Compounding Investment Returns After Annual Expense Fees
Summary
The document reverse-engineers an investment-growth table using a starting balance of 10,000 and a constant annual return of 10%. It calculates balances with annual fees by reducing the assumed return to 9.5% for a 0.5% fee and 9% for a 1% fee, then compares those calculations with figures attributed to an Investopedia table. The comparison suggests that some reported yearly balances do not follow a consistent annual net return, though the answer speculates that rounding may explain the differences.
A second response says it attempted to reproduce the table over 20 years using the same equation, but the excerpt provides no visible results or supporting detail. The material offers a basic illustration of how recurring fees affect compounding, not a general fee-accounting rule: actual expense ratios are applied according to fund accounting conventions, and the excerpt does not establish how the source table handled timing, rounding, or fee accrual. Its calculations assume a fixed return and fee each year, so they omit market variability and other costs.
Key ideas
- A constant annual return can be modeled by multiplying the portfolio balance by the same growth factor each year.
- Under the document’s simplifying assumptions, annual fees reduce the modeled return before compounding.
- Small inconsistencies in a displayed balance series can make implied annual returns differ from the stated rate.
- The excerpt does not determine how the original table handled fee timing, rounding, or other expenses.
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Full text
# Expense ratio over time # Expense ratio over time I'm trying to reproduce the results in the table below from this article of Investopedia, but none of my calculations match. What is the correct way to calculate the expense ratio in this case? ## Answer by Dimitri Vulis (score 6, accepted) https://quant.stackexchange.com/a/63607 Generally, anything on Investopedia needs to be taken with a big grain of salt. (Wikipedia sometimes has correct information, but Investopedia - almost never.) Let us try to reverse-engineer Sabrina Jiang's table on Investopedia. The first column is easy to reproduce. We start with 10,000. Every year we earn 10%. So our assets are: year 1: 10,000.00 year 2: 10,000.00 * 1.1 = 11,000.00 year 3: 11,000.00 * 1.1 = 12,100.00 year 4: 12,100.00 * 1.1 = 13,310.00 year 5: 13,310.00 * 1.1 = 14,641.00 year 6: 14,641.00 * 1.1 = 16,105.10 etc Now suppose the asset manager charges 0.5% in fees. We again start with 10,000. Every year we earn 10%, but pay 0.5% in fees, so we actually earn 9.5%. So our assets are: year 0: 10,000.00 year 1: 10,000.00 * 1.095 = 10,950.00 year 2: 10,950.00 * 1.095 = 11,990.25 year 3: 11,990.25 * 1.095 = 13,129.32 year 4: 13,129.32 * 1.095 = 14,376.61 year 5: 14,376.61 * 1.095 = 15,742.39 etc Sabrina Jiang's table in Investopedia is very close, but not quite that: year 0: 10,000.00 year 1: 10,000.00 * 1.095 = 10,950.00 year 2: 10,950.00 * 1.09497716894977 = 11,990.00 year 3: 11,990.00 * 1.09499582985822 = 13,129.00 year 4: 13,129.00 * 1.09490441008455 = 14,375.00 year 5: 14,375.00 * 1.09419130434783 = 15,729.00 etc As you see, for year 1 she uses the correct return (exactly 9.5%), but for the subsequent years it's off by a small amount. Let us repeat this exercise for the 1% fee column. Every year we earn 10%, but pay 1% in fees, so we actually earn 9.0%. Sabrina has: year 0: 10,000.00 year 1: 10,000.00 * 1.09 = 10,900.00 year 2: 10,900.00 * 1.09 = 11,881.00 year 3: 11,881.00 * 1.0899755912802 = 12,950.00 year 4: 12,950.00 * 1.09003861003861 = 14,116.00 year 5: 14,116.00 * 1.0899688296968 = 15,386.00 As you see, for years 1 and 2 she uses the correct return (exactly 9%), but for the subsequent years it's off again. I have no idea why. I would guess that Sabrina was just being extra sloppy, rounding where she shouldn't. Looking at the quality of her other work on Investopedia, this seems very likely. ## Answer by JK Chai (score 0) https://quant.stackexchange.com/a/75410 I was trying to reproduce the same exact table from Investopedia but was not able to. Below is the result that I reproduced using exactly the same equation given from "@Dimitri Vulis" post. Assuming Expense Ratio is the only fees component and asset growing constantly at 10% for 20 years. Not sure if this table is a correct representation of the return values, but feel free to correct me if I am wrong. Thanks. #### Updated table #### OLD table
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