# How does one stock fund's charge of 1% more in operating expenses than another fund lower expected returns by 10%?

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%.

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 '19 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 '19 at 18:56
• 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 '19 at 18:59
• @Barmar Ok, I checked long-term data and to my surprise that 10% is actually right. Thanks! – amon Jul 13 '19 at 19:12
• TER = total expense ratio – Nayuki Jul 14 '19 at 0:21

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.

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.