One of my favourite tales of investment stupidity is the story of the Beardstown Ladies. This group of grannies from a tiny Illinois town became famous in the 1990s when their investment club reported annualized returns of more than 23% for a decade. These Buffetts in bonnets wrote five books about their stock-picking acumen, which sold hundreds of thousands of copies, and they toured the US, celebrated as folksy, common-sense geniuses. Then someone checked their numbers.

It turned out that when the ladies calculated their returns, they included new money they had added during the year. Their actual investment returns over the decade were 9.1% annually, compared with almost 15% for the S&P 500. If you happen to find a Beardstown Ladies guide in a used bookstore one day, grab it: they’re collectors’ items now.

As the year-end approaches, you’ll likely want to know how well your own portfolio has done during the last 12 months. If you didn’t add or withdraw any money during the year, calculating your return is easy. Let’s say your portfolio’s value was $50,000 last December 31, and at the end of this year it has grown to $60,000. You can figure out the rate of the return with this simple formula: ($60,000 – $50,000) / $50,000 × 100 = 20%.

But as the Beardstown Ladies discovered — unfortunately, it was only after they appeared on *Donahue* — this formula doesn’t work if your account has experienced cash flows, either in or out. What if the above portfolio started the year at $50,000 and you contributed another $500 on the 15th of each month? Your balance has increased by $10,000, but $6,000 was new money and only $4,000 came from investment growth. Now what is your rate of return for the year? Not so simple anymore.

### You don’t have to do the math

Most annual statements from brokerages, mutual fund companies, and financial advisors do not include your personal rate of return, also called the internal rate of return, or the dollar-weighted return. So you’re probably on your own when it comes to figuring it out.

There are several formulas for calculating a portfolio’s return when money has moved in and out during the year. Most use that squiggly line that looks like a sideways W, and I’m pretty sure one of them includes the emblem of the Green Lantern. You are welcome to use these.

Fortunately for people like me, Weigh House Investor Services in Toronto created this handy online calculator that will do the math for you. All you need to do is enter the value of your portfolio at the start of the year, the value at the end of the year, and the dates and amounts of any contributions or withdrawals.

I used the calculator to figure out the rate of return in my own RRSP, taking into account three lump-sum contributions I made during the year. (My ETF retirement portfolio is 30% bonds and 70% equities, spread across Canada, the US, and international developed and emerging markets.) How did I do? Just over 10% for the year. That means I accomplished my investment goal: beating the 10-year performance of the Beardstown Ladies.

“Buffets in bonnets,” that’s a good one.

Speaking of math accuracy, what is the math behind how that calculator works?!

I use IRR to calculate my portfolio’s performance. I use the XIRR function in excel which works great.

Oh c’mon…they were just a bunch of senile old ladies. Be nice.

Looks like a useful calculator.

Have a great holidays Dan!

Mike

We practically need a GAAP formula for rate of returns I have had questions on whether my performance numbers included inflation or not and it gets crazy to compare with all the different ways that one does the math … I am fortunate to not have many withdrawals in my accounts so it’s not that complicated form that perspective. On the other hand, I have lots of dividends that are re-purchased and I make sure that I differentiate dividends re-invested from initial capital invested. Not all tracking software can easily make that distinction.

Cheers! Happy Holidays.

The calculator answers the following question: if I had made my transactions in a daily compounding bank account instead of the market, what yearly interest rate would I have earned?

Say that you start with $1000 on January 1, add $500 on July 1, and end up with $2000 on December 31. What you want to know is your yearly interest rate X%. Your daily interest is Y% = (x/365) (not quite, but for clarity assume that it would be). You’ll have the following calculations:

January 1 = $1000

January 2 = $1000 * (1 + Y%) (add the daily interest)

January 3 = $1000 * (1 + Y%) * (1 + Y%) (add the compounded daily interest)

…

July 1 = $1000 * (1 + Y%) ^ 183 (that’s 1+y% to the power of 182 — half a year).

Now you add $500, so the Value on July 1 is:

July 1 = $1000 * (1 + Y%) ^ 183 + $500

July 2 = ($1000 * (1 + Y%) ^ 183 + $500) * (1 + Y%) (add the compounded interest)

July 3 = ($1000 * (1 + Y%) ^ 183 + $500) * (1 + Y%) * (1 + Y%) (continue)

…

December 31 = ($1000 * (1 + Y%) ^ 183 + $500) * (1 + Y%) ^ 182.

