## Monday, July 16, 2012

### 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?

1. Thanks (again) for your blog!!

How come I get slightly different numbers if I do the calculation outlined in the text:

1 - .98^2 = 3.96%

versus the formula:

1 - exp(-2*.02) = 3.92%

Shouldn't they be exactly the same? Am I screwing something up?

The differences are small but persistent, for example for 25 years @ 5% MER,
1 - .95^25 = 72.26%
1 - exp(-25*.05) = 71.35%

2. Hi, me again... actually, I guess the difference is what you were talking about later in the article. Wish I could understand the "technical reasons", but I'll just assume the formula you gave is correct.

Thanks again!

ps, the captchas are a bit too challenging... had to try many many before found one I could read...

3. @Anonymous: The "technical reasons" are that the MER is calculated as total year's costs divided by the average fund level. This makes the MER an instantaneous percentage. If the MER is 2%, then you actually lose just slightly less than 2% of your money by the end of the year. The difference is quite small and tends not to add up to much even over many years.

Sorry about the captchas. Google controls them. Unfortunately, without them I get hit with so many spam comments that I can't manage. Even with captchas I usually get a couple of spam comments per day.

4. Too bad the "they only charge me 2%" gang won't see this. Thanks for the ammo for my next discussion with one of them.

1. @David: Glad to help. Rather than seeking a large reader base, I'm happy to help a small number of people who hopefully pass along the parts that resonate.