What's the Difference? Time-Weighted Return vs. Internal Rate of Return

October 27, 2017  | by Commonfund

Industry Knowledge | Investment Strategy

Investors often ask about the difference between time-weighted return (“TWR”) and internal rate of return (“IRR”).

In general, TWR is used by the investment industry to measure the performance of funds investing in publicly traded securities.  By contrast, IRR is normally used to gauge the return of funds that invest in illiquid, non-marketable assets—such as buyout, venture or real estate funds.

Investors want to know why public and private investment returns are reported differently and how the calculation methodologies differ.

Therefore, this article will:

  • Explain why public and private investment performance is reported differently,

  • Define TWR and IRR, and

  • Highlight the differences between IRR and TWR by calculating both numbers from the return stream of a hypothetical

While investor knowledge of TWR is widespread given its broad adoption with marketable investments, familiarity with IRR continues to be less extensive. However, IRR remains the standard for private investments.

Why Public and Private Securities Returns are Reported Differently

Managers of public securities funds typically do not control investor cash flows. Investors in these funds enter and exit at will. On the other hand, investors in many private or alternative funds face restrictions on their ability to invest additional assets or to redeem existing assets. These restrictions can take the form of multi-year “lock-ups” or no ability to achieve liquidity absent the sale of underlying assets1.

As discussed below, this difference in the nature of fund cash flows constitutes the main reason why public and private securities returns are reported differently.

Time-Weighted Return, What Is It?

TWR measures a fund’s compounded rate of growth over a specific time period. (Fabozzi, Frank, Investment Management, © 1995, pp 611-618).

While TWR measures the return of a fund’s investments, it does not consider the effect of investor cash moving in and out of a fund. Thus, TWR is suitable for measuring the performance of marketable investment managers because they do not control when investor cash enters or exits their funds.

TWR... does not consider the effect of cash moving in and out of a fund.

According to the CFA Institute, “Time-weighted rate of return allows the evaluation of investment management skill between any two time periods without regard to the total amount invested at any time during that time period.  The measure is independent of the total amount invested because the manager normally does not control the inflow and outflow of money.”

How Time-Weighted Return Works

The example below illustrates the mechanics of TWR for the hypothetical ABC Equity Mutual Fund (numbers in bold are used for the TWR calculation).

TableA

On December 31, Year 1, ABC had $1000 in assets. During the first quarter of Year 2 it had a 10% return, but this return ranked far below its peers, so $730 exited the fund. In the second quarter, ABC earned 3% and $300 more dollars came out. In the third quarter, the fund lost 4% and $70 was withdrawn. In the fourth quarter, ABC gained 6% and did not lose assets.

What is the annual TWR for ABC Equity Mutual Fund?

The TWR formula in this case is:

[(1+R1)(1+R2)(1+R3)(1+R4)] –1 = TWR, where R is the quarterly return.

Using the quarterly return numbers from above gives the following result:

[(1.1)(1.03)(.96)(1.06)] –1 = 15.3% = Annual TWR

Thus, ABC earned a 15.3% return.  Note that the fund’s cash outflows had no impact on performance.

Now let’s turn our attention to IRR, a measure for which fund cash flows have major significance.

Internal Rate of Return, What is it?

According to the CFA Institute, IRR is the annualized implied discount rate calculated from a series of cash flows. It is the return that equates the present value of all invested capital in an investment to the present value of all returns, or the discount rate that will provide a net present value of all cash flows equal to zero.

Said differently, IRR is the discount rate that equates the cost of an investment with the present value of the cash generated by that investment.

IRR... equates the cost of investment with the present value of the cash generated by that investment.

The CFA Institute recommends that IRR be used to measure the return of investments in private securities.  A major reason for this recommendation is that private investment managers typically exercise a greater degree of control over the amount and timing of their funds’ cash flows. How private managers exercise this control is crucial in assessing their investment skill.

Thus, private fund managers need a return calculation method that takes into account their control over fund cash flows.  IRR does this.

How Internal Rate of Return Works

To see the importance of cash flows in the IRR calculation, let’s use the same quarterly returns and cash flows presented above to calculate the IRR of the hypothetical XYZ Private Investment Fund (numbers in bold are used for the IRR calculation).

As will be seen, IRR uses different numbers than TWR.

TableB

In this case, on December 31, an investor makes a $1000 investment in XYZ. In the first quarter, XYZ’s investments are written up in value by 10% and the fund distributes assets to investors totaling $730. In the second quarter, XYZ’s investments are written up 3% and $300 of portfolio assets are distributed. In the third quarter, XYZ writes down investments by 4% and distributes $70 worth of assets. In the fourth quarter, remaining fund investments are written up 6% and distributed at $8.3.

