# How to Compare Two ETFs, Accounting for Expense Ratio?

I'm attempting to compare ETFs but am not understanding how to account for expense ratios. (I'm assuming that the annual returns do not account for expense ratios already -- is this correct?)

For example, take the IVW - iShares S&P 500 Growth ETF and the RPG - S&P 500 Pure Growth ETF. Both of these ETFs track the S&P 500/Citigroup Growth Index.

The 5 year return of IVW is 125.43%, with an expense ratio of 0.18%.

The 5 year return of RPG is 183.31%, with an expense ratio of 0.35%.

Let's say I put in \$100 to both of these funds 5 years ago. Not accounting for the expense ratio, today, that \$100 would have grown to \$225.43 and \$283.31 for IVW and RPG, respectively.

When I see the "5 year return" of an ETF or mutual fund, I am assuming this is the return not accounting for the expense ratio and dividend; is this correct? Otherwise, this question is mute.

My question is essentially: when and on what basis do I pay the expense ratio?

• When I sell the ETFs, after which I pay the expense ratio multiplied by the market value of my shares of the ETF? I.e., (0.0018 * 225.43 == 0.4058) or (0.0035 * 283.31 = 0.9916) for IVW and RPG, respectively? This would push the profit down to \$225.02 and \$282.32, respectively.
• At the end of each year, after which I pay the expense ratio multiplied by the market value of my shares of the ETF at that point? Given an expense ratio and a n-year return, how would I calculate this? Simply divide the growth (183.31 and 125.43, respectively) by n-years, multiply this amount (average annualized growth) by the end of the previous year, multiply by the expense ratio for n-years, and sum the results? For example, for RPG:

``````                   RPG
End of Year# |  Market Value | Fee(\$) |
1            136.662      0.478  |
2            173.324      0.607  |
3            209.986      0.735  |
4            246.648      0.863  |
5            283.310      0.992  |
---------|
3.675  |
``````

facepalm After I did this by hand I realized that I forgot the subtract the fee from the market value at the end of each year before adding the average growth per year.

Regardless, is that the appropriate way to calculate expense ratios and compare two ETFs based on expense ratios and annual growth, or is it too naive to sum the average annualized growth (n-year growth / n) to the end of year market value less fee?

• I plan to use the brokerage firm that offers the ETF so that I pay no commission fees. – Matthew Moisen Jul 26 '14 at 21:50
• Expense ratios are factored into the returns by reducing the dividends generally so there isn't a "paying the expense ratio" component. – JB King Jul 26 '14 at 22:46
• @JBKing So when I see that an ETF or Fund has a 1-year return of 10%, that means I would have \$110 after selling the shares if I put \$100 into it a year ago (less taxes)? – Matthew Moisen Jul 26 '14 at 22:48
• Correct, assuming no friction which is quite a bit of an assumption. Consider that you buy at one price and sell at another price so that getting exactly 10% could be a bit tricky though 9.999% or 10.00001% may happen that just gets rounded off to 10%. – JB King Jul 26 '14 at 22:50
• @JBKing Could you post that as an answer? "The return accounts for the expense ratio" or something. – Matthew Moisen Jul 26 '14 at 23:50