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Personal Finance For Canadians For Dummies (2018). p 224. I changed "percent" to %.

With stock funds, expenses are a less important (but still significant) factor in a fund’s performance. Don’t forget that, over time, stocks average returns of about 10% per year. So, if one stock fund charges 1% more in operating expenses than another fund, you’re already giving up an extra 10% [I bolded.] of your expected returns.

Why the bolded 10%? Why isn't it 1%?

Yearly, you earn 9% yearly on the costlier fund (with the +1% in expenses), rather than 10% on the cheaper fund. Thus your yearly expected return differs by 1%.

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The 10% refers to the change in return, not the the change in principal.

Case 1: you invest $1000 with a 0% TER and 10% return. That means your return is $100. Your balance would be $1100.

Case 2: you invest $1000 with a 1% TER and 10% return, where the fee is subtracted immediately. After the fee you are left with $990, and your gross returns will be $99. Your balance would be $1089.

Case 3: you invest $1000 with a 1% TER and 10% return, where the fee is subtracted after one year. Your gross returns are $100, your fees are $11, and your net returns are $89. Your balance would be $1089.

Note that case 2 and 3 are identical since you can directly combine the 10% returns and 1% fee into a 8.9% net return (1.10 × 0.99 = 1.089).

Now, when we compare your returns, we see a 11% difference in returns (only $89 of $100). I.e. that 1% TER amounts to roughly 10% of 10% returns even though there's only a 1% difference in total.

Note that TER doesn't just affect the immediate returns, but has a compounding effect since you can't reinvest those fees. With these example numbers, the 1% TER would cause a 30-year investment to perform 26% worse in total.

Note that these numbers are just illustrative. 1% TER is high for an ETF, and average 10% growth is optimistic.

  • 10% is the historical average return of the S&P 500. However, when you adjust for inflation it drops to about 7%. – Barmar Jul 13 at 18:16
  • @Barmar and since '57 it's only 7.96% pre-inflation (arithmetic mean, useful as an expected value for a single year) or 6.64% pre-inflation (geometric mean, useful as an expected value for the growth rate). Simple average values are misleading for long-term performance. – amon Jul 13 at 18:56
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    And of course, returns in any shorter period will be much more volatile. The 10% figure is used frequently, and has some justification, it wasn't pulled out of thin air. Your suggestion of "invalid mathematics" is a bit extreme. – Barmar Jul 13 at 18:59
  • @Barmar Ok, I checked long-term data and to my surprise that 10% is actually right. Thanks! – amon Jul 13 at 19:12
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    TER = total expense ratio – Nayuki Jul 14 at 0:21
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On a $100 investment, a 10% return is $10. A 1% fee is $100 * .01 = $1

$1 of the $10 is 10%

There are times we talk about a 4% safe withdrawal rate in retirement. And people ask about paying a pro 1% to manage their money. To me, this means 3% for you, 1% for the planner. Or 25% of your withdrawals go to the planner you hired.

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What you are missing is that the expense ratio is for the total investment, not just the profit.

Lets say the cheap fund has a ratio of 1% and the expensive one a ratio of 2%.

$100, 10% gain = $110, 1% takes $1.1, leaving 108.9, for a net 8.9% gain. $100, 10% gain = $110, 2% takes $2.2, leaving 107.8, for a net 7.8% gain.

You actually give up more than 10% of your profit this way.

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