What is the IRR on this investment?

The IRR formula in this instance involves two steps: 3

IRR Equation

Analysis of the Differences Between Time-Weighted Return and Internal Rate of return in the Examples

In the foregoing examples, we demonstrated TWR using hypothetical returns of the ABC Equity Mutual Fund, and we showed IRR using hypothetical cash flows of the XYZ Private Investment Fund.

These two methods reflect the differing nature of cash flows for public and private fund managers. Public fund managers do not control their funds’ cash flows, and TWR does not account for the timing of these flows. Private fund managers, on the other hand, exercise a degree of control over the timing and magnitude of their funds’ cash flows, and IRR takes these flows into account.

In the two examples, IRR was roughly twice the TWR. However, TWR and IRR will not always differ. Sometimes the two may be similar, depending on returns and cash flows.

IRR was higher than the TWR due to the “front loading” and strongest quarterly return in the initial quarter of XYZ Private Investment Fund’s cash outflows, i.e., most of the cash ($730) was returned to investors in the first quarter.

Download the full article to access the TWR vs. IRR Cheat Sheet

1 An additional means of achieving liquidity is through a secondary sale, which is not within the scope of this paper and often can require taking a significant discount to net asset value to enable such a sale.

2 Step one calculates the subperiod IRR from the quarterly cash flows. Step two annualizes this number. Many spreadsheet programs have IRR calculation functions as a standard feature.

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Information, opinions, or commentary concerning the financial markets, economic conditions, or other topical subject matter are prepared, written, or created prior to printing and do not reflect current, up-to-date, market or economic conditions. Commonfund disclaims any responsibility to update such information, opinions, or commentary. To the extent views presented forecast market activity, they may be based on many factors in addition to those explicitly stated in this material. Forecasts of experts inevitably differ. Views attributed to third parties are presented to demonstrate the existence of points of view, not as a basis for recommendations or as investment advice. Managers who may or may not subscribe to the views expressed in this material make investment decisions for funds maintained by Commonfund or its affiliates. The views presented in this material may not be relied upon as an indication of trading intent on behalf of any Commonfund fund, or of any Commonfund manager. Market and investment views of third parties presented in this material do not necessarily reflect the views of Commonfund and Commonfund disclaims any responsibility to present its views on the subjects covered in statements by third parties. Statements concerning Commonfund’s views of possible future outcomes in any investment asset class or market, or of possible future economic developments, are not intended, and should not be construed, as forecasts or predictions of the future investment performance of any Commonfund fund. Such statements are also not intended as recommendations by any Commonfund entity or employee to the recipient of the presentation. It is Commonfund’s policy that investment recommendations to its clients must be based on the investment objectives and risk tolerances of each individual client. All market outlook and similar statements are based upon information reasonably available as of the date of this presentation (unless an earlier date is stated with regard to particular information), and reasonably believed to be accurate by Commonfund. Commonfund disclaims any responsibility to provide the recipient of this presentation with updated or corrected information. Past performance is not indicative of future results. For more information please refer to Important Disclosures.

Disclaimer

Information, opinions, or commentary concerning the financial markets, economic conditions, or other topical subject matter are prepared, written, or created prior to printing and do not reflect current, up-to-date, market or economic conditions. Commonfund disclaims any responsibility to update such information, opinions, or commentary. To the extent views presented forecast market activity, they may be based on many factors in addition to those explicitly stated in this material. Forecasts of experts inevitably differ. Views attributed to third parties are presented to demonstrate the existence of points of view, not as a basis for recommendations or as investment advice. Managers who may or may not subscribe to the views expressed in this material make investment decisions for funds maintained by Commonfund or its affiliates. The views presented in this material may not be relied upon as an indication of trading intent on behalf of any Commonfund fund, or of any Commonfund manager. Market and investment views of third parties presented in this material do not necessarily reflect the views of Commonfund and Commonfund disclaims any responsibility to present its views on the subjects covered in statements by third parties. Statements concerning Commonfund’s views of possible future outcomes in any investment asset class or market, or of possible future economic developments, are not intended, and should not be construed, as forecasts or predictions of the future investment performance of any Commonfund fund. Such statements are also not intended as recommendations by any Commonfund entity or employee to the recipient of the presentation. It is Commonfund’s policy that investment recommendations to its clients must be based on the investment objectives and risk tolerances of each individual client. All market outlook and similar statements are based upon information reasonably available as of the date of this presentation (unless an earlier date is stated with regard to particular information), and reasonably believed to be accurate by Commonfund. Commonfund disclaims any responsibility to provide the recipient of this presentation with updated or corrected information. Past performance is not indicative of future results. For more information please refer to Important Disclosures.