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*.

JustinApril 21, 2017 at 5:07 pm@Chis: Purchases and sales of securities do not need to be entered into the calculator.