Annual Returns
Where do they come from?

The published annual returns used to compute long-term average returns can be calculated in two ways - one produces monthly returns, the other doesn't. Both compound incremental returns over the course of the year and are computed as holding period returns as described on the Mutual Funds Return page under The Geometric Mean. Net asset values (NAVs) and distributions from dividends and capital gains are used to perform these calculations.

The simpler of the two computes the return from the beginning of the year to the date that the first distribution is made, then from each distribution to the next and from the last distribution to the end of the year. Those incremental returns are then used to compute a compound annual return. The following table uses this method to compute the 2006 return for Cohen & Steers Realty Shares (CSRSX), a real estate mutual fund.

Annual Return of Cohen & Steers Realty Shares, 2006

If you need monthly returns to compute the standard deviation of returns or for some other reason, compute the returns from the beginning of each month to the end of each month except any months in which distributions were made prior to the last trading day of the month. In the months when distributions were made prior to the end of the month, compute the return from the beginning of the month to the distribution date then from the distribution date to the end of the month and compound the two returns to arrive at the return for the month. This is shown in the following table, which also computes the 2006 return for CSRSX.

Monthly returns for those months in which distributions were made are calculated by compounding the two incremental returns for those months. For example, the return for March is equal to [(1.0402 x 1.0118) - 1] x 100% = 5.25%

Annual Return of Cohen & Steers Realty Shares, 2006

• The beginning NAV is the ending NAV from the prior period. That's because NAVs are quoted at the end of each trading day. Tomorrow's beginning NAV is today's Ending NAV, 2007's ending NAV is 2008's beginning NAV and 2008's ending NAV is just that, the NAV at the close of trading on the last trading day of 2008.
• Compound returns are computed as the holding period returns as described on the Mutual Funds Return page under The Geometric Mean.
• This process works for any holding period.
• When distributions are made, they are deducted from a fund's assets on the day of the distribution, thus reducing the NAV by the per-share amount of the distribution. Adding distributions back into the NAV on the distribution date and computing the incremental return to that date will result in the correct return. When distributions are made prior to the end of a month, adding them back in at the end of the month and computing the return for the full month will not yield the correct return for that month.

Computing returns under the assumption that distributions occur at the end of the month will produce returns that are incorrect to varying degrees in all cases when distributions are made on some day other than the last trading day of the month. The degree of error is a function of the amount of the distribution and the amount by which the NAV changes between the date of the distribution and the end of the month. When there are multiple distributions over the holding period, the error is compounded. In the example above, computing CSRSX's 2006 return under the assumption that the distributions were made at the end of the month yields a return of 36.79%, which is reasonably close but not correct.

Computing returns under the assumption that distributions occur at the end of the year results in even greater error. This quick and dirty method yields a return of 36.42% for CSRSX in 2006. 0.7% is pretty significant when compounded over many years. For mutual funds that only make one distribution per year and make the distribution near the end of December, this method will produce a fairly close approximation if the amount of the distribution is small relative to the fund's NAV.

Now you know how annual returns are computed for mutual funds. Reliable sources of published returns will compute returns by this or a very similar method.

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