# How contributions affect your rate of return

## Try using this handy time-weighted return calculator

Whenever I update the returns of my model portfolios, readers ask how the performance would have been different had they added money to the portfolios money each month. This question gets to the heart of the difference between time-weighted and money-weighted returns, which I introduced in my previous post.

In our new white paper, Understanding Your Portfolio’s Rate of Return, Justin Bender and I explain the differences between these two methods using two hypothetical investors with a \$250,000 portfolio: the first makes a single \$25,000 contribution while the other makes a \$25,000 withdrawal. Now let’s look at a different example that includes monthly cash flows.

### A tale of two accounts

Meet Buster, an investor with an RRSP and a TFSA that both hold an index fund of Canadian stocks (I’ve used the MSCI Canada Investable Market Index for the calculations). At the beginning of 2014, Buster’s RRSP had a balance of \$200,000 and he made \$500 monthly contributions throughout the year. Buster’s TFSA has valued at \$30,000 at the beginning of the year and he made a single lump-sum contribution of \$10,000 in September.

At the end of the year, Buster decides to calculate the money-weighted rate of return (MWRR) for his two accounts and compare his results to the index benchmark. His first step is to check the MSCI website, where he learns that the return on the index for the year was 9.79%:

Then Buster calculates the annual return on his RRSP using Justin Bender’s Money-Weighted Rate of Return Calculator. He simply enters the starting value of the portfolio (\$200,000), the ending value from his December 2014 account statement (\$225,680.80), and the date and amount of each contribution he made during the year:

He then does the same for his TFSA: now Buster uses a starting value of \$30,000 and a final value of \$42,380.79, and then he enters the date and amount of his one lump-sum contribution:

When the results are in, Buster is shocked to find that his RRSP performed very similarly to the index (it lagged by just 0.09%), but his TFSA appeared to underperform by more than 2.5%. Since both accounts have identical holdings, shouldn’t the returns have been the same?

Not necessarily. Had Buster measured his performance using a time-weighted rate of return (TWRR), the figures for his TFSA and RRSP would have been identical, and they would have matched the returns of the MSCI index. But because Buster used a money-weighted method, he got different results for the two accounts. Now he wants to know why.

The culprit turns out to be the size and the timing of the contributions he made to his two accounts. While a TWRR (the method used by ETFs, mutual funds and index benchmarks) is not affected by cash flows, contributions and withdrawals will affect an investor’s MWRR. The degree of influence depends on two factors:

The size of the cash flows in relation to the overall portfolio. In Buster’s RRSP, each \$500 contribution represented only about 0.25% of his account. These relatively small cash flows will have little effect on the portfolio’s MWRR. But Buster’s lump-sum TFSA contribution was about 33% of the account’s starting value, so it had a significant impact. That’s why the return on his TFSA was so far off the index benchmark.

The timing of the cash flows. Buster’s TFSA contribution in September wasn’t just large, it also came at a bad time: just before a sharp downturn in the Canadian equity market. That unlucky timing had a negative effect on his MWRR. Had the markets moved sharply upward after his contribution, he would have seen a much higher MWRR. Meanwhile, his smaller RRSP contributions were spread over 12 months, which reduced the effect of timing.

### A more useful method

This example reveals why a money-weighted rate of return can be highly misleading, especially if you’re comparing your portfolio’s rate of return to an index. The size and timing of your contributions and withdrawals can make it seem like you are outperforming or lagging the benchmark.

If you have made one or more very large contributions during the year, a time-weighted rate of return is likely to be more useful. Justin’s popular Rate of Return Calculator uses the Modified Dietz method to calculate an approximate TWRR by using month-end values. When we use this calculator with Buster’s TFSA, his rate of return is much closer to that of the index benchmark because the influence of the single ill-timed contribution is reduced and his rate of return is much closer to the index benchmark:

Let’s return to the question I referred to at the top: “How would the performance of the model portfolios have been different if an investor added money each month?” Because the model portfolio performance is reported using TWRRs, the answer is that monthly contributions would make no difference at all.

It would be possible to run the model portfolio performance numbers again using a MWRR, but you would need to assign an arbitrary starting value and an arbitrary amount for each contribution. The results would be meaningless for any investor whose situation was not exactly the same as those assumptions—which would be everyone.

For DIY investors interested in measuring their own portfolios against the models, an approximate time-weighted return using Justin’s calculator is likely to be the most useful method.

1. I think people should be told how to calculate their own time-weighted return (the mutual fund method). Using the example above work with the per-unit values assuming you start with an arbitrary 1,000 units. This is the same way mutual funds add/subtract #units when funds are added/withdrawn.

Starting portfolio = \$30,000 with 1,000 units each valued at \$30/unit.

Just before the contribution is made the portfolio = \$34,356 or \$34.356/unit.
Adding \$10,000 is the same as a mutual fund creating 291.07 more units (10,000 / 34.356).

Ending portfolio = \$42,380.79 with 1,291 units or \$32,826 /unit

The rate of return was ending/beginning less 1 using per-unit values.
32,83 / 30.00 -1 = 9.4%