Starting in July 2016, dealers and portfolio advisors will be required to report investment performance to their clients. The money-weighted rate of return (MWRR) was chosen by the Canadian Securities Administrators (CSA) as the industry standard for these performance calculations. Although the MWRR is arguably more relevant to the individual investor (as it can reward or penalize investors for the timing of their cash flows), it is considered by most advisors to be inadequate for benchmarking purposes. This is because the timing of the investor’s cash flows (which most advisors have little to no control over) can cause the performance to be over or understated, relative to the time-weighted rate of return (TWRR).

The money-weighted rate of return can be thought of as the rate of return,** r**, which equates the right hand side of the following equation to the ending portfolio value, V_{1}.

*Source: CFA Institute*

This method can be useful for calculating the rate of return when there have been only small external cash flows during the measurement period, relative to the size of the portfolio. It may also be the only available option for investors who do not have access to daily or month-end portfolio values (I often come across investors who receive quarterly statements, as opposed to monthly).

As the MWRR assumes all cash flows receive the same rate of return while invested, its return can differ substantially from the time-weighted rate of return (TWRR) when large cash flows occur during periods of significantly fluctuating portfolio values. This makes the MWRR less ideal for benchmarking portfolio managers or strategies than the TWRR. For example:

- When a large
*contribution*is made prior to a period of relatively good (bad) performance, the money-weighted rate of return (MWRR) will overstate (understate) a portfolio’s performance, relative to the time-weighted rate of return (TWRR). - When a large
*withdrawal*is made prior to a period of relatively good (bad) performance, the money-weighted rate of return (MWRR) will understate (overstate) a portfolio’s performance, relative to the time-weighted rate of return (TWRR).

Without the help of computers, the calculation is just a series of trials and errors. Using the above equation and the values from our original example, Investor 1 would begin by plugging in return “guesses” for **r **until the right-hand side of the equation equals the ending portfolio value, V_{1}. They would eventually stumble across **8.98%** as the plug return that equates the right-hand side of the equation to 298,082 (or as close as possible).

**Example: Manual MWRR calculation for Investor 1**

r “guess” |
Right-hand side of the equation: |

10.00% |
300,708 |

9.00% |
298,140 |

8.99% |
298,114 |

8.98% |
298,088 |

8.97% |
298,063 |

An easier way for investors to calculate their MWRR would be to download the ** Money-Weighted Rate of Return Calculator**, available in the Calculators section of the

*Canadian Portfolio Manager Blog*. This calculator requires minimal inputs and is fairly intuitive to use. It also annualizes (averages) returns over periods longer than a year.

After downloading the Excel spreadsheet, select the start and end dates for your measurement period, entering the total portfolio value to the right of each date. Next, enter the dates and amounts of any portfolio contributions (+) or withdrawals (-) during the measurement period. I’ve included examples for both investors below.

**Money-Weighted Rate of Return (MWRR): Investor 1**

**M****oney-Weighted Rate of Return (MWRR): Investor 2**

The MWRR results are noticeably different than the TWRR results from our first example. Investor 1 contributed $25,000 to their portfolio before a period of underperformance (**-5.56%** versus **+16.25%**) and ended up with a significantly lower MWRR of **8.98%**. On the other hand, Investor 2 withdrew $25,000 from their portfolio before a period of underperformance, which resulted in a significantly higher MWRR of **10.64%**. This makes intuitive sense; Investor 1 made a bad timing decision by adding funds right before the markets went down, while Investor 2 made a good timing decision by withdrawing funds right before the markets went down.

*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% |

Each investor’s cash flow decision resulted in a higher or lower MWRR, relative to the TWRR. Their investment strategy was exactly the same in each case (i.e. to track the MSCI Canada IMI Index). By comparing their MWRR to an index return, both investors may incorrectly conclude that their portfolio manager has underperformed or outperformed the benchmark (which is why a money-weighted rate of return should not be used for benchmarking purposes).

Next up, we will examine the * Modified Dietz Rate of Return*.

Is MWRR the same as the XIRR function found on spread sheets (e.g. google sheets)?

