Using Brinson Attribution to Explain the Differences between Time-Weighted (TWR) and Money-Weighted (IRR) Returns (Digest Summary)

Time-weighted returns (TWR) and money-weighted returns (internal rate of return, or IRR) may produce divergent or even conflicting results from time to time. The IRR method weights the investment return against the cash flow inputs and outputs. The TWR method focuses on specific time intervals, compounding them geometrically. Practically, the IRR method works better for such investments with unpredictable cash flows as private equity. In contrast, the TWR method is more appropriate for benchmark comparisons of liquid investments—for example, bonds and stocks.

The problem with the TWR method is that the ultimate return rate is a geometric total of partial rates; it ignores the influence of the investment’s underlying amounts. The time-weighted return on the investment may have a positive sign even though its money-weighted counterpart has a negative sign. The IRR method is not free from drawbacks either. For instance, it imputes a reinvestment rate equal to the internal rate of return, which is an unlikely occurrence. Moreover, investment managers seldom have discretion over the timing and sizes of cash flows. All this strengthens the position of the TWR method, which is recommended by the Global Investment Performance Standards (GIPS^®).

Using the Brinson attribution model, the author presents a quantitative decomposition of the discrepancy between the two methods. Given the pros and cons of the TWR and IRR methods, it seems reasonable to proclaim both methods an industry standard for estimating rates of return. Both rates should be presented to investors, accompanied by an obligatory reconciliation. The author argues that presenting the two return measures will not confuse investors if a proper disclosure is made. He also suggests a report template for making such disclosures.

The author’s research might be of interest to various market participants, including regulatory bodies, investment managers, and investors. Investors face the challenge of picking the “right” investment managers for their savings. The methodology and background the author outlines might prove helpful to these participants.

The author presents several theoretical examples of performance attribution, with particular attention paid to the Brinson model introduced by Brinson, Hood, and Beebower (Financial Analysts Journal^® 1986). In general, investment performance attribution is a set of techniques that can be used to analyze the difference between portfolio returns and benchmark returns. As presented by the author, the attribution analysis focuses on two potential sources of portfolio returns (selection and allocation of securities), although it may include such other factors as currency. The Brinson model decomposes the portfolio return into three components: selection, allocation, and the interaction between the two. The author finds that the key difference between the TWR and IRR methods is that the TWR method equally weights variable reinvestment rates and the IRR method takes a fixed reinvestment rate and applies the different weights resulting from the portfolio’s cash flows.

Theoretical examples are used to illustrate the author’s viewpoint. Therefore, it is difficult to quote particular numbers. The methodology presented nevertheless allows one to simultaneously zero out the impact of the different weights on the return estimation and isolate both timing- and selection-related effects. Thus, the factor that is not within management’s discretion is effectively removed.

The author’s conclusion implies that both the discussion of the differences between the two methods and the attempts to justify the superiority of one method over the other are not important needs of the investment industry. The real need can be addressed by understanding the actual reasons for the discrepancy between portfolio and benchmark returns. The author presents a quantitative methodology that enables a concise and coherent analysis of that discrepancy. The ultimate goal is to help investors pick the best investment managers and measure their effectiveness. Thus, the author makes an important contribution. Although the author’s research probably has limited academic value, it can be applied immediately to real-life situations.

This paper joins a substantial block of literature and a multilayered discussion on the industry standard for investment return estimation and presentation. This discussion has powered the investment world for many years and offers a voice of common sense in this important matter.