Originally Published: November 5, 2013, Phocion Investments Inc.
There is a differing opinion on the use of IRR (Internal Rate of Return) or TWR (Time Weighted Return) in performance measurement of investment firms, individuals and their portfolios. Some investors and firms prefer the IRR as it is viewed as a more complete return measure while others prefer the TWR, which focuses on the manager’s skill. This year, the CSA (Canadian Securities Administrators) issued its opinion on the matter and has required the use of a Money Weighted Return, such as the IRR, as the mandatory performance measure. On the other hand, GIPS has required the TWR as the most appropriate performance measure in reporting.
Canadian Securities Administrators
*NATIONAL INSTRUMENT 31-103: 14.19 Content of investment performance report
1. An investment performance report required to be delivered under section 14.18 by a registered firm must include all of the following in respect of the securities referred to in a statement in respect of which subsections 14.14(1), (2) or (3) [account statements] or 14.14.1(1) [additional statements] apply:
i. the amount of the annualized total percentage return for the client’s account calculated net of charges, using a Money-Weighted rate of return calculation method generally accepted in the securities industry;
Global Investment Performance Standards
*Global Investment Performance Standards Handbook : Third Edition – 2012
Calculation Methodology— Requirements:
2.A.2. Firms must calculate Time-Weighted Rates of return that adjust for external cash flows. Both periodic and sub-period returns must be geometrically linked. External cash flows must be treated according to the firm’s composite-specific policy.
Discussion: The GIPS standards require a time-weighted rate of return because external cash flows are generally client driven. By removing the effects of external cash flows, a time-weighted rate of return best reflects the firm’s ability to manage the portfolio according to a specified investment mandate, objective, or strategy, allowing prospective clients the best opportunity to fairly evaluate the past performance of the firm and to facilitate comparison between investment management firms.
There are areas of investment where the application of money weighted returns are more appropriate measures than TWR, such as in Private Equity and Real Estate where the manager does have discretion over the cash inflows and outflows. For investments in equity and bond portfolios the argument for favouring one return measure over the other can be made for both measures, as the of the CSA and the GIPS Council statements demonstrate.
From a performance point of view, where the main objective is to extract as much relevant feedback as possible, the use of BOTH should be employed. Whether it is for a single investor who wants to view the average growth of his/her funds over a period of time or a portfolio manager who wants to demonstrate his/her ability without the impact of any cash flow decisions, the information available from comparing both measures is of significant value. This argument’s foundation lies in the mechanics of the Time Weighted Return and the Money Weighted Return, in this case we will be focusing on the IRR.
Mechanics of Return Measures
When investors and managers view performance it is more of a “How well did I do?” approach rather than a “How and why did I do…?.” Some possible reasoning behind this is that most investors and investment practitioners either lack the necessary knowledge or often overlook the importance of the mechanics of return measures. Some fundamental knowledge in this area would go a long way in furthering the discussion of their performance.
The main difference between the Money Weighted Return and the Time Weighted Return is that the former places an emphasis on the magnitude and timing of external cash flows while the latter eliminates the effects of any external cash flows and isolates the return to the manager’s discretionary portion of the portfolio. From a technical point of view, a Money Weighted Return such as the IRR is the “average growth of all money invested in an account”  while the Time Weighted Return can be described as “the growth of a single unit of money invested in the account.”
Looking at the formula of the IRR, the return is affected by the size and timing of the cash flows (i.e., CFn & tn) and requires that the portfolio be valued at the beginning and end of the measurement period (i.e., MVBegin & MVEnd).
MVEnd of Period = MVBeg of Period (1+IRR)T +CF1(1+IRR)^(T-t1) +…+CFn(1+IRR)^(T-tn)
Relative to a scenario where no cash flows are present, the impact on performance of a contribution prior to a period of positive performance will result in a higher return. On the other hand, if a withdrawal was made prior to the same period of positive performance, the return would be impacted negatively. The opposite holds for a period of negative performance; that is, a contribution would negatively impact performance and a withdrawal would positively impact it.
