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Money-Weighted vs. Time-Weighted Rates of Return

September 19, 2014 - 4 comments

Investment performance has always been a touchy subject for the financial industry. Portfolio rates of return are rarely disclosed, and investors are often left in the dark on how they are actually doing. Phase II of the Client Relationship Model (CRM II) is about to change all of that. Starting in July 2016, dealers and portfolio advisors will be required to provide performance reports to their clients every year.

The money-weighted rate of return (MWRR) was chosen by the Canadian Securities Administrators (CSA) as the industry standard for these performance calculations. Their rationale was that the money-weighted rate of return was more relevant to the individual investor. Other industry groups, such as the Portfolio Management Association of Canada (PMAC), requested that the CSA reconsider their decision, and instead allow dealers and portfolio advisors to use either the money-weighted or the time-weighted rate of return (TWRR). They argued that the time-weighted rate of return was a more appropriate method, as it allowed investors to directly compare their performance to suitable benchmarks and to other advisors and portfolio managers.

To better understand both sides of this debate, let’s look at a hypothetical investor who receives performance reporting using the money-weighted rate of return, but then attempts to compare it to an appropriate index return.

Money-Weighted Rate of Return Example  

At the end of 2003, an investor contributes $100,000 to a Canadian stock portfolio managed by an advisor. After four years of stellar returns, the investor decides to place an additional $100,000 under their management. The financial crisis quickly unfolds, and the investor ends 2008 with only $189,600 (wiping out all previous gains and leaving them with less than their total investment).

Example:  Transaction history for hypothetical investor                                                                               

Shortly after year-end, the investor receives a performance report from their advisor, indicating that their 5-year annualized money-weighted rate of return is -1.78%1. They are not surprised by this figure, but decide to compare it to a suitable benchmark, the S&P/TSX Composite Index. To their horror, they find that over the exact same period, the index returned 4.15% on an annualized basis.

If we recalculate the investor’s return using the time-weighted rate of return method, we end up with a 5-year annualized return of 4.16%2 (almost identical to the benchmark return). But how can that be? The investor has clearly lost money – they are down $10,400.

The reason for this is because the money-weighted rate of return is more dependent on when the dollars are actually contributed or withdrawn from the portfolio. In the example above, the investor doubled the amount they had initially contributed right before the market declined, resulting in a lower return relative to the time-weighted rate of return. The results of this method often make more sense for the investor, as it is a better representation of how they have actually done.

The time-weighted rate of return ignores all contributions and withdrawals from the portfolio.  In the example above, the investor’s bad luck or timing had no effect on their return. The calculation basically assumes that they invested $1 at the beginning of the period (with no further contributions or withdrawals). This method is ideal for comparing managers or funds to benchmark indices.

The CSA has stood firm on their decision, so it is up to advisors to familiarize themselves with both methods so they can explain them to their clients. In order to help with this task, I’ve posted several rate of return calculators (in the Calculators section of the blog) that use the Modified Dietz method (an approximate time-weighted rate of return). This will allow advisors and clients to calculate a more appropriate return for benchmarking purposes.

1 MWRR =

Source:  Weigh House Investor Services:  Calculate Your Portfolio’s Return

2 TWRR = [(1 + 0.13) × (1 + 0.27) × (1 + 0.17) × (1 + 0.09) × (1 + (-0.33))](1/5) – 1 = 4.16%

By: Justin Bender with 4 comments.
  10/02/2015 9:44:23 AM
Justin Bender
@Stan Huang - you can use a monthly Modified Dietz method for most months, and then calculate a daily value for months in which a large contribution/withdrawal is made.

I've illustrated an example of the limitation of a TWR in the blog post above. The investor lost money in reality, but their TWR would suggest that they made money.
  10/02/2015 1:46:58 AM
Stan Huang
Thanks for the quick response.
Can you still use less frequent valuation periods (monthly), as long as you perform the pre/post cash flow valuation the day of?

On a side note, I can't seem to find any limitations on TWR calculations - are there any that you've experienced?
Particularly, high volatility, large cash flows (as a % of portfolio) effects.
I was thinking about this the other day. Consider a $100k portfolio that drops to $50k 6 months later. Another $50k is added to the portfolio, bringing it back to $100k. 6 months later (end of December), portfolio value doubles to $200k.
The TWR calculation for 1 year would be effectively zero (0.5*2)-1 = 0.
However, MWR would be around 40% or so. (portfolio value +$50k at the end)
Is it fair to say the return was zero? Or should it be weighted somehow (similar to weighting asset class returns in a portfolio)
  09/02/2015 10:14:43 AM
Justin Bender
@Stan Huang - they should likely be using a "true" time-weighted rate of return, which would require daily portfolio valuations (this is how mutual funds calculate their returns).
  08/02/2015 7:32:11 PM
Stan Huang
Hi Justin,

Great article. Which return calculation should an advisor use if there were significant client cash flows during the measurement period?
For example, from $100 to $900k ($800k inflow), which distorts the MWR significantly?

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