On MERs, Taxes and Partners

Malcolm Hamilton, an actuary and pension consultant with William M. Mercer Ltd., in the Introduction to Jonathan Chevreau's The Wealthy Boomer, provides this handy "rule of 40":

Take 40. Divide by your mutual fund's MER. And presto, you've got the number of years it takes management expenses to consume one-third of your investment.

The "rule of 40" is just an approximation¹
Assume a mutual fund's MER is 2%. In the first year you pay 2% of your fund as an MER, leaving 98%, i.e.

   1 - MER = 1 - 0.02 = 0.98

In the second year you pay 2% on the remaining 98%, leaving 96.04%, i.e.

   (1 - MER) x (1 - MER) = (1 - 0.02) x (1 - 0.02)

In the third year you pay 2% on the remaining 96.04%%, leaving 94.12%, i.e.

   (1 - MER) x (1 - MER) x (1 - MER) = (1 - 0.02) x (1 - 0.02) x (1 - 0.02)

So in general after n years the percentage of your money that you get to keep is:

   (1 - MER)ⁿ x 100

See the effect of this erosion graphically courtesy of gummy.

Note from the above formula that the rate of erosion is independent of the fund's rate of return. It doesn't matter if your fund performs well or not -- the MERs continue to eat into your portfolio unabated.

But that's not all!
Now if you think this sounds bad, stop reading any further. It gets worse. Much worse. Those nasty little MERs don't include the cost of brokerage fees, bid/ask spreads and other expenses that are charged directly to the fund. Those extras can easily add another 1% or even more to the annual erosion of your fund. Actively-managed funds incur higher costs due to their usually higher levels of trading. And small cap funds lose even more each time they trade a stock due to the wider bid/ask spreads.

And remember, like MERs these extra fees pile up regardless of how your fund performs.

But wait there's more!
For others, not you dummy. So far the analysis applies only to tax-sheltered accounts like RRSPs. In a taxable account you'll also have to share your returns with the taxman.

Here's a calculator that lets you estimate the effects of factors like MERs, returns, inflation and taxes on your fund. But before you go there, another warning: this won't be a pretty picture.

For example, in a taxable account at 50% marginal tax rate, assuming an average annual return of 10%, inflation at 3% and an MER of 2.5%, after 25 years you get to keep 36.89% of your money, the fund company 44.62% and the taxman 18.47%.

Ouch!
Bet you didn't realise you had mutual fund companies, brokerage houses and the government as major partners -- with "controlling interest" -- in your investment portfolio. And unlike you, they all get paid whether your investments make money or not.

After N years, your portfolio is reduced by a factor (1-MER)^N

If the MER consumes 1/3, you're left with 2/3, so

(1-MER)^N = 2/3

Take (natural) logs of each side:

N log(1 -MER) = log(2/3) = -.4 from a table of logs

It is intuitively obvious (haven't had a chance to say that in six years!)

that log(1 - MER) = - MER approximately ... from the Maclaurin series expansion

That gives N (MER) = .4, or, if MER is expressed as a percentage, N (MER) = 40

so N = 40/MER.