The brain-bending world of money-weighted returns

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A new performance measurement is beginning to appear on brokerage statements in Canada. It's called a money-weighted return and it has the potential to cause a great deal of confusion.

Until recently, investors were presented with time-weighted returns when looking at the performance of mutual funds, indexes and other investments. These returns assume an initial amount of money is put into an investment and then it is held (with dividends or interest payments reinvested) for the period in question.

Money-weighted returns are more complicated because they account for changes in both the value of the investment and for any purchases or withdrawals that are made during the period. As a result, it is a measure of how a particular portfolio has fared in practice.

Interpreting the difference between money-weighted and time-weighted returns can be tricky. The difference is often thought of as being an indicator of an investor's ability to time the market.

While it's true that investors who buy high during bubbles and sell low during crashes suffer from low money-weighted returns relative to their time-weighted returns, more consistent investors can also be afflicted by a similar divergence.

Practically speaking, most of us start with small portfolios that grow over the years as we save money. The portfolios then shrink as we take money out in retirement. Rather than buying in booms and selling in busts, we put money into, and take money out of, our portfolios in a fairly regular fashion. Nonetheless, this sort of steady approach can result in relatively poor money-weighted returns in some periods.

Consider the case where a steady Eddie adds $1,000 to a fund at the start of each year, which grows 10 per cent in the first year and falls 4 per cent in the second. His average annual time-weighted return for the period would be 2.76 per cent. But his annual money-weighted return would be 0.53 per cent because he put more money into the fund just before it fell in the second year.

It is unfair to say that Eddie has a behavioural problem. After all, he was following a rational approach of adding money to his portfolio each year when he earned it. His timing might be better described as being unlucky rather than unskillful.

If we were to reverse the sequence of returns (minus 4 per cent in year one followed by plus 10 per cent in year two) the time-weighted return would remain unchanged but the money-weighted return would climb to 5.11 per cent. The better result should again be attributed more to luck than to skill.

Complicating matters, it is unwise to compare a portfolio's money-weighted return to a benchmark's time-weighted return despite the natural temptation to do so.

To see why, it's useful to compare Eddie's results to a benchmark index. The index happened to climb 10 per cent in the first year and then fall 5 per cent in the second.

Due to the relatively poor showing in the second year, the index was an inferior investment over the period. It's something that's reflected in its annual time-weighted return of 2.23 per cent, which is lower than the 2.76-per-cent time-weighted return of the fund portfolio.

If Eddie were to compare his annual money-weighted return of 0.53 per cent to the index's time-weighted return of 2.23 per cent, he might be unhappy with his result.

But his cheer would return when he calculates the index's money-weighted return. If he had invested $1,000 at the start of each year in the index instead of the fund, he would have earned an annual money-weighted return of minus 0.17 per cent.

As a result, one shouldn't mix the two types of returns when comparing investments. In most cases, investors should stick to time-weighted returns when sizing up their options.

Unfortunately, I suspect the well-intentioned move to add money-weighted returns to brokerage statements will lead to more confusion than clarity for many investors.

Norman Rothery is the value investor for Strategy Lab. Globe Unlimited subscribers can read more in the series at tgam.ca/strategy-lab.