Perhaps you've encountered a situation like this: A client loses money in his account but the performance report he receives shows a positive return.

The client is understandably perplexed by this and requests an explanation. After kicking around various ways to describe why this happens, you settle on a one-liner that you hope will satisfy the client's curiosity: “Our returns are time-weighted, and they occasionally generate some crazy numbers.”

Unfortunately, the truth is more complex than that, and helping clients to understand this is one of the great challenges facing financial advisors.

In fact, on an account statement like the one referenced above, the returns the client is seeing probably are accurate — even if they don't make a lot of sense from the client's perspective. The key is to understand what time-weighted numbers represent and perhaps to consider an alternative: dollar-weighted returns.

Definition Time

Let's begin with a brief explanation of terms. Time-weighted returns are appropriate for reflecting the performance of a money manager because they eliminate the affect of cash flows. This is done because the manager does not usually have any control over the cash flows.

Dollar-weighted returns, on the other hand, are affected by cash flows. If the client adds money at the right time, he might realize a greater gain than would be reflected by the time-weighted return; alternatively, if the client's timing is off, he may actually lose money while the fund shows a gain.

Take this example in which two investors each make three purchases in the same mutual fund over the course of a year (the accompanying figure shows the end-of-month net asset values [NAVs] for the fund during the year).

Both investors begin by buying 100 shares at the end of the year's NAV ($10), so they each start off with an initial investment of $1,000.

Investor No. 1 makes two subsequent purchases of 100 shares each, one at the end of May (with an NAV of $14) and the other at the end of August (NAV of $15). The second investor also makes two additional purchases of 100 shares each, but hers are at the end of April (NAV of $8) and September (NAV of $9). We can see that the fund's NAV closes the year at $11, meaning the fund is up by 10 percent (an NAV of $11 at the end of the year vs. $10 at the start). While our second investor benefits from buying low and selling high, the same cannot be said for Investor No. 1, who made purchases at the peaks of the NAV during the year. Consequently, the first investor shows an unrealized loss of $600, while the second shows a gain.

What it Means

In time-weighted terms, the fund manager, as well as the two investors, will each show a return of 10 percent. While our second investor might accept being told that the fund is up 10 percent, the first might question this, since he suffered a loss.

Here is how the advisor can put the concept of the dollar-weighted return to use, using internal rate of return (IRR). If we calculate the IRR for our first investor, we find that his portfolio lost 24.86 percent, while our second investor's IRR is up 35.16 percent! Quite a difference.

Some refer to the IRR in this situation as the “personal rate of return.” It provides the investor with the return on his or her portfolio, as opposed to the manager's return (i.e., the time-weighted return).

The first time I encountered the problem of explaining time-weighted returns to clients was in early 1988, following the “market adjustment” the prior October. Many of our clients continued to add to their portfolios during the year, expecting the market to continue to go up and up, but that October, the market took a significant dip. Although the returns we reported were not very large (e.g., 1.1 percent), we got calls from some clients who had lost money and could not understand how we could report a positive return.

Problems like this frequently crop up when the market is volatile and when the timing of client contributions (or their withdrawals) is such that they suffer a loss.

Time-weighted returns have their place. They are the industry standard for rating investment managers — and for good reason. They provide an accurate measurement of how those managers are doing their jobs.

But when it comes to explaining returns to clients, dollar-weighted processes, including the IRR calculations, are the way to go. Thankfully, more and more firms are awakening to this fact. And, for those nondiscretionary clients who make their own investment decisions, the IRR is a better measure since the client controls both the flows and the investment decisions.

Contributions and Profits/Losses of Each Investor.
Investor No. 1 Investor No. 2
Initial Investment $1,000 $1,000
April Purchase $0 $800
May Purchase $1,400 $0
August Purchase $1,500 $0
September Purchase $0 $900
Total Contributions $3,900 $2,700
Year-end Market Value $3,300 $3,300
Profit/Loss -$600 $600
Time-Weighted ROR 10% 10%