@Jim R – you are correct! The XIRR function found in excel is a money-weighted rate of return (MWRR).

Hi Justin,

Seems like both MWR and Modified Dietz have limitations when it comes to large external cash flows, particularly cash flows that are 10x+ larger than initial starting balance.

What do you do when you have those types of cash flows?

For example: End of December PV = $100k.

Cash inflow of $1M on July 15, 2015

July 30, 2015 (15 days later), PV $1M.

Although a dollar amount of loss is $100k, it’s hardly a 50.8% HPR loss using the XIRR function in excel.

Similarly, if the ending value is at $1.2M, the XIRR function gives a return of 64.1%.

Using MD, the first scenario shows a -58% loss, while second shows a gain of 58%

Those are clear limitations of both methods so what would you recommend?

Thanks

@Mario – the best method to use would be the “true” time-weighted rate of return (TWRR), but this may be difficult if you do not have access to daily portfolio values: http://www.canadianportfoliomanagerblog.com/how-to-calculate-your-time-weighted-rate-of-return-twrr/

So. When CRM2 is fully implemented, and all firms providing money management services are supposed to be providing MWR….how much better off will investors be, when compared with having previously had only TWR-type returns?

Firms should simply say ” the timing of when you made your own deposits and withdrawals from the account have a primary affect on the ROR. To truly evaluate whether or not you…or the account manager..are responsible for a particular return…is now pretty much impossible to ascertain. Best of luck with your evaluation.”

And it will be impossible to ascertain with any certainty.

I honestly do not understand why MWR is being mandated by CRM2? As an idea, it has some merit…but after some consideration, it just seems to break down so qucikly? What information does a client get that can help them manage their money when they have this figure? Including an advisor who can wash their hands of the entire mess? maybe it’s a self-directed investor “play” vs otherwise…but if so, that’s pretty easy to identify in the marketplace, and deal with.

All the performance reporting requirements up to, but not including, MWR, should have been more than sufficient to inform investors of how they were doing. Deposits minus withdrawals = return, indicate income as well, and you have a great indicator. Start fiddling around with the reported ROR? And mandating a methodology that is far from being an industry standard, and subject to errors…misunderstanding…and god forbid, an inability on the part of firms to actually calculate correctly? Especially given the lack of guidelines provided by regulatory bodies in this subject for the calculations themselves…it’s simply astounding that they would cite “industry standard calculation methods for MWR” without providing any actual examples. Espcially when the entire industry simply does not perform MWR calculations as a rule!

That’s my vent…now I have to figure out what to do for the firm I work for.

Thanks Justin,

But even if one has access to daily values, TWR also has limitations no? Particularly when large cash flows come in prior to positive/negative market returns.

I’m just trying to figure out the best fits all metric to calculate performance – regardless of a benchmark.

Thanks for the help. I’ve been following your other posts and seems like you’re one of the best at understanding these concepts

@Mario – TWR still has limitations, but in your scenarios, it appears to make the most sense. Using the TWR (and assuming no change in the portfolio value from December 31, 2014 to July 15, 2015), the TWR would equal -9.09% in your first example, and +9.09% in your second example (which would be closer to what an investor would expect).

This is what can make rate of return calculations so confusing…they are all technically correct, based on their definitions, but their conclusions are not always intuitive.

Hi Justin,

Just in response to the other post where I’ve said that I probably need to utilise the money weighted return. Using your example, how would I implement it on a monthly basis since I want to show the fluctuations in performance from month to month?

@George: You would need to calculate your monthly money-weighted rate of returns, and then geometrically link the various monthly returns together (which means, add 1 to each month return, multiply these values together, and then subtract 1).

Using my monthly Modified Dietz calculator should give you roughly the same return as a “linked” money-weighted rate of return.

Also, in your example you’ve used a single cashflow of $25k. How would you calculate it if there were cashflows before and after that date, and you wanted to calculate the performance from 31/12/2013 to 31/12/2014

@George: If there were cash flows before or after that date, they would need to be included in the same manner as the $25,000 cash flow.