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.

I found your post and the white paper extremely helpful. However, I assume its not possible to calculate a mutual fund using one of the three methods, is it?

@Joel: Mutual funds calculate and report their own returns using the time-weighted method. If your portfolio holds one or more mutual funds you can use any of these methods to calculate your personal rate of return.

I don’t understand how to calculate the TWRR in a portfolio with more one two security.

Let’s say I have $100 in Stock1 and $100 in Stock2 at the beginning of the month.

I buy $50 more of Stock1 on the 15th of the month at 1PM.

In theory to calculate a 100% accurate TWRR I need to know exactly how much my full portfolio was worth exactly on the 15th of the month at 1PM tso that I will be able to calculate the ROR of period 1 and the ROR of period 2 accurately. And that’s pretty hard to know with historical data having only hi low open close.

Am i missing something here?

@BG: You’ve identified the problem with TWRR for the average investor. You would need to know the portfolio’s value on the day of the cash flow (though not the exact hour!) and this is often difficult or impossible if you receive only monthly statements. This is discussed in the white paper.