Absolute Investment Risk on the CFP Board Exam: Part I
Good to Know
This blog is the first in a four-part series that includes:
- When to trust the “mean” return,
- Using standard deviation to forecast outcomes,
- Skewness—Do we want negative or positive skew in our portfolio?
- Kurtosis of a return distribution—Is more kurtosis a good thing?
We will begin with the average or mean return. Specifically, we’ll call out the mean return you should NOT trust to provide an accurate average.
Do Not Trust the Simple Arithmetic Mean Return
The arithmetic mean is not an appropriate measure of average return because it can hide volatility and completely ignore compounding effects. For example, at first glance, the returns listed in the table below produce the same average return of 7%. However, they are two very differently performing investments.
| YEAR | RETURN 1 | RETURN 2 |
| 1 | + 10% | + 9% |
| 2 | - 10% | + 5% |
| 3 | + 10% | + 7% |
| 4 | - 15% | + 6% |
| 5 | + 40% | + 8% |
| Arithmetic Average Return | 7% | 7% |
| $100,000 initial investment at end of Year 5 |
$129,591 | $140,194 |
The 7% average return #2 puts another $10,603 into your pocket at the end of the 5th year. What’s our takeaway? The arithmetic mean should not be trusted whenever there are negative returns or multiple years in our calculation.
You Can Trust the Geometric Mean Return
The average return can also be calculated using a geometric mean or time-weighted return. The geometric mean measures the compound rate of growth over more than one time period and is a more accurate average than the arithmetic mean. It is often used in investments and finance to reflect the steady growth rate of investment funds over some past period; that is, the uniform rate at which money actually grew over time per period.
When a person refers to an annualized return, compounded rate of return, or time-weighted return, the reference is to the geometric mean. The geometric mean values for the returns in the previous example are displayed below.
| YEAR | RETURN 1 | RETURN 2 |
| 1 | + 10% | + 9% |
| 2 | - 10% | + 5% |
| 3 | + 10% | + 7% |
| 4 | - 15% | + 6% |
| 5 | + 40% | + 8% |
| Arithmetic Average Return | 7% | 7% |
| Geometric (Time-Weighted) Return | 5.2% | 6.99% |
Bottom Line
The geometric return can always be trusted. It produces an accurate mean return even in the presence of negative returns and returns spanning multiple years.
Coming Attractions
Our next blog in this series will build upon the geometric mean to understand an extraordinarily powerful tool in designing risk-compliant portfolios and forecasting a likely range of future returns.
Disclaimer
The information presented herein is provided purely for educational purposes and to raise awareness of these issues; it is not meant to provide and should not be used to provide gift, estate, generation-skipping, or financial planning advice of any kind. An experienced estate planning attorney should advise clients in these transfer tax issues. There are variations, alternatives, and exceptions to this material that could not be covered within the scope of this blog.
