Use a worked example to show how a yearly cost difference compounds over 20 years.
A yearly investment cost acts like a lower return. Over one year it takes very little, but over twenty years the gap it opens between two growth rates compounds into a large sum, so cost is the first thing to compare between similar funds.
Wei Ling (an invented example) saw that her fund's expense ratio was 1.75% and thought it sounded small, less than two cents on the dollar. Arjun's robo portfolio costs 0.78% all in, which sounded even smaller to her. The gap between the two is about one percentage point (1.75% minus 0.78% is 0.97%), and she thought it was hardly worth arguing about. Most people judge yearly costs this way, and over one year they are right, but over twenty years they are badly wrong.
You met compounding in How money works, lesson 2.1, "Simple interest pays on what you put in, compound pays on what you earned". Returns compound because each year's growth is earned on a balance that already includes earlier growth. Costs compound the same way in reverse.
A yearly charge is a percentage of the balance, taken every year. In year one the charge comes from the starting sum, and in later years it comes from a larger balance. Every dollar taken in year one also stops growing for the remaining nineteen years. So the cost of a fee is the fees themselves plus all the growth those fees would have earned had they stayed invested.
For this reason a yearly cost behaves like a lower return. Take the return before costs and subtract the cost, and you get the approximate growth rate. A fund returning 6% before costs with a 1.5% charge grows at roughly 4.5% (example figures). The gap between the two growth rates compounds into a large sum over long periods, and it widens the longer you hold and the more you add.
This course uses the simple method of subtracting the cost from the return. In practice, a fund's yearly cost is deducted directly from the fund's assets rather than billed to you, so exact results differ slightly from this method, but the overall picture stays the same. MoneySense explains how this charge works.
Take S$10,000 invested once, growing at 6% a year before costs, for 20 years (hypothetical figures chosen to make the effect easy to see; nobody can say what a fund will actually return).
Start with a rough check. The rule of 72 from How money works, lesson 2.3, "Estimate doubling time in your head with the rule of 72", says 6% doubles money in about 12 years (72 / 6 = 12). By year 20 you should expect a little over three times the starting sum.
For exact figures, use the spreadsheet function =FV(rate, years, 0, -starting sum), with the starting sum entered as a negative number. For each cost level, subtract the cost from 6% to get the growth rate, then run FV with that rate:
No cost: =FV(6%, 20, 0, -10000) gives S$32,071.35, about S$32,100 0.5% yearly cost, growth 5.5%: =FV(5.5%, 20, 0, -10000) gives S$29,177.57, about S$29,200 1.5% yearly cost, growth 4.5%: =FV(4.5%, 20, 0, -10000) gives S$24,117.14, about S$24,100
The no-cost result fits the rule of 72 check. To see what costs took, subtract each result from the no-cost figure. At 0.5%, costs took about S$2,900 (S$32,100 minus S$29,200). At 1.5%, they took about S$8,000 (S$32,100 minus S$24,100).
Now compare the two cost levels with each other. One percentage point a year, over 20 years on S$10,000, comes to about S$5,060 (S$29,177.57 minus S$24,117.14), which is more than half the original investment.
Real returns vary from year to year, can be negative, and nobody knows the average in advance. Cost is close to certain: a fund charging a given percentage takes about that percentage every year, whatever the market does.
When you compare two funds holding similar assets, the before-cost return is uncertain for both, but the difference in cost is close to certain. Every year, the cheaper option starts ahead by the size of the cost gap, so compare cost first. The arithmetic of costs applies to every fund, every year, and it is the reason lesson 6.1, "Why active funds as a group trail the market after costs", matters.
The cheapest option is not always the right one. A more expensive option may give you advice you would act on, a service you need, or a strategy that genuinely suits you better. Lesson 3.1, "What a bank adviser does for the money", made the case for paying for advice or service. Before you agree to pay for those extras, know their price in dollars over the time you will hold them.
Wei Ling rebuilt the example in a spreadsheet in about five minutes, with one column for the years and three columns for the three cost levels. She then changed the starting sum to the amount she actually holds, and changed the 1.5% to her fund's 1.75%. The final number in that column made her look at her fund differently.
Your version follows the same steps. Choose a starting sum invested once, a before-cost return and a period, and check the result against the rule of 72. Work out the no-cost result with FV. Subtract each cost from the return and run FV again at each growth rate. Subtract each result from the no-cost figure to see what costs took, and compare the cost levels with each other to see the gap in dollars. Finally, put in the amount you hold and the actual cost of your fund, as Wei Ling did.
In the activity below you will recreate the example and rerun it with your own amount, a different return and the costs of a fund you hold.
Rebuild the example in a spreadsheet. Then run it again with your own amount, a different return and the costs of a fund you hold.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).