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Have you ever been shown impressive returns by an investment advisor, only to find your actual gains were much lower than expected? This is no coincidence. Today, we're uncovering one of the most common misleading practices in the financial world.
Investment returns aren't as straightforward as you might think. Many parents planning their children's financial future are often deceived by surface numbers. Let me tell you why understanding the difference between geometric average (a.k.a. Compound Annual Growth Rate "CAGR") and arithmetic average returns might be one of the most important financial decisions you'll make.
The Mathematical Trap: The Truth About Average Returns
Imagine this: You invest $10,000. In the first year, you gain 100%, doubling your investment to $20,000. Great! But in the second year, you lose 50%, leaving you with $10,000. If someone told you this investment had an average return of 25%, would you believe them?
Let's calculate:
(100% - 50%) ÷ 2 = 25%. Mathematically, this is correct, but this is the arithmetic average, which is completely misleading!
In reality, after two years, your money is exactly where it started. The true annualized return is 0%, not 25%! This is why we need to understand CAGR or geometric average.
Geometric Average (CAGR) vs Arithmetic Average: Key Differences
CAGR considers the compounding effect and reflects the actual growth rate of an investment over time. It calculates what constant annual growth rate would take you from the initial value to the final value.
The arithmetic average simply adds all returns and divides by the number of periods. It ignores a fundamental fact: percentage losses have a bigger impact on your portfolio than the same percentage of gains.
Let's look at a real example.
Kopi runs an apple store with the following profit growth over the past 9 years:
Year 9: -5.33%
Year 8: 32.76%
Year 7: 18.69%
Year 6: 6.41%
Year 5: -7.78%
Year 4: 24.20%
Year 3: 38.46%
Year 2: -26.95%
Year 1: -15.03%
If we calculate the arithmetic average return:
(-5.33 + 32.76 + 18.69 + 6.41 + (-7.78) + 24.20 + 38.46 + (-26.95) + (-15.03)) ÷ 9 = 7.27%
An average growth of 7.27% each year sounds good, right? But is this the real situation? What if I told you that the CAGR is only 5.22%? Do you see the difference? The arithmetic average is 7.27%, but the actual average return is only 5.22%. This gap can have a huge impact on long-term investments!
Volatility: The Hidden Enemy
Why does this difference occur? The answer is volatility. The greater the fluctuation in investment returns, the larger the gap between the arithmetic average and CAGR. In a highly volatile environment, CAGR is usually lower than the arithmetic average, meaning the actual situation is worse than it appears. This is why many investment advisors prefer to quote arithmetic average returns rather than CAGR.
Comparing Two Business Models
Let's explore Kopi's case further and compare it with another business model.
Across the street from Kopi is another apple store that partners with a local supermarket. Every week, leftover apples can be returned to the supermarket at no cost, but their growth is capped at 10% per year.
Assuming both stores have similar total profits growth over the past 9 years, this store's growth looks like this:
Year 9: 0%
Year 8: 10%
Year 7: 10%
Year 6: 6.41%
Year 5: 0%
Year 4: 10%
Year 3: 10%
Year 2: 0%
Year 1: 0%
Which business model is better?
Let's calculate the second store's arithmetic average return and CAGR.
Arithmetic average = (0 + 10 + 10 + 6.41 + 0 + 10 + 10 + 0 + 0) ÷ 9 = 5.16%
CAGR = approximately 5.37%Do you see? Although Kopi's arithmetic average is higher (7.27% and 5.16%), the second store's CAGR (5.37%) is higher than Kopi's store (5.22%).
This is the cost of volatility! Stable returns usually lead to better long-term results, even if the peaks are less impressive.
How to Calculate CAGR
CAGR = (Ending Value/Beginning Value)^(1/Number of Years) - 1
For example, if your initial investment is $10,000 and after 5 years it becomes $15,000:
CAGR = (15,000/10,000)^(1/5) - 1 = 1.5^0.2 - 1 = 0.0845 = 8.45%This means your investment grew at a constant rate of 8.45% per year, taking 5 years to grow from $10,000 to $15,000.
What They Don't Tell You
Many financial products emphasize arithmetic average returns because they usually look better. This isn't necessarily fraud, but it can mislead consumers about expectations for future performance. Especially in highly volatile investments, such as stocks or certain mutual funds, the gap between the arithmetic average and CAGR can be very significant.
Conclusion: Informed Parents Make Informed Choices
As parents, we want to make the best financial decisions for our families. Understanding the difference between CAGR and arithmetic average is the first step to avoiding common investment traps.
Remember, when an investment advisor shows you impressive returns, don't be deceived by surface numbers. Ask clearly whether this is an arithmetic average or CAGR, because it really matters! Stable, predictable returns are usually more valuable than highly volatile returns, even if they don't look as impressive. By understanding these mathematics concepts, you can make smarter, safer financial decisions for your family's future.
For tutees of Gets Education, next time when a salesman approaches your Papa to invest and shows fancy % past returns, do ask if it's arithmetic or annualized return because it matters.
