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Performance Analytics: Time Weighted and Money Weighted Returns – A Deeper Dive

The answer is not “cashflows”

The Money Weighted Returns (MWR) and Time Weighted Returns (TWR) are two return measures that are frequently used in investment performance reporting. As a result, performance experts are often asked to explain the difference between the two methodologies.

The typical answer to the above question is the “treatment and timing of cashflows”. However, the two performance measures can yield significantly different results for the same time periods which can at times raise more detailed questions from stakeholders.

If it is not cashflows what is the answer?

To address these questions, it is important for performance analysts to understand the difference between TWR and MWR at the technical level and in turn understand which circumstances each measurement will be of greatest informational value to the end user.

TWR provides a methodology to calculate investment performance solely attributed to the portfolio manager’s actions. TWR eliminates the impact of the timing of cash flows and measures only the effects of the market and the portfolio manager’s actions.  The current industry standard is to primarily rely on the TWR for performance reporting.[1]

MWR provides a methodology to calculate the performance from the end investor perspective in that the calculation includes all the portfolio impacts including cashflows.  MWR return is sometime referred to as the ‘true’ portfolio return as it captures all the impacts on a portfolio’s value. 

Exhibit 1: Summary of TWR & MWR Methodologies

The answer can be confusing though

What can be somewhat confusing for non-performance professionals is that an MWR and TWR measure can yield significantly different results for the same time periods using the same datasets.

In a recent engagement Shoreline conducted a detailed study to identify relevant methodologies to reconcile TWR and MWR returns and provide a framework to explain the differences in returns.  

The objective of the engagement was to obtain a greater understanding of the cashflow, reinvestment rate and timing effects that have an impact on the two performance return methodologies.

Using a combination of prior experience, academic research, peer group profiling and the researchers friend Google, we confirmed our initial hypothesis that the reconciliation between the two methodologies is not commonplace across the industry.   

The proposed solution…Brinson is your friend

Undaunted Shoreline discovered a methodology which can be utilised by performance teams to reconcile its TWR and MWR.

The proposed reconciliation methodology was in a research paper originally presented in the Journal of Performance Measurement by Joe D’Alessandro.[2]

To mathematically reconcile the TWR and MWR formulas and to isolate the effects, D’Alessandro proposed utilising the Brinson-Hood-Beebower[3] (‘Brinson’) attribution framework as an appropriate reconciliation methodology.

Brinson is a form of relative attribution commonly used widely in the investment management industry and first appeared in 1986.

The Brinson attribution model helps us evaluate why a portfolio manager out-performs or under-performs a benchmark.  In other words, what active decisions or actions did a portfolio manager take to generate alpha.

By extending the Brinson model to evaluate the TWR and MWR we can explain how much of the TWR & MWR performance differential is due to:

  • The timing and size of cashflows and
  • The difference in reinvestment rates.

The application of the Brinson model in this context is premised on the fact that there are two situations where the TWR and MWR will be equal.

  1. When there are no additional subsequent cashflows other than the initial contribution and final reversion.
  2. Where the return is earned evenly for every measurement period throughout the holding period.

The methodology combines weights and returns, a form of contribution to return, in a way such that the drivers of over or under performance of TWR versus MWR can be clearly identified and better understood.

In Exhibit 2 we have provided an example summary of the effects that contribution to the differences in TWR and MWR.

Exhibit 2: Effects Summary

Summary
Description Month Annualised
TWR 0.98% 12.81%
Weights Effect 0.00% 0.00%
less rate diff if TWR was value-weighted like MWR -0.03% -0.07%
less MWR bad timing -0.01% -0.01%
MWR 1.02% 12.89%
TWR – MWR “spread” -0.04% -0.08%

To conclude

What was concluded from our study was that both measures have applications for which Shoreline believe there are times where it is more appropriate to use one instead of the other.

The TWR is appropriate to measure manager returns, assuming the manager has no control over external flows to the specific investments being measured.

The MWR measures how the portfolio ac­tually performed, which is important to the end investor. External cash flows have an impact on portfolio growth and performance and are generally controlled by a party to the investment process, although that party may not be the invest­ment manager.

By understanding the effects causing the difference between the two methodologies, performance professionals can provide greater insight for their stakeholders into the drivers of investment returns.

If you are looking to explore this concept or your general performance and analytics needs further, please don’t hesitate to contact the team at Shoreline.  

Chris Robertson

Associate Director


[1] The GIPS standards require a time-weighted rate of return because it removes the effects of external cash flows, which are generally client-driven. GIPS guides that “a time-weighted rate of return best reflects the firm’s ability to manage the portfolios according to a specified mandate, objective, or strategy, and is the basis for the comparability of composite returns among firms on a global basis.

[2] Joe D’Alessandro, A new measure for the investment management industry: Time- & money-weighted return (TMWR), Journal of Performance Measurement, Summer 2011

[3] Gary P. Brinson, L. Randolph Hood, and Gilbert L. Beebower, Determinants of Portfolio Performance, The Financial Analysts Journal, July/August 1986

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