Personal Rate of Return/Investment Performance Calculation Methodologies & Assumptions
dailyVest EnterpriseROR implements several investment performance calculation methods
calculating an investor's personal rate of return. Results may be calculated and
rendered in real-time at the individual holding level (one investment), at the plan
or account level containing many holdings, and at a consolidated portfolio or "multi-plan"
level containing many plans/accounts. Furthermore, the user can select any time
period for which analysis is desired.
This section outlines the standards and underlying calculation assumptions employed
by dailyVest’s investment performance calculation engine (also referred to as the
FOM or Financial Object Model) for time-weighted and dollar-weighted
rates of return.
In its performance reporting, dailyVest
uses only calculation methods 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 application notes, this
website or dailyVest software.
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 fund. It measures how well he or she performs in increasing
the dollars that have been invested. Cash flows moving in and out of the fund do
not affect the time-weighted rate of return (unlike with dollar-weighted rates of
return or “IRR”). Time-weighted rates of return can be calculated on a daily basis
(one method known as Daily Valuation) or on a slightly less accurate monthly basis
(known as Modified Dietz) where inflows/outflows are averaged for the month. This
time-weighted methodology used for calculation of personal rate of return provides
a truer measurement of how investments are performing.
Dollar-Weighted Rate of Return.
Dollar-weighted rate of return, or “DWRR” for short, is also known as "Internal
Rate of Return" or simply "IRR." It 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
that inherent capacity in a client's web-based computer system.
About Global Investment Performance Standards (GIPS®).
dailyVest’s FOM is capable of calculating personal investment performance using
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.
Time-Weighted Rate of Return - Modified Dietz...
CALCULATION OF PERIOD RETURNS IN PRESENCE OF CASH FLOWS
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 TWRR.) 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 (contributions to the portfolio are positive
flows, and withdrawals or distributions are negative flows), and…
…is 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, Wi is then calculated as (31–20)/31 = 0.35483871.
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GEOMETRIC LINKING: LINKING PERIOD RETURNS
After computing monthly returns, they are linked geometrically to compute a quarterly
return using this formula…
…where Rqtr is the portfolio quarterly return and Rmonth-1, Rmonth-2, and Rmonth-3
are the portfolio returns for months 1, 2, and 3, respectively. dailyVest computes the annual rate of return from portfolio returns calculated quarterly using the following formula…
… where Rqtr-1, Rqtr-2, Rqtr-3, and Rqtr-4 are returns for Quarters 1, 2, 3, and 4, respectively.
Alternatively, dailyVest may geometrically link the twelve monthly returns to calculate
the annual return.
PROS/CONS: TIME WEIGHTED RATE OF RETURN - MODIFIED DIETZ
The chief advantage of the Modified Dietz Method is that it does not require portfolio
valuation on the date of each cash flow. (This is not usually an issue with dailyVest's
customer systems since daily account valuations are usually a de-facto standard.)
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:
- one or more large cash flows occur;
- cash flows occur during periods of high market volatility
dailyVest customers should note that the Modified Dietz approximation method
will not conform with GIPS® standards beginning 1 January 2010 when the Standards
will likely require the use of calculations methods that use actual valuations
at the time of external cash flows (such as with the Daily Valuation method).
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Time-Weighted Rate of Return - Daily Valuation...
ACTUAL VALUATIONS AT TIME OF EXTERNAL CASH FLOWS
The actual valuation of the position, account or 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 dailyVest customer 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.
PROS/CONS: TIME WEIGHTED RATE OF RETURN - DAILY VALUATION
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.
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Dollar-Weighted Rate of Return ("IRR")...
IRR MODIFIED TO TAKE INTO ACCOUNT EXACT TIMING OF EACH CASH FLOW
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, dailyVest software
uses iteration to solve the following equation for the 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…
…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.
For example, if a cash flow occurred on January 20th, Wi is then calculated as (31–20)/31
= 0.35483871. (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…
Where the value of R can be obtained by iterating through values of R until the
result equals EMV.
NOTES ON THE IRR METHOD
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.
PROS/CONS