In my recent blog post, I explained that the Modified Dietz rate of return gives a decent estimate of the money-weighted rate of return (MWRR). However, both types of returns are not ideal choices for investors who are interested in benchmarking their performance against appropriate indices.

Some investment firms mitigate this issue by approximating a time-weighted rate of return for their clients. This can be accomplished by calculating the Modified Dietz rate of return over monthly time periods, and then geometrically linking the results (going forward, I will refer to this methodology as the “approximate time-weighted rate of return”). This requires month-end portfolio values, but avoids having to value the portfolio whenever an external cash flow occurs (which is required when calculating the time-weighted rate of return).

The approximate time-weighted rate of return (ATWRR) can differ substantially from the time-weighted rate of return (TWRR) when large cash flows occur during months of significantly fluctuating portfolio values. This makes the ATWRR less ideal for benchmarking portfolio managers or strategies than the TWRR (but generally does a better job than the MWRR or the Modified Dietz rate of return). For example:

- When a large
*contribution*is made prior to a sub-period month of relatively good (bad) performance, the ATWRR will overstate (understate) a portfolio’s performance, relative to the TWRR. - When a large
*withdrawal*is made prior to a sub-period month of relatively good (bad) performance, the ATWRR will understate (overstate) a portfolio’s performance, relative to the TWRR.

To make the ATWRR calculation easier for investors, I’ve created a user-friendly Modified Dietz annual rate of return calculator (with geometric linking of the monthly returns), available for free download on the Canadian Portfolio Manager Blog. Simply input the month-end portfolio values for the year in column E, and any contributions (+), withdrawals (-), and the day of the month that each cash flow took place in the columns to the right of column E (the calculator allows for up to five cash flows per month). I’ve included the calculator screen snapshots below for both investors, based on values from our original example.

**Approximate Time-Weighted Rate of Return: Investor 1 **

###### *Source: Canadian Portfolio Manager blog*

**Approximate Time-Weighted Rate of Return: Investor 2**

*Source: Canadian Portfolio Manager Blog*

In order to help us better understand the differences between the ATWRR and the TWRR, we must first calculate the sub-period returns during the months when any external cash flows occurred (using the TWRR methodology). In our example, the only cash flows that occurred were during the month of September.

**Example: Time-Weighted Rate of Return for the Month of September – Investor 1**

**Example: Time-Weighted Rate of Return for the Month of September – Investor 2**

For both investors, their sub-period rate of return before the cash flow occurred was **-0.85%**. After the cash flow occurred, the portfolio returned **-3.42%** for the remainder of the month (a relatively worse return than the first half of September). Over the entire month of September, the portfolio returned **-4.24%**.

Investor 1 had a relatively worse ATWRR in September of **-4.35%** (when compared to the TWRR of -4.24%). This was because Investor 1 contributed $25,000 before a monthly sub-period of relatively bad performance (-3.42% versus -0.85%). They also had a lower ATWRR of **9.67%** during the 2014 calendar year, when compared to the TWRR of 9.79%.

Investor 2 had a relatively better ATWRR in September of **-4.13%** (when compared to the TWRR of -4.24%). This was because Investor 2 withdrew $25,000 before a monthly sub-period of relatively bad performance (-3.42% versus -0.85%). They also had a higher ATWRR of **9.92%** during the 2014 calendar year, when compared to the TWRR of 9.79%.

Although the ATWRR can differ from the TWRR when large external cash flows are made during a volatile month, it is still a decent choice for investors who are looking for an approximate method of calculating a rate of return that can arguably be benchmarked against index returns. As most investors will not be provided with a TWRR on their account statements going forward (and collecting daily portfolio valuations when external cash flows occur is not realistic), the approximate time-weighted rate of return would be my recommended choice for investors who are interested in benchmarking their portfolio returns.

*Performance Results*

Methodology |
Investor 1 |
Investor 2 |

Time-Weighted Rate of Return (TWRR) | 9.79% | 9.79% |

Money-Weighted Rate of Return (MWRR) | 8.98% | 10.64% |

Modified Dietz Rate of Return (ModDietz) | 8.97% | 10.66% |

Approximate Time-Weighted Rate of Return (ATWRR) | 9.67% | 9.92% |

Justin – this is off topic for this post, but I didn’t see a place to comment on your model portfolios.

I’m wondering — why do you use ETFs of a single provider for all your portfolios? For example, all BMO funds, or all Vanguard, etc. Is there a reason? Does it leave investors with too much exposure to one asset manager?

