Measuring Fund Performance - TWRR, Simple and Modified Dietz
Introduction
In our last discussion, Measuring Fund Performance - Part 1, we explored several methodologies available for private equity funds to measure their aggregate fund performance and the performance provided to their investors.
The methodologies we explored were mainly meant for closed-end funds, where the manager has some control over the timing of the fund’s cash flows. In contrast, for funds where the timing of each cash flow is uncertain, such as for open-ended funds where investors may contribute (subscribe) additional funds or request distributions (redemptions) at will, these methodologies may provide a distorted picture of the real performance of the fund.
In this article we will explore methodologies that are more suited for such open-ended funds, starting with the Time Weighted Rate of Return, and proceeding to alternatives available when daily valuations of portfolio holdings are not available.
Table of Contents
- Introduction
- Calculation Methodologies
- GIPS Standards on Calculation Methodology
- Summary
- References
- Comments
Time-Weighted Rate of Return (TWRR)
The Time-Weighted Rate of Return aims to provide the true return of an investment by eliminating any distorting effects of investor cash in- and outflows during the life of the investment.
The TWRR is a geometric mean return, where the individual periodic returns calculated for the sub-periods between cash in- and outflows are linked geometrically to achieve the final return of a portfolio.
To calculate the Time Weighted Rate of Return:
First, determine each period book-ended by a cash (or capital) in- or outflow, and find the value (NAV) of the portfolio as of the ending date of each sub-period.
Next, calculate the simple return of each investment period as:
$$Period_n\space Simple\space Return = \frac{Ending\space Value - Beginning\space Value}{Beginning\space Value}$$
Finally, link each period’s return together to attain the final TWRR:
$$(1 + Period_1\space Simple\space Return) \times (1 + Period_2 \space Simple\space Return) \space\times ... \times\space (1 + Period_n\space Simple\space Return)$$
Calculation Example
The following example illustrates the calculation of the TWRR, using a calendar year with an initial investment, two additional cash inflows, and one partial redemption during the year:
| Date | Description | Amount | Period Return | Calculation |
|---|---|---|---|---|
| December 31, 2015 | Initial investment (or contribution) | $1,000,000 | ||
| March 31, 2016 | Period ending value | 1,035,000 | 3.50% | = (1,035,000 - 1,000,000)/1,000,000 |
| March 31, 2016 | Add-on investment outflow | 200,000 | ||
| March 31, 2016 | Adjusted value | 1,235,000 | ||
| June 30, 2016 | Period ending value | 1,350,000 | 9.31% | = (1,350,000 - 1,235,000) / 1,235,000 |
| June 30, 2016 | Add-on investment | 100,000 | ||
| June 30, 2016 | Adjusted value | 1,450,000 | ||
| September 30, 2016 | Period ending value | 1,290,000 | –11.03% | = (1,290,000 - 1,450,000) / 1,450,000 |
| September 30,2016 | Partial redemption | (500,000) | ||
| September 30,2016 | Adjusted value | 790,000 | ||
| December 31, 2016 | Period ending value | 800,000 | 1.27% | = (800,000 - 790,000) / 790,000 |
Advantage
As stated above, the main advantage of the TWRR over IRR and similar return calculations is that the calculated return is not affected by cash contributions and distributions into and out of the fund or investment. This makes it possible to benchmark returns of different fund managers against each other or against general market returns regardless of investment activity during the performance period.
Disadvantage
The problem with this methodology from an investor’s perspective is that the sub-period ending NAV is require for any period where an cash in- or outflow occurs. These valuations may not be available for sub-periods not falling on typical month- or quarter-end dates, or in the case of non-liquid portfolios, the valuations may not be available without additional valuation information from the underlying investments.
Simple Dietz
An alternative methodology available for fund managers or investors to measure the portfolio
performance during a period that incorporates cash in- or outflows, but where the portfolio value
is not required on the cash flow dates is the Simple Dietz method.
To calculate the Simple Dietz rate of return of an investment:
Obtain the beginning and ending portfolio values of the period under consideration (i.e. total investment period, such a year)
Factor in the amounts of any cash flows occurring during the evaluation period. This method assumes that cash flows occur at the mid-period point, hence the exact dates of the cash flows are not used in the actual calculation.