Now, we know that the end value is $2000, so we just need to determine Y in the following:

$2000 = ($1000 * (1 + Y%) ^ 183 + $500) * (1 + Y%) ^ 182

Wolfram Alpha (amazing tool says that Y is approximately 0.093625%.

From that we can easily determine X (because Y = X/365). So X = 34.17%.

Great, we’re done. (If you check the math with the web page you’ll get 39.3%, but that’s because Y isn’t quite X/365 — but close enough for this explanation.).

Obviously, that’s quite a complicated equation. But we’ve performed only one transaction! You could continue to do the math, but I doubt it would be very easy to compute the answer by direct means. What the calculator page does is guess at the right value, calculate the end result as I did above, and then narrow down the guess based upon the result. If the result is within $0.01, close enough. If not, try again and keep going until a value close enough is found or something goes wrong (e.g., too many guesses required because the series isn’t converging).

The calculator is not able to deal with a bunch of scenarios, but will generate a fairly good answer for most purposes.

Hope that answers your question.

RBC Direct Investment website shows the portfolio performance which I assume uses IRR. They do include this on statements as well.

Yes, Excel’s XIRR function would be an easy way to calculate a similar answer (though not exactly the same because a different algorithm & approximation is used.). If you want to do this, set up a date and a value column. The first row should contain the portfolio start amount (entered as negative). The following rows should contain the additions (positive) and withdrawals (negative). The final row should contain the ending value of the portfolio. =XIRR(values column, dates column) gives the answer.

As The Passive Income Earner says, comparing returns is an issue.

Yeah!!!! Thanks so much! I’ve been looking around for an easy rate of return calculator for a while now. You are swell!

Hi Dan,

This article is interesting, I am always adding extra cash into my TFSA and RRSP with every paycheque. So without having to go into complex algorithms that only an accounting guru could use, what is the solution ?

Maybe I completely missed the point, but if you add funds doesn’t that just become part of your ACB (Adjusted Cost Base) and cash holdings ? And the market value of the entire portfolio becomes your Proceeds of Disposition if you were to sell at that point ? If anything my portoflio goes down when I add funds, becuase it increases my ACB.

Thanks ! and best X-Mas wishes for you and your family

Chris,

Your calculation regarding “Say that you start with $1000 on January 1, add $500 on July 1, and end up with $2000 on December 31.”

You give your result of daily interest Y = 0.093625% and subsequent simple yearly interest X = 34.17%

The form to convert from daily rates to yearly rates is (1+Y/100)**365 = (1+X/100) so your result gives X = 40.72%, closer to the web page result of 39.3%

My calculation for the IRR for your stated problem (-1000, -500, 2000) with half year intervals is an yearly IRR of 40.69% – this is very close to your calculated result.

This is understandable since your calculation is an exact IRR calculation and is equivalent to the other definition of IRR, namely setting the net present value NPV equal to zero.

You have given an excellent demonstration of IRR.

Just a clarification for the less mathematically inclined: the calculator I linked to in the post will provide only an approximate internal rate of return. An exact calculation is impossible without knowing the path of returns. The calculator assumes that the investment returns were achieved consistently and gradually, as with a savings account. It can’t account for a situation like 2010, where the equity markets returned almost nothing for the first six months, then went up like gangbusters over the final six months. But it’s the best most of us can do.

Canadian Couch Potato

You say: “An exact calculation is impossible without knowing the path of returns.”

IRR is path independant.

IRR only depends on the cash flow and not on the actual balances during the project, so it only depends upon the initial value, the final value and the amounts invested or taken out during the project.

An exact calculation for IRR only requires the cash flow for the project so if equity markets have large variations during the project and do not effect the cash flow then this volatility has no effect on the IRR.

For the example given by Chris, “Say that you start with $1000 on January 1, add $500 on July 1, and end up with $2000 on December 31.”, the balance at any day between the dates of January 1 and December 31 have no effect on the calculation for IRR.

Hi,

Great article, and very well timed!

