Personal rate of return is a person's own investment performance based on his or her OWN
transaction history and resulting cash flows. This section outlines the standards and
underlying calculation methods for calculating time-weighted and dollar-weighted personal rate of
PLEASE NOTE: For the information presented in this section
and in the performance reporting available through dailyVest software, dailyVest
uses only calculation methods which are based on guidelines established by the Investment Performance
Council of the CFA Institute (formerly the Association for Investment Management and
Research or AIMR) in its "Global Investment Performance Standard" (GIPS®) handbook.
Please note that dailyVest does not claim compliance with GIPS®, as only firms that manage assets
can claim compliance. Furthermore, the Investment Performance Council of the CFA Institute
has NOT been involved in the preparation or review of these notes nor has it been involved with
dailyVest in any way.
Time-Weighted Rate of Return.
A time-weighted rate of return takes into account the amount of time an investor
has been invested in a certain security such as a stock, bond or mutual fund.
It measures how well he or she performed in increasing the dollars that were invested.
Cash flows moving in and out of the investment(s) do not affect the time-weighted rate of
return, unlike with the dollar-weighted rate of return or “IRR” method which is affected by the
timing and amount of cash flows. Time-weighted rates of return can be calculated on a
daily basis using a method known as Daily Valuation, or by
using a slightly less accurate but in some cases more convenient monthly method known as
Modified Dietz where inflows and outflows are averaged for the month.
These time-weighted methods used for calculation of personal rate of return provide a truer
measurement of how investments have performed.
Dollar-Weighted Rate of Return.
Dollar-weighted rate of return (“DWRR”), also known as "Internal Rate of Return" or more
commonly "IRR" is used to determine the rate of return on an investment. IRR equates the
present value of an investment's cash inflows (dividends, interest, and sales proceeds
received) with the present cost of the investment. That is, for an investment that produces
a number of cash flows over time, the IRR is defined to be the discount rate that makes the
net present value of those cash flows equal to zero. Stated another way, the IRR is “…the
interest rate that will make the present value of the cash flows from all the sub-periods
in the evaluation period plus the terminal market value of the portfolio equal to the initial
market value of the portfolio.” (Fabozzi, Frank J.,
Fixed Income Mathematics, ©1993 1997, pp 157). The IRR method (DWRR) requires an iterative
solution for determining a rate of return and therefore leverages the inherent capacity of a
computer for iterating through to arrive at a solution.
Time-weighted ROR vs. Dollar-weighted ROR.
The table below summarizes the main points behind the time-weighted and dollar-weighted rate of return calculation methods.
Global Investment Performance Standards (GIPS®).
The performance reporting tools provided by dailyVest are capable of calculating personal investment performance using
the Dollar-Weighted Rate of Return (DWRR) and Time-Weighted Rate of Return (TWRR) methods.
When employing time-weighted rate of return calculation methods, dailyVest follows
the recommendations of the Investment Performance Council of the CFA Institute's Global
Investment Performance Standard (GIPS®) used for calculating investment performance
returns. Click here to learn more about GIPS®.
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When no cash flows are present, calculating total return is accomplished for a given
period using the following equation:
…where EMV is the market value of the asset at the end of the period, including any accrued income. BMV is the market value
of the asset at the beginning of the period.
When cash flows are present, dailyVest uses the Modified Dietz approximation method. (The TWRR - Modified Dietz method
provides an approximate time-weighted return whereas the TWRR - Daily Valuation method is a true time-weighted return.)
TWRR – Modified Dietz uses the beginning and ending portfolio value for the month, and weights each cash flow (contribution
or withdrawal) by the amount of time it is invested. The monthly portfolio returns are then geometrically
linked to arrive at a quarterly or annual return. The formula for estimating the time-weighted rate of return using the
Modified Dietz Method is…
…where EMV is the market value of the portfolio at the end of the period, including all income accrued up to the end of the period,
and BMV is the portfolio's market value at the beginning of the period, including all income accrued up to the end of the previous
period. CF is the net cash flows within the period where contributions to the portfolio are positive flows or "inflows" and withdrawals or
distributions are referred to as negative flows or "outflows."
The equation above represents the sum of each cash flow CFi multiplied by its
weight Wi. The weight Wi is the proportion
of the total number of days in the period that cash flow CFi has been held in (or
out of) the portfolio. The formula for Wi is…
…where CD is the total number of calendar days in the period and Di is the number
of calendar days since the beginning of the period in which cash flow CFi occurred.
(The numerator is based on the assumption that the cash flows occur at the end of the day.) For example, if a cash flow occurred
on January 20th and if the month of January has 31 days, the ratio Wi is then calculated
as (31–20)/31 = 0.35483871.
After computing monthly returns, they are 'geometrically linked' to produce a quarterly return using this formula…
Rqtr is the portfolio quarterly return and
Rmonth-1, Rmonth-2, and
Rmonth-3 are the returns for months 1, 2, and 3, respectively.
Similarly, the annual rate of return may be calculated by linking quarterly portfolio returns using this
Again, Rqtr-1, Rqtr-2,
Rqtr-3, and Rqtr-4 are
returns for quarters 1, 2, 3, and 4, respectively. Alternatively, one can geometrically link the twelve
monthly returns to arrive at the annual return.
The chief advantage of the Modified Dietz Method is that it does not require portfolio valuation on the date
of each cash flow. This used to be an advantage with older systems that were not capable of producing daily
valuations of all holdings. Its chief disadvantage is that it provides a less accurate estimate of the true
time-weighted rate of return. The estimate suffers most when a combination of the following conditions exists:
Note that the Modified Dietz approximation method will not conform to GIPS® standards after 1 January 2010.
