Fun with Investment Math

Time for an investment quiz (no worries–this is just one question). You can choose from one of the following two hypothetical mutual funds. The Racy Fund gained 75% in 2010 but lost 45% in 2011. For the two years, its average return was 15%. The Boring Fund gained a positive 4% in each year, so its average return was (you guessed it) 4%. Which fund would you want to own?

On the face of it, most of us would take the Racy Fund. But if we did, we’d actually find the Boring Fund was the better choice. Let’s translate those percentage returns into actual dollar amounts. Assume you had $1,000 invested in each fund at the start of 2010.

The Racy Fund was worth $1,750 at the end of 2010 but then fell in value to $963 by the end of 2011. Meanwhile, the Boring Fund was worth $1,040 in 2010 and $1,082 by the end of 2011. Even though the “average” return of the Boring Fund was quite a bit less than the Racy Fund, the final account value of the Boring Fund was over $100 more. How can that be???

Mathematically, the difference is between a simple arithmetic average and a compound (or geometric) return. Arithmetic returns (simple averages) can hide what an investor really experiences in dollar terms. In geometric terms, the Racy Fund actually had about a negative 2% return on average. The Boring Fund’s geometric return was an even 4%.

Okay, so now that you really can use your old high-school math as an adult after all (you remember saying as a teenager, “when will I ever use this stuff?”), so what? As an investor, you win or lose in dollar terms. Percentages and return numbers might make for bragging rights at work with your buddies, but what really matters is what you earn in dollar terms. You can’t spend percentages.

If you haven’t done this in a while, take out your old calculator and add up what you’ve put into your investments. Then compare that to what they’re actually worth now. What the advertisements proclaim may not be (and very likely won’t be) what you’ve actually earned. And if what you’ve actually made in dollar terms isn’t what you’re seeing advertised, it may be time to change investments, advisors, strategies, your investment mix, whatever. Do the math yourself in dollar terms; it won’t lie. But this exercise may help motivate you to make some investment changes to better maximize your retirement readiness!


About Mike Wilson

Michael L. Wilson, MBA, CFP®, CRC®, is the owner of Integrity Financial Planning. Prior to founding Integrity in 1998, he worked for two years as a faculty member at the College for Financial Planning in Denver, training other financial advisors. Mike has 10 years of experience in the mutual fund industry, having worked with Fidelity Investments and Invesco Mutual Funds. He holds an MBA in Finance from Baylor University. Learn more about his work at
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