Thanks…

@JW – great question! I posted 3 plain-vanilla ETF providers to make a point – it doesn’t really matter which provider you choose (or if you mix and match providers). I currently use a mix of VAB/VCN/VUN/XEF/XEC for taxable accounts, but an investor would not be making a terrible choice by using a different combination of the suggested ETFs.

Thanks. And in your opinion, is there any risk to a whole portfolio being with one asset manager?

@JW – there is always risk in any investment. If you feel more comfortable diversifying across asset managers, feel free to do so (the asset class returns will likely be similar).

I am a self-managed superannuation fund investor in Australia. I am very interested in your “user-friendly Modified Dietz annual rate of return calculator (with geometric linking of the monthly returns)” but in Oz we work on financial years (July to June) rather than calendar years. I hesitate to ask, but are you able to provide calculators for FY 14-15 and FY 15-16?

Hi DGT – I’ve sent you an email with updated calculators – please let me know if these work for you.

Hi Justin,

You mentioned above you use an ETF mix for your taxable accounts. Is there a reason you wouldn’t use them for non-taxable accounts, that a noob investor like me wouldn’t know about? I currently have your previously published Vanguard ETF portfolio for my TFSA (VAB, VCN, VUN, VDU, VEE) and contribute to this portfolio bi-weekly through a commission free discount broker (Commision free to purchase ETF’s). Where I contribute money to my portfolio a couple times a month, which rate of return calculation do you think would be my best bet? I have been keeping track of my contributions to each ETF. If I’m understanding all the options correctly, the Modified Dietz? As a side note, thanks for the time you put into this site, it is much appreciated by new DIY investors like me.

@Nic – I tend to use the Canadian-domiciled ETFs for taxable accounts and TFSAs, and US-listed ETFs for tax-deferred accounts (i.e. RRSPs/RRIFs/Locked-in-Accounts). The reason for this is to reduce the impact of foreign withholding taxes in tax-deferred accounts: https://www.pwlcapital.com/pwl/media/pwl-media/PDF-files/Justin%20Bender%20Assets/PWL_Bender-Bortolotti_Foreign-Withholding-Taxes_v04_hyperlinked.pdf?ext=.pdf

The calculation method will depend on your objective. If you’re interested in benchmarking your portfolio returns to index returns, you should use the Modified Dietz Method. If you’re just interested in how you’re doing personally, the Money-Weighted Rate of Return should be sufficient.

So if I used a separate copy of the spreadsheet you’ve created to find out the returns for 3 separate years, how would I find out the annualized return of those three years? I’m assuming a simple average would be the wrong choice here, but a little rusty on more complicated math so I’m at a bit of a loss here. Any help?

@James – I’ve written about the procedure here: http://www.canadianportfoliomanagerblog.com/how-to-calculate-your-average-annual-rate-of-return/

Thanks for the quick reply Justin!

Hi Justin,

Avid read of both you and Dan. I use the e-series for my investing but I wanted to calculate my return to see how it compares with the one that webbroker spits out. I began investing in Feb 2016 from $0. Since then I’ve transferred cash into the account and bought e-series funds as per the aggressive portfolio 90/10.

Anyways, TD says my YTD rate of return has been somewhere around 7.6%, but your spreadsheet has my YTD at -70%, along with wild swings in the monthly categories (from +947% to -98%). I’m sure I’m doing something wrong, but not sure what.

In column E I put the starting balance of each month (ie in Feb it was $0), and in Cash flow 1 I put $460 on day 29. Then in March column E I put $460, and add my cash flows for March in. March was the first month I bought funds, and so in Apr my starting balance was a market value of $703 (an additional $240 of contribution, with a few bucks worth of growth). The spreadsheet tells me my return in March was an astounding 947%.

Any suggestions on what I’m doing wrong here?

Thanks!

@Arsalan: Would you please provide me with a copy of the spreadsheet: jbender@pwlcapital.com

Sometimes there are issues with the calculation if you start the portfolio part-way through a month. It may be better to simply start the performance calculation in the first full month (March 2016).

I’ve also heard of people using the Compound Annual Growth Rate (CAGR) as an accurate method for calculating portfolio growth rate over multiple years. Thoughts?

@skube: The CAGR is just a way of annualizing (i.e. averaging) a total return that is longer than a year. You still need a rate of return methodology (like the true time-weighted, money-weighted or Modified Dietz method) to calculate your total return (taking into account contributions and withdrawals): http://www.canadianportfoliomanagerblog.com/how-to-calculate-your-average-annual-rate-of-return/

Just so I’m clear, you’re referring to ATWRR and _Monthly_ ModDietz as the same thing by different names?

@skube: You got it!