MERQ as a Better Measure of Fund Costs

Reader B.C. sent the following question about the Management Expense Ratio per Quarter century (MERQ):

I have been reading through some of the old posts on your blog, and came across your idea of the MERQ as a more valuable indicator of management expenses than the MER, and I wholeheartedly agree.

What is not obvious to me though is what equation you are using to calculate the MERQ. Would you be able to provide me with the equation? I'm sure that I am just forgetting some basic math :-)

A fund’s Management Expense Ratio (MER) is the management expenses and certain other fund costs for the year divided by the average assets under management during the year. This is then expressed as a percentage. The problem with this measure is that it gives a low-looking percentage (usually between 0.1% and 3%) that seems harmless. But, this bite out of your savings gets taken out of the same money year after year.

Suppose that Fund A’s expenses lead to year-end assets being 2% lower than they would have been if there were no expenses. This doesn’t sounds so bad, but consider what happens after 2 years. After the first year, 98% of the money stays, and after the second year, only 98% of that remaining money gets to stay again. This means that after 2 years, 98%x98% = 96.04% of the money is still there. Expenses have accumulated and now nearly 4% of the money is gone.

To carry this forward 25 years, we multiply 98% by itself 25 times to get about 60%. This means that 40% of the money is gone after 25 years (an MERQ of 40%). Suddenly, the 2% loss each year seems much more painful.

You may wonder how the fund’s return each year factors into all of this. The answer is that it doesn’t really enter into the calculation. Certainly costs are more palatable when a fund performs well, but for a given MER percentage, fund returns don’t affect what percentage of your money gets consumed in costs. So, if Fund A would have grown your money to a million dollars over 25 years without expenses, the after-expenses figure would be about $600,000. If Fund A performs very poorly and would have grown your money to only $100,000 without expenses, the after-expenses figure would be about $60,000. The 40% MERQ is the same whether returns are good or poor.

For technical reasons related to the way that MER figures are calculated, an MER’s impact on your savings is just slightly less than it would seem because of the compounding effect during the year. Because MERs are negative percentages, compounding actually works in your favour in this case. Here is the formula for calculating MERQ:

MERQ = 1 – e^(–25*MER)

This is easily calculated on a scientific calculator using the e^x or INV ln button.
On a spreadsheet, use 1 – EXP(–25*MER).

It’s not possible to run a fund without any expenses at all, but it certainly pays to keep costs down. A mutual fund with a 2.5% MER has an MERQ of 46.5%, but an ETF with a 0.25% MER has an MERQ of only 6.1%. After 25 years, would you rather have a portfolio of $535,000 or $939,000?