## How to Calculate Your Portfolio’s Rate of Return

Starting in July 2016, dealers and advisors will be required to provide a personal rate of return to their clients.  Although this disclosure is a step in the right direction, it will likely lead to more confusion and frustration amongst clients and advisors if the results are not properly explained.  There are various ways to calculate a rate of return – and each of them can add to your understanding of how your portfolio is doing.  In my next series of blog posts, I will explain some of the most popular rate of return methodologies, and also provide some easy to use calculators for those investors who prefer to get their hands a little dirty.

To illustrate the impact that a chosen return methodology can have on a portfolio’s reported performance, we will compare two investors who invest \$250,000 on December 31, 2013 into an index fund that tracks the MSCI Canada IMI Index.  We will assume that neither investor pays any product fees, and that the security tracks the index perfectly (Note:  I have used actual index values in my examples in order to make the results more relevant).

After a period of relatively good performance, Investor 1 decides to contribute an additional \$25,000 to their portfolio on September 15, 2014.  Investor 2 decides that they would like to take some profits off the table, and instead withdraws \$25,000 from their portfolio on September 15, 2014.

In the charts below, the month-end market values for 2014 are included for both investors.  The dates and amounts of any contributions (positive external cash flows) and withdrawals (negative external cash flows), have also been included (as well as the new market values after the cash flow occurs).

Throughout the examples, you will need to continually refer back to these charts, so keep them handy as you work through each calculation.

For the next blog post, we will examine the time-weighted rate of return (TWRR).

Chart 1:  Investor 1 – \$25,000 Contribution

 Date Market Value (MV) Cash Flow (CF) MV After Cash Flow December 31, 2013 250,000 January 31, 2014 251,938 February 28, 2014 262,212 March 31, 2014 265,256 April 30, 2014 271,900 May 31, 2014 270,962 June 30, 2014 282,868 July 31, 2014 287,098 August 31, 2014 293,108 September 15, 2014 290,621 + 25,000 315,621 September 30, 2014 304,818 October 31, 2014 297,125 November 30, 2014 299,406 December 31, 2014 298,082

Chart 2:  Investor 2 – \$25,000 Withdrawal

 Date Market Value (MV) Cash Flow (CF) MV After Cash Flow December 31, 2013 250,000 January 31, 2014 251,938 February 28, 2014 262,212 March 31, 2014 265,256 April 30, 2014 271,900 May 31, 2014 270,962 June 30, 2014 282,868 July 31, 2014 287,098 August 31, 2014 293,108 September 15, 2014 290,621 – 25,000 265,621 September 30, 2014 256,530 October 31, 2014 250,055 November 30, 2014 251,975 December 31, 2014 250,860
By | 2017-01-17T15:01:55+00:00 May 18th, 2015|Categories: Rates of Return|6 Comments

1. Daniel S. May 19, 2015 at 6:53 pm - Reply

Hi Justin. Looking forward to your next two postings. Will you be able to show us how to input these numbers in the BA II Plus calculator? it will,be helpful.

• Justin May 19, 2015 at 8:43 pm - Reply

Hi Daniel S. – I’m not planning to specifically look at using the BA II Plus calculator, but I will be walking through how to use my Modified Dietz Rate of Return calculator with monthly geometric linking (approx. time-weighted rate of return) and my Money-Weighted Rate of Return calculator – hopefully you will find that one of these calculators to be useful for your specific purposes.

2. Davie215 May 19, 2015 at 12:36 pm - Reply

Hi Justin,

Another gem in the making. From previous correspondence in providing benchmark data using broad-market ETFs, I used your ROR spreadsheet.

In 2014, we had a large withdrawal from our portfolio to provide cash for a new residence purchase. When I put the values and the date in the spreadsheet, I noticed the monthly ROR was substantially different from the benchmark values, and was puzzled when I moved the withdrawal to the previous month and found that the monthly RORs were much better aligned with the benchmark returns for those monthly periods.

I suspect that it has a lot to do with the time-weighted and money-weighted differences, and anxiously await the next in your series to help explain what may have happened in the spreadsheet calculations.

This is really confusing, as you know by offering this series, and when I’m trying to measure my portfolio ROR versus weighted indices I hope to find the best way to compare the RORs.

From Investopedia I have read the definitions and can do the math OK, but the meaning and how best to use it has escaped me.

Thanks as always for your ongoing education efforts!

• Justin May 19, 2015 at 8:48 pm - Reply

@Davie215 – it sounds like your situation may be a case of withdrawing a relatively large lump-sum during a month prior to a period of over or under-performance (for example, the first 15 days of the month returned -5%, but the last 15 days of the month returned +10%). The future posts should help to clarify those situations (unfortunately, the best way to avoid this issue is by using a true time-weighted rate of return, which requires daily portfolio valuation).

3. Hyacinthe May 18, 2015 at 12:21 pm - Reply

Very interesting, Justin. I can’t wait to read the next posts. 🙂 Thanks!

• Justin May 18, 2015 at 12:24 pm - Reply

@Hyacinthe – hopefully you will find the posts useful. Dan and I are currently working on a rate of return white paper, but I’ve been receiving a lot of questions about calculating rates of return, so the posts should help explain the main concepts in the meantime.