[Note: A more up-to-date discussion of this idea, including a spreadsheet to help you with the math, can be found here.]

This week I got an email from a reader who is in the process of firing her advisor and becoming a Couch Potato. “I have decided it’s time to take matters into my own hands,” wrote Sarah. “I have \$25,000 in mutual funds in my RRSP with my current adviser. I want to create a Couch Potato portfolio with ETFs, but I’m a little intimidated. I don’t even know how to set up a brokerage account.”

I surprised Sarah with my response: I suggested that she not open a discount brokerage account, and that she forget about ETFs for now. That’s because \$25,000 is not enough to make ETFs efficient—index mutual funds are a much better option. The trading commissions Sarah would pay to buy and sell ETFs would outweigh the benefit of the lower annual fees. In fact, index mutual funds beat ETFs for most small portfolios.

I recently wrote an article in MoneySense about this issue, but I wasn’t able to go into detail about the math. Doing the calculations is important, though: choosing the wrong option can cost you a lot of money. If you’re considering your first Couch Potato portfolio and you’re not sure whether to use index funds or ETFs, here’s how to figure it out:

### 1. Determine the total MER of each portfolio option.

In general, ETFs have lower annual fees than index mutual funds, but the gap isn’t necessarily large, especially if you’re comparing ETFs to TD’s e-Series mutual funds. To determine the total MER of a portfolio, multiply the annual fee of each individual fund by the percentage you’ve allocated to that fund, then add them all up. For example, here are the calculations for two versions of the Global Couch Potato portfolio:

 Index mutual fund % MER Weighted MER TD Canadian Index – e 20% 0.31% 0.2 × 0.31 = 0.06% TD US Index – e 20% 0.48% 0.2 × 0.48 = 0.10% TD International Index – e 20% 0.50% 0.2 × 0.50 = 0.10% TD Canadian Bond Index – e 40% 0.48% 0.4 × 0.48 = 0.19% Total MER for portfolio 0.45% Exchange-traded fund % MER Weighted MER iShares S&P/TSX Composite (XIC) 20% 0.27% 0.2 × 0.27 = 0.05% iShares S&P 500 (XSP) 20% 0.26% 0.2 × 0.26 = 0.05% iShares MSCI EAFE (XIN) 20% 0.55% 0.2 × 0.55 + 0.11% iShares DEX Universe Bond (XBB) 40% 0.33% 0.4 × 0.33 = 0.13% Total MER for portfolio 0.35%

If you’re investing in only these four asset classes, the MERs are not dramatically different. The iShares version has an edge of just 10 basis points.

### 2. Multiply the total MER by the value of your portfolio.

This step will determine your annual cost in dollar terms. We’ll use Sarah’s \$25,000 portfolio value to make the comparison:

\$25,000 × 0.45% with TD e-Series Funds = \$112.50
\$25,000 × 0.35% with iShares ETFs = \$87.50

Turns out the difference in MERs works out to only \$35 a year on Sarah’s portfolio. Fractions of a percent don’t add up to much in small portfolios. Had Sarah been investing \$200,000, the difference between the two options would have been \$200 a year and more of a concern.

### 3. Determine how many ETF trades you’d make annually.

At a minimum, count on making one trade per ETF each year. (If you make an annual lump-sum contribution and rebalance the portfolio at the same time, that’s as efficient as you can get.) Multiply the number of trades by the commission charged by your brokerage. For example:

4 trades with big-bank brokerage at \$28.95 = \$115.80
4 trades with low-cost brokerage at \$9.95 = \$39.80

### 4. Add the cost of the MER and the cost of the trades.

You need to consider both the annual MER and the trading commissions to determine the overall cost of your portfolio. Let’s compare the different versions of the Global Couch Potato portfolio at \$25,000:

 MER in Trades Cost of MER dollars per year trading Total TD e-Series Funds 0.45% \$112.50 0 \$0 \$112.50 iShares ETFs @ \$28.95 0.35% \$87.50 4 \$115.80 \$203.30 iShares ETFs @ \$9.95 0.35% \$87.50 4 \$39.80 \$127.30

You’ll notice that for a \$25,000 account, the total cost of maintaining the portfolio is less with the TD e-Series funds, despite the lower management fees of the ETFs. It’s a lot lower compared with the \$28.95 trades, and even a few bucks less with super-cheap \$9.95 trades.

### 5. Find the break-even point for the two options.

As your portfolio grows in size, the dollar cost of the MER goes up, but the cost of trades remains the same. That’s why ETFs are more cost-efficient in large portfolios. The trick is to find the break-even point. If your portfolio is more the break-even point, use the ETFs. If it’s lower, use the index mutual funds.

Here’s an illustration that assumes you’re comparing an ETF portfolio with a total MER that  is half that of comparable mutual funds, and that you’re making eight trades per year. In this case, let’s use a portfolio value of \$75,000:

 MER in Trades Cost of MER dollars per year trading Total Index mutual funds 0.60% \$450 0 \$0 \$450 ETFs @ \$28.95/trade 0.30% \$225 8 \$231.60 \$456.60 ETFs @ \$9.95 trade 0.30% \$225 8 \$79.60 \$304.60

When comparing index funds with ETFs at a big-bank brokerage, \$75,000 turns out to be the break-even point: the price difference between the two options is less than \$7. (With the low-cost brokerage option, the break-even point is about \$27,000, at which point the annual cost of the ETFs and index funds in this example is about \$161.)

Keep the cost differences in perspective: in the above example, the low-cost brokerage would save you about \$145 over the mutual funds, or 0.19% of a \$75,000 portfolio. Those small savings come at the cost of flexibility: you can’t make monthly contributions with ETFs (unless you use Claymore’s PACC plan), and your dividends sit in cash until your annual rebalancing date.

While ETFs dominate almost every discussion of index investing (I’m guilty here, too), the fact is they are not cost-efficient for small portfolios. In Sarah’s case, at \$28.95 per trade, her portfolio would have to be \$120,000 before iShares ETFs were less expensive than TD e-Series Funds (assuming four trades per year). At \$9.95 per trade, she would need only \$40,000 to make ETFs cheaper. However, she would also be unable to make monthly contributions to each fund, something she does with her current RRSP.

There’s another factor to consider here: Sarah was nervous about even opening a discount brokerage account. With an ETF portfolio, she would need to be comfortable making her own trades, which is intimidating for many inexperienced investors. A couple of errors when entering orders would instantly wipe out any potential cost advantage of ETFs. And when investing makes you nervous, you’re liable to abandon your strategy, which is just about the worst thing you can do as a Couch Potato.