Calculating your portfolio’s rate of return

It’s not as straightforward as you might think

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Perhaps no number is more important to investors than the rate of return on their portfolio. Yet this seemingly simple calculation is fraught with problems. If you’ve made contributions or withdrawals during the year, calculating your rate of return is not straightforward. What’s more, there are several ways to perform the calculations: the results can differ significantly, and each method has strengths and weaknesses. No wonder so many investors have no idea how to measure or interpret their returns.

In our new white paper, Understanding Your Portfolio’s Rate of Return, Justin Bender and I introduce the various methods used to calculate a portfolio’s rate of return, explain how and why they can produce different results, and help you determine which method is most appropriate to your circumstances. Justin has also updated his popular calculators, which you can download for free on the new Calculators section of the PWL Capital website.

Time and money

Rate of return calculations fall into two general categories: time-weighted and money-weighted. If a portfolio has no cash flows (that is, the investor makes no contributions and no withdrawals), both methods produce identical figures. The key point to understand, therefore, is that any differences in reported returns come about as a result of cash inflows and outflows.

To illustrate this idea, our white paper looks at each methodology as it would apply to two hypothetical investors. We assume both have a portfolio of Canadian equities valued at $250,000 at the beginning of 2014. Investor 1 contributes an additional $25,000 on September 15, while Investor 2 withdraws $25,000 on the same date.

Our examples use actual index values to make the results more relevant. Recall that in 2014 the Canadian equity markets enjoyed strong returns during the first eight months of the year, but then experienced a significant downturn in September and October. If you made a contribution or withdrawal around the time of that downturn, how would it have affected your rate of return?

We’ve got nothing but time

A time-weighted rate of return (TWRR) attempts to eliminate the effect of cash flows into or out of the portfolio. It’s the method used by mutual funds and ETFs when preparing their published performance reports, as well as the method used for measuring the performance of my model portfolios.

In our example above, both investors would have had exactly the same TWRR, even though Investor 1 made a large contribution right before a downturn, while Investor 2 made a large withdrawal. Both investors’ time-weighted returns were also identical to that of the index their portfolios were tracking.

When a TWRR is appropriate: A true time-weighted return is ideal for measuring the performance of portfolio managers against a benchmark.

Consider an advisor working with our two hypothetical clients. Investor 1 receives a $25,000 windfall and asks the advisor to add it to his portfolio. On the same day, Investor 2 requests a $25,000 withdrawal to meet an unexpected expense. Since the portfolio manager used the same strategy for both investors, he should not be rewarded or penalized for the effect of cash flows over which he had no control.

Shortcomings of the TWRR: TWRRs are generally impossible for individual investors to calculate on their own. You’d need to know the value of your portfolio on each day a cash flow occurred, but discount brokerages typically don’t make this information available.

Many people also feel TWRRs are irrelevant to individual investors, because the timing of cash flows can have a big effect on how we perceive performance. Justin offers a dramatic example of how an investor who made a large contribution just before the financial crisis of 2008–09 could have had a TWRR over 4% even though his portfolio actually lost value.

How to measure your own TWRR: While you can’t measure your true TWRR without advanced tools, the Modified Dietz method can calculate an approximate time-weighted return if you have access to month-end values for your portfolio. Use the Rate of Return Calculator available on the PWL Capital website.

Show me the money

A money-weighted rate of return (MWRR) does not attempt to eliminate the effect of contributions and withdrawals: on the contrary, it specifically adjusts for them. For this reason it can differ substantially from the time-weighted rate of return when large cash flows occur during volatile periods.

In our example, the MWRR for Investor 1 would be significantly lower than the time-weighted rate of return because he made a large contribution prior to a period of relatively poor performance. Meanwhile, while the MWRR for Investor 2 would be significantly higher, because she made a large withdrawal prior to that downturn.

When a MWRR is appropriate: If you add or withdraw funds from your portfolio right before a big move in the markets an MWRR better reflects your personal investment experience. The Canadian Securities Administrators seem to agree: beginning in July 2016 they will require investment advisors to produce money-weighted rates of return for their clients.

Shortcomings of the MWRR: Because it is highly dependent on the timing of cash flows, the MWRR is not ideal for benchmarking portfolio managers or investment strategies. A lump-sum RRSP contribution or RRIF withdrawal, for example, can cause the portfolio’s MWRR to outperform or underperform its benchmark, which is highly misleading.

A traditional money-weighted rate of return is also calculated using an equation that can only be solved through trial and error. However, computers have made this shortcoming less important.

How to measure your own MWRR: As long as you have the starting and ending values of the portfolio and the dates of all the cash flows you can use the Money-Weighted Rate of Return Calculator available on the PWL Capital website.

In my next blog post, I’ll use other examples to help investors better understand the important differences between time-weighted and money-weighted rates of return.

This article originally appeared on canadiancouchpotato.com.

2 comments on “Calculating your portfolio’s rate of return

  1. Although a lot of that material could have been inspired by my webpage at http://www.retailinvestor.org/tracking.html there is also a lot I disagree with.

    My site’s examples also show how the IRR (Internal Rate of Return = what these authors call MoneyWeighted RofR) can create misleading numbers. But this article does not state the implicit assumption of the model that causes its results to be irrelevant. It presumes that while any cash inflows/outflows are NOT in the investment being measured, they are earning the same RofR as while IN the investment.

    That presumption does not reflect the reality of young investors adding savings from each paycheque, or retirees withdrawing cash to pay living expenses. It is the wrong metric for us. Yes it ‘considers’ cash flows, but its result does not produce a meaningful measure of your personal performance by any stretch of the imagination.

    The fact the IRR will soon be the required metric all brokers must report does NOT validate it. It just shows that the broker industry is self-serving. Since IRR needs only the data the brokers already keep on file, reporting IRR will not cost them nothing. In contrast, reporting with the Time Weighted method would require them to keep track of additional data. So OF COURSE they chose IRR.

    The author’s claim that TimeWeighter RofR (like mutual funds use to report performance) cannot be measured by us is false. All discount brokers have displays showing the portfolio’s current market values. True they don’t store that information, but when you add/remove cash you are on the site anyways so you just record the info at the time. My website includes an example that shows how the ‘per-unit’ values are tracked and adds/draws create/reduce units. My spreadsheet for tracking a portfolio’s performance has it automated. http://www.retailinvestor.org/Portfolio.xls

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  2. All your articles talk about contributions and withdrawals. These are of course real issues. But about the returns of a portfolio where there is no withdrawal and contribution but buying and selling and stocks with different weights. How to treat the profit/loss and sales proceeds?

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