Whenever you see a ‘total return’ for a mutual fund or exchange-traded fund, it is assuming that the dividends are reinvested. How do they calculate this? It’s a fairly easy but time-consuming exercise. Regardless of whether or not you want to calculate total returns on your own, it is still a good idea to know the math.

For this exercise I have chosen the iShares Russell Midcap Index Fund (IWR):

We are going to calculate the 2006 total return for IWR. To do so, you will need the following information:

1. The beginning date and price. For this exercise, I chose the beginning date of 12/30/2005, which had a closing price of $88.08.

2. The **distribution history** and the closing price on the ex-date (the date in the first column).

3. The closing prices on the last day of each year, which you can easily obtain by downloading the NAV History (download from iShares) into Excel. You can also find this information on Yahoo!

Here’s the information we need in order to make the calculation:

To calculate the total return for 2006, we will assume that we bought ONE share at $88.08 on 12/30/2005. The transaction history for 2006 would look like this (don’t worry if you don’t understand all the columns as I’ll explain each one):

As I said in the last paragraph, we assume we owned 1 share at the beginning of the year. We continued to own just one share until the first distribution of $.29138 was paid on 3/24/2006. Since we owned one share, our total amount received from that distribution was $.29138 (a little less than 30 cents). Remember that total returns are calculated by reinvesting dividends and distributions. So, we have to reinvest our $.29138. To calculate out how many shares our $.29 will purchase you divide $.29138 by the closing price on the distribution date, which was $94.12.

**$.29138 ÷ $94.12 = 0.0030958**

So, our $.29 distribution purchased us an additional .0030958 shares! Wooo Hooo! So we now own 1.0030958 shares until the next distribution date (6/22/2006). Notice on the second distribution date that we are receiving a distribution of $.332862 on 1.0030958 shares. This is the beauty of compounding.

We continue this same process for the rest of the year and end up the year with 1.013984 shares for a total value of $101.3274.

**1.013984 × $99.93 = $101.3274**

One share was worth $88.08 on 12/30/2005 and $101.3274 on 12/29/2006 (with dividends reinvested). Our total return for the year was:

**($101.3274 ÷ $88.08) – 1 = .1504 or 15.04%**

Notice that our total return calculation MATCHES the return that iShares has:

Pretty cool, eh? Now you know how total returns are calculated.

I get a little confused when I try to make these calculations to work with (1) purchases that occur at different times and (2) account fees. As an example of each:

– Suppose I buy somes shares in January. I earn a dividend in March and reinvest that. Then in April, the price has changed, and I buy more shares. I earn another dividend in September, then December. Can I calculate a “combined APY” that represents my return on both those transactions together?

– Suppose everything is the same as above, except that in August, I have to pay a $20 fee to maintain the account. It matters -when- this fee is paid, right? How do I consider that in my calculations? Are there any good reference books for this?

When investing for myself and others, I compare my returns to two benchmarks: 1) The DowJones Wilshire 5000 Equal Weight index, and 2) The TSP F Fund. Soon I will be adding a third comparison such as the DVY. The former is harder to beat than the S&P500 since it is not capitalization weighted. The latter has very low expenses making it tough to beat as well. Since I can invest my money anyway I like, I chose these benchmarks to cover the investment universe. Some years I have done better than others but it is never easy.