Steve TeSelle, CFA, CFP ™
August 2002
The reason to calculate a return on your portfolio is that you'd like to know just how well or how poorly your portfolio performed. Then you can compare that with some kind of benchmark, so you know whether your returns are in line with similar investments and your expectations, or whether you have some questions to ask. For example, you might feel good if your portfolio of stocks increased 5%; but maybe not so good if an index for the stock market increased 20%.
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Calculating the return on a portfolio can be a happily simple process, or it can be as complicated as following a recipe in a fancy cookbook. The easy calculation is when you make no contributions to or distributions from your account. In this case, you simply take the amount at the end of the period, divide by the amount you started with, and subtract one. For example, suppose you start with $100. One month later, you have $105. 105/100 equals 1.05, minus one equals .05, or 5%. The return for the month is 5%.
Dorato calculates a return for each account every month. Each client's returns
are linked geometrically (meaning that the monthly returns are multiplied) to
generate quarterly, yearly, and since-inception returns.
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All quite simple, until people make contributions to and distributions from an account. Say an investor adds money to her account in the middle of a month. Using the simple formula above will overstate her return for the month. So we have to use more complicated formulas to calculate return. Dorato uses the Modified Dietz method to calculate returns for periods in which clients have added to or taken distributions from accounts. I won't include the formula here; the key is that the calculation is based on a time-weighted rate of return, not a dollar-weighted rate of return (such as internal rate of return).
A time-weighted rate of return means that portfolio returns are given equal weight throughout the period; a dollar-weighted rate of return attaches higher weight to periods when you have more money in the account. Hmm. Perhaps an example will help.
Suppose you start with $100. At the end of the month, your account is worth $105; you earned 5%. At that point, you decide to add another $400 to your account. But in the second month, you lose 10%, so your account balance is now $454.50. Over the two-month period, the dollar-weighted rate of return would show -7.7%, but the time-weighted rate of return would show -5.5%. The negative return you earned in the second month had a larger impact on the dollar-weighted return.
The reason investment managers should be judged using a time-weighted method
is that we normally do not control cash flows, the investor does. Investment
managers should neither be penalized nor rewarded for decisions beyond their
control. Indeed, the Association for Investment Management and Research (AIMR)
requires that all members use a time-weighted rate of return.
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People may disagree on which time-weighted return calculation is best, but most investment professionals agree that if you see someone touting an annualized return based on performance of less than a year, you should run the other direction. These are the same kinds of people who sold cure-all tonic from the back of a horse-drawn wagon. Say you get 5% from an investment in a month. Pretty dang good. If you annualize that ((1.05^12)-1), you get a return of 79.6%; early retirement is right around the corner. The problem is that most investments that earn 5% in a month are unlikely to keep that pace up, and the people who boast about their annualized returns are perfectly aware of this. So don't be fooled.
If you made it to the end of this article, then I think you qualify as a glutton
for punishment, or an investment aficionado. Either way, my hat's off to you.[top]
I'd like to make a few investments -- and could you super-size the returns?
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