I use Google Finance to track my simple portfolio of TD e-series funds and I’m curious if anyone knows if the method it uses to calculate “overall performance” is similar to the Weight House calculator. Each time I make my monthly purchase of units I add that transaction to my portfolio recording the date and cost of units. Google shows me an Overall Return percentage for each fund as well as a total for the portfolio.

So far, I’ve assumed the overall return figure is an accurate representation of my true rate of return for the portfolio and the funds therein. Am I making a big mistake?

Thanks so much!

Mike

Using the “handy online calculator” on the problem stated by Chris which was

“Say that you start with $1000 on January 1, add $500 on July 1, and end up with $2000 on December 31.”, Chris said “(If you check the math with the web page you’ll get 39.3%, … “.

For this problem, the answer using the “handy online calculater” is 40.64% not 39.3%.

When solved by Chris, almost by hand calculation and corrected to an annual rate 40.72%.

My calculation for the IRR for the stated problem (-1000, -500, 2000) with half year intervals is an yearly IRR of 40.69%

In summary, the three independant results are 40.64%, 40.72% and 40.69%.

Thanks to Canadian Couch Potato for bringing to our attention the “handy online calculator” which appears to be very accurate on this problem.

Does anyone have another simple test problem so that we can check out the “handy online calculator” against our own favourite calculator.

I found this great tutorial from Morningstar, explains it pretty clearly as well, IF you would like to play around with Excel.

http://news.morningstar.com/classroom2/course.asp?docId=3228&page=1&CN=sample

It matches with the weighhouse.com page when the sample values at the end are entered (except the use of negatives, just use the funds added/funds removed columns, and positive starts and ends). Not sure if it has something to do with Excel, but I was off by about .2%, perhaps some internal rounding errors.

Does anyone know if Google Finance figures all this out for a portfolio? I’m assuming so since my return looks awfully low lol

CC, Thanks for the post. The biggest challenge I had was dealing with cash inflows (Quarterly investments, rebalancing, Dividend purchase plans (DPP , DRIP) and cash outflows (dividends, sales). After some research I have been able to implement an Internal Rate of Return Calculation using Excel’s IRR function. More details on using XIRR and calculating you compounded annual growth rate can be found here:

http://joebcan.blogspot.com/2010/11/check-out-my-latest-photo-book-project.html

There is an app in the Apple app store called Total Return which does an excellent job at handling this task. Just like the Beardstown Ladies, be prepared for a lower number than you were expecting.

Hi Dan,

I have a question for you. If I am not reinvesting my dividends, would I add the the sum of these amounts along with FMV into the “ending balance” when using the weigh house online calculator?

For example: My January 1, 2012 contribution was $1,000, My dividends during the year were $5.00 and the fair market value of my portfolio was $1,125 on December 31. should my “ending balance” be $1,130?

@Jonathan: If you are not withdrawing the dividends from the account, then just include the cash balance when you calculate the portfolio value. If you are spending the dividends, then enter the dates and amounts of the withdrawals.

Thanks!

What a(nother) great article! I have spent the last few hours playing with the Weigh House rate of return calculator. To be honest I’m not sure I trust the results – not for any math reason, I’m just doubting that my portfolio is doing that well.

I transfered half my RRSP’s into the TD e-funds as per the couch potato portfolio, except I did a 25-25-20-30 split between the Cdn, US, Int’l and Bond funds respectively. The money has been invested since June of 2012 and I doubled the investment when I saw how well it was doing in August of this year. According to the Weigh House calculator I am averaging a 35.18% annual return. Does this seem feasible? When I do a simple (ending balance – beginning balance)/beginning balance calculation I get 27%. Being as I challenged my financial advisor to a “contest” I’d love to tell him this number as I pull the balance of my funds out of his accounts (to heck with the back-load fees!) but of course I need to make sure the calculations are correct. Is there another calculator you are aware of that I can compare results?

Wow! If I had only played for 5 more minutes before sending the previous comment I would have realized I overlooked a $10,000 deposit made in February. Doh! So now I’m getting a more realistic but still VERY nice 19.36%.

I probably should have mentioned I only included deposits I made and didn’t include re-invested dividends. I think those are included in the book value posted by the bank in my account.

@Jacqui: For an Excel spreadsheet that allows you to save your results, visit the PWL Capital website, click Rate of Return Calculator on the right and enter your email address to get a copy of the spreadsheet and instructions:

https://www.pwlcapital.com