Correctly measuring investment performance is a problem for many investors.
The problem has two parts.
First, many investors don’t even bother to measure their investment performance. Most brokerage account statements do not report the investment performance for the period in question. No investment return is reported for the month, quarter or year. It’s common for do-it-yourself investors to measure their performance by looking at their starting balance and comparing it with the ending balance. That may be better than nothing, but it’s far from adequate. Even many investors who work with a financial adviser receive little more than account statements without any meaningful performance report.
The simplistic approach of comparing starting and ending balances does not give a meaningful insight into how well or poorly investments have performed. It fails to take into account the cash flows in or out of an account; it fails to consider how different asset classes are performing; and it fails to measure performance against a relevant market benchmark or blend of benchmarks.
The second part of the problem is that even investors who are trying to measure their performance often end up looking at the wrong number. Investors who want to know the average annualized performance of their investments often end up looking at the wrong average. They gravitate to the “arithmetic” average, which is easy to calculate but is the wrong number for investors to use.
A simple example illustrates the point. Assume that in year 1 your $100,000 investment loses 50% and then in year 2 it gains 100%. At the end of year 2, the investment is still worth $100,000. If you were to calculate your investment return by taking the simple arithmetic average, you would add -50 plus 100, divide by two and arrive at 25%. Clearly that is not correct. Your actual return is 0%, and that is the result you would have found if you were looking for the correct average, the “geometric” average.
Consider a slightly more complicated example looking at three years of returns on the S&P 500. In 2008 the S&P 500 lost 37%, in 2009 it gained 26.5%, and in 2010 it gained 15%. The simple arithmetic approach would add the returns for the three years, divide by three, and arrive at a three-year return of 1.5%. That would be wrong. A $100,000 investment starting in 2008 would only be worth about $92,000 by the end of 2010. The correct annualized three-year return (the geometric average) was actually a negative 2.86%.
Finally, let’s consider another slightly more complicated example drawn from the historical record and then reach some conclusions. Below are the returns of three very different assets classes over the past 17 years: U.S. stocks, emerging market stocks and Treasury bills.
|S&P 500||MSCI Emerging Markets Stock||3-month Treasury|
|17-year arithmetic average||6.2||11.1||1.69|
|17-year geometric average||4.5||6.2||1.67|
|Source: Craig Israelsen|
Note the gap between the arithmetic average of the S&P 500 (6.2%) and the geometric average (4.5%). Compare that with the even wider gap for emerging market stocks: an arithmetic average of 11.1% versus a geometric average of 6.2%. And finally, for 3-month Treasury bills, which experienced minimal volatility, we can see that two averages are very close: 1.69% arithmetic average versus 1.67% geometric average.
What is going on here? First, the data tells us that the arithmetic average becomes less and less accurate as returns become more volatile, especially as returns range widely from positive to negative. Emerging market stocks showed the widest range of returns — from a low of negative 53% to a high of 79%. The arithmetic average return for emerging market stocks overstates the actual investment return by nearly 80%.
Second, the simple arithmetic average does not accurately reflect the rate at which investments grow or decline in value. It always overstates investment performance and it would only be appropriate to use with an investment that experiences no volatility, a rare thing.
Here are the key points for investors to consider:
- You need to accurately measure investment performance. If you don’t, you can’t make informed decisions about how your investment or fund manager has performed or about how different asset classes are performing.
- Calculating your average annual investment return using a simple arithmetic average is the wrong way to do this. The math is easy, but it overstates your actual performance.
- You need either to get acquainted with using a financial calculator or spreadsheet to properly calculate your investment return or you should find an investment adviser who has the tools to do this for you.
David Peartree, JD, CFP® is the principal of Worth Considering, Inc., a registered investment advisor offering fee-only investment and financial advice to individuals and families. Offices are located at 160 Linden Oaks, Rochester, NY 14625, [email protected]