Turning our attention to the TWR formula, the return is not impacted by cash flows and requires the portfolio to be valued at every sub-period while taking into account the impact of cash flows on the market values during the sub-period (i.e., MV1, MV2, …, MVn & CF1, CF2, …,CFn).
TWRtn = [(MVEnd of Period – SumCF) – MVBegin of Period] / MVBegin of Period
To calculate the total period’s return, each sub-period’s TWR is geometrically linked, as shown below:
TWR = (1+TWRt1) x (1+TWRt2) x … x (1+TWRtn) -1
Unlike the IRR, any contributions or withdrawals prior to periods of positive/negative performance would have no impact on the return. Furthermore, in the scenario where there are no cash flows during a measurement period, both the TWR and IRR would produce the same results.
From the above, we can say that the IRR measure would produce a higher return versus the TWR in the scenario where a contribution is made prior to a period of positive performance. From a numerical point of view, the following examples will demonstrate the impact of a contribution and a withdrawal prior to a period of positive performance. In both cases below, we are using a 30-day period with a beginning market value of $100, a cash flow of +/- $30 occurring on the 20th day of the period, and corresponding ending market values.
In the first case, where a contribution of $30 was made to the portfolio, the TWR produces a return of 23.08% while the IRR, which weights the cash flow, returns the higher value of 27.47%. The difference of 4.39% is significant and tells us that the investor’s decision to contribute increased his performance.
In the second case, the opposite occurs; a withdrawal is made of $30 prior to a period of positive performance and the TWR measure now produces a higher return of 42.86% versus an IRR return of 32.99%. Here again, the decision to withdraw funds prior to the positive period had a significant impact.
The information that both these returns provide is important enough that investors and firms alike should consider using both returns as part of a more comprehensive approach to evaluating their performance.
A Comprehensive Approach
A comprehensive approach in evaluating performance should include a thorough review of the qualitative and quantitative aspects of performance. One important component of this review is the return analysis and what it says about the impact of the decision making process. Using only one of the measures above is a missed opportunity in capturing the effect funding decisions had on the portfolio.
Considering that most portfolio managers do not have discretionary control over external cash flows, the contribution of the investor to performance is often overlooked. For example, let’s take a manager who has no discretion over external cash flow decisions and is managing a passive portfolio with its benchmark set as the S&P 500 Total Return. If during the twelve month period between October 2012 and September 2013, the client made contributions and withdrawals to the portfolio, the IRR and TWR would deviate in performance. In the following table, the TWR represents the total return of the S&P 500 while the IRR includes the impact of the cash flow decisions.
If the client was to only view the IRR, he/she would be under the impression that the manager was not capable of passively managing his/her portfolio to the benchmark. Would the investor be informed enough to understand that the published benchmark is calculated using the TWR? Perhaps, but what is important is that they understand the difference and why it occurs. Capturing that information and understanding what it means should represent an important component of an investor’s performance evaluation.
In the case of investment firms such as pension and endowment funds, where a board holds discretion over the funding of its strategies, using the TWR and IRR together would provide them the opportunity to evaluate their own decision making process and avoid unfairly assigning complete responsibility to the firms’ portfolio managers. Most, if not all, pension funds and endowments use IRR at the firm level to determine whether they are meeting their payment obligations but how aware are they of the difference between IRR and TWR and the reasons behind it? This key component should be part of every firm’s performance evaluation process.
Cash flow decisions are not negligible and do make up a part of the investment decision making process. Capturing that information by analyzing and understanding both return types will allow investors and managers alike to gain a more complete understanding on the effectiveness of the portfolio management. Taking care to properly assign responsibility in the performance evaluation process is a key factor in effectively analyzing what happened and by whom. Omitting valuable information can lead to the wrong conclusions and consequently the wrong solutions.
 Managing Investment Portfolios: A Dynamic Process, 3rd Edition(John Wiley & Sons, 2007)