
Dollar Weighted (Internal Rate of) Return
You may see comparisons between time weighted (geometric) and dollar weighted returns (internal rate of return).
Dollar weighted returns calculate the interest rate that equates the present value of the cash flows from all investment periods under consideration plus the end portfolio market value to the portfolio’s beginning market value.
In essence, it is the internal rate of return for the portfolio.
For example, on January 1, 2015 you invest $1000 in a 1 year term deposit earning 10% interest. On January 1, 2016 you reinvest the proceeds of $1000 into another 1 year term deposit earning 15%. You also invest an additional $2000 into the same term deposit. On December 31, 2016 you receive $3565 in cash.
Going through the manual calculations starts to get tricky here. Fortunately there are many good financial calculators that do the work. Or, if simply analyzing data, returns are often provided in different forms.
As for our example, by plugging the data into my handy HP 12C we get a return of 13.66%.
Dollar weighted returns provide useful information as to growth of a portfolio.
However, dollar weighted measures are not usually very useful in evaluating portfolio performance. That is because the return is affected by events outside the control of the portfolio manager.
Changes in funding, such as client contributions or withdrawals, will impact the dollar weighted return. This makes it difficult to compare the performance of two managers over time.
When evaluating two separate funds in which you wish to invest, do not put too much emphasis on the dollar weighted returns in your comparison.
That concludes our initial look at investment returns.
Next up, we will consider how risk and return relate to investor profiles.