And while Modified Dietz is slightly less accurate as compared with the Daily Valuation method, the real motivation
behind this change is to have the standard keeps pace with modern technology. Nowadays, little additional effort
is required to value the holdings within a portfolio at the time of external cash flows -- not only daily but
sometimes even in real-time. The Daily Valuation calculation method is not only the most accurate method, it is
perfectly suited for systems which value assets daily.
The actual valuation of a holding/position, account or entire portfolio each time there
is an external cash flow will result in the most accurate time-weighted rate of return
calculation. In practice, this can only be met by having the ability to obtain daily
valuations on all portfolio holdings on a continuous basis. (Again, this is standard
in most modern-day systems.) Returns are calculated under these conditions using the
“Daily Valuation Method.” This method calculates the true TWRR rather than an estimate.
The Daily Valuation Method breaks the total performance period into sub-periods, the
boundaries of which are based on the occurrence of cash flows. The formula for calculating
a sub-period return is…
…where EMV is the market value of the portfolio at the end of the sub-period, before
any cash flows in the period, but including accrued income for the period. BMV is
the market value at the end of the previous sub-period (i.e., the beginning of the
current sub-period), including any cash flows at the end of the previous sub-period
and including accrued income up to the end of the previous period.
Boundaries of sub-periods can be depicted in the following example which contains two cash flows
CF1 and CF2…
The sub-period returns (e.g., R1, R2,
R3) are then geometrically linked according to the following formula…
…where Rtr is the total return and R1,
R2…Rn are the sub-period
returns for sub-period 1 through n, respectively. Sub-period 1 extends from the first
day of the overall period up to and including the date of the first cash flow (excluding
the value of that cash flow but including all accrued income for that sub-period).
Sub-period 2 begins the next day and extends to the date of the second cash flow
(again, excluding the value of that cash flow but including accrued income), and
so forth. The final sub-period extends from the day of the final cash flow through
the last day of the overall period. Based on how the sub-period boundaries were
defined above, this method assumes that the cash flow is not available for investment
until the beginning of the next day. Accordingly, when the portfolio is revalued
on the date of a cash flow, the cash flow is not reflected in the Ending Market
Value, but is added to the Ending Market Value to determine the Beginning Market
Value for the next day.
The chief advantage of this method is that it calculates the true time-weighted
rate of return rather than an estimate as with the Modified Dietz Method.
dailyVest uses a modified form of the IRR equation to take into account the exact
timing of each cash flow within a period. Known as a "Modified IRR" method, one will need
to use iteration to solve the following equation for Internal Rate of Return “R…”
…where EMV is the market value of the asset at the end of the period, including any accrued
income. The weight Wi is the proportion of the total number of days
in the period that cash flow CFi has been held in (or out of) the portfolio. The
formula for Wi is as before…
Again, CD is the total number of calendar days in the period and Di is the number
of calendar days since the beginning of the period in which cash flow CFi occurred.
For example, if a cash flow occurred on January 20th, Wi is then calculated as (31–20)/31
= 0.35483871. (Notes: the month of January has 31 days and the numerator is based on the assumption that the
cash flows occur at the end of the day.)
Cash flows are treated the same way as in the Modified Dietz method with one important
exception: the beginning market value is treated as a cash flow, or CF0 = BMV. Therefore,
the IRR equation above can be represented as…
Here, the value of R can be obtained by iterating through all the possibilities of R until the result equals EMV.
GIPS® recommends that IRR be used to measure the return of investments in private
securities. This is so because private investment managers (or in dailyVest’s case,
individual investors themselves) exercise a greater degree of control
over the amount and timing of their holdings’ cash flows. How participants and investors
exercise this control is of course tied to their investment skill and their success
in achieving a retirement goal. Thus, individual investors who use IRR are using
a return calculation method that takes into account the amount and timing of their
cash flows. Also, returns for periods exceeding 1 year are typically annualized.
An advantage of the IRR method is that it takes into account the amount and timing
of an investor’s cash flows. A disadvantage of the IRR method is that it is possible
to have multiple returns if there are cash inflows and cash outflows within the
same evaluation period. There is no closed “formula” for the IRR and the expression
must be solved iteratively using numerical analysis.
GIPS® (formerly AIMR-PPS) requires calculation of a time-weighted rate of return, which
takes into consideration the cash flows that occur and the market value of the asset
on the beginning and ending period dates. dailyVest makes monthly valuations using
the Modified Dietz Method, which does not require daily valuations. (Although, we
understand that for the majority of our clients daily valuations are available.)
Modified Dietz uses beginning and ending asset values for the period and weights
each cash flow by the amount of time it is invested within that period. Consistent
with GIPS® recommendations, dailyVest treats a "cash flow" as an external flow of
cash and/or securities (capital additions or withdrawals) that is investor initiated.
(Reinvested income is not considered a cash flow. Instead, reinvested income represents
an appreciation/depreciation in the value of the portfolio and must be taken into
account when calculating historical beginning and ending sub-period market values.)
According to their website, "The GIPS standards are a set of ethical principles used
by investment management firms in order to establish a globally standardized, industry-wide
approach to creating performance presentations that communicate investment results to
prospective clients." Full GIPS® compliance is
composed of many components of which calculation methodology is only one. dailyVest
does not and cannot claim “compliance” with GIPS®. It claims only to follow some
of the guidelines contained within the standard relating to calculation methodology.
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