The formula for the Simple Dietz is:
$$Simple\space Dietz\space Return = {EV - BV - CF_{net}\over BV + \frac{CF_{net}}{2}}$$
where,
EV is the investment’s ending value for the evaluation period,
BV is the investment’s beginning value, and
CF net is the net cash in- and outflows during the period
Disadvantage
Although the Simple Dietz method makes it possible to calculate an investment’s return factoring in the cash flows that occur during a period, the timing of the cash flows can have a significant effect on the real return experienced by the investor, particularly if significant cash in- our outflows occur prior to periods with relatively good or poor performance.
Modified Dietz
The Modified Dietz methodology improves on the Simple Dietz formula by incorporating the impact of the timing of any cash flows in the calculation of the investment return for a period.
To calculate the Modified Dietz of an investment, again, obtain the beginning and ending values of the investment, in addition to the amounts and dates of each cash flow that occur during the period.
The formula for the Modified Dietz is:
$$r_t = {EV - BV - \sum_{i=1}^{n}CF_{i,t}\over BV + \sum_{i=1}^{n} CF_{i,t}\times w_{i,t}}$$
where,
rt is the Modified Dietz for the period t under consideration,
EV is the investment’s ending value for the evaluation period,
BV is the investment’s beginning value,
CF i, t is the i’th cash flow during the period t, and
w i,t is the time-period weight of the i’th cash flow, calculated as:
\[w_{i,t} = {Days_t - Days_i \over Days_t}\]
where,
Days t is the total number of days in the investment period
Days i is the number of days from the start of the period t to the date of cash flow i
Disadvantage
The Modified Dietz improves on the Simple Dietz by incorporating the timing of cash flows, however, it still lags the TWRR in terms of accuracy of the calculated return, given that the investment value is not taken into account as of the exact cash flow dates.
Modified Dietz with Monthly Linking
A way to improve the accuracy of the Modified Dietz is to approximate the TWRR by linking periodic Modified Dietz returns. A good approximation can be obtained by linking monthly returns, and can be used if the investment value can be obtained on a monthly basis (albeit if daily valuations are not available).
To obtain the monthly-linked Modified Dietz return:
First calculate the Modified Dietz for each month in the investment period.
Then, link the monthly returns geometrically:
With this method, the daily valuations are not needed, but the accuracy is improved, and yields a total return closer to that of the true Time Weighted Rate of Return.
TWRR versus Modified Dietz
There are a number of scenarios that make the Monthly Linked Modified Dietz return
differentiate from the TWRR:1
When a large cash outflow (contribution) occurs prior to a sub-period experiencing relatively good performance, the Modified Dietz will understate performance (relative to the TWRR)
When a large cash outflow occurs prior to a sub-period experiencing relatively poor performance, the Modified Dietz will overstate performance
When a large cash inflow (distribution) occurs prior to a sub-period with relatively poor performance, the Modified Dietz will overstate performance
When a large cash inflow occurs prior to a sub-period with relatively good performance, the Modified Dietz will understate performance
Naturally, the smaller the sub-period length, the closer the Modified Dietz method will come to approximating the TWRR.
GIPS Standards on Calculation Methodology
The CFA Institute publishes a set of standards aimed to promote comparability in returns published by investment managers. The guiding principles state that ”the return must be calculated using a methodology that incorporates the time-weighted rate of return concept for all portfolios except for private equity”.2
The Guiding Principles provide the following key points regarding the calculation methodology used for returns:
The calculation method chosen must represent fairly, must not be misleading, and must be applied consistently.
Firms must calculate time-weighted rates of return that adjust for external cash flows. External cash flow is defined as capital (cash or investment) that enters or exits a portfolio.
For periods beginning on or after January 1, 2010, firms must calculate performance for interim sub-periods between large cash flows and geometrically link performance to calculate periodic returns.
The GIPS allow for some flexibility when choosing the methodology to use when calculating the returns of the sub-periods delineated by cash flow activity, as long as the sub-periods are then geometrically linked.
However, for periods beginning on or after January 1, 2010, firms are required to value their portfolio holdings on the date of significant cash flows, which promotes the use of the true time-weighted rate of return calculation.
Summary
The last several years have seen an increased interest by traditional private equity managers to launch funds that blend or wholly incorporate non-private equity investment holdings alongside their typical private equity investments.
For software platforms that cater to such managers, it is imperative to offer a flexible approach to performance measurement of total fund and individual investment holdings, that provide means of calculating performance figures for both private and public portfolio holdings.
Also, from an investor’s perspective, is is critical to be versed in the performance fee calculation methodologies used by their fund managers, in order to be able to competently benchmark their holdings across vehicles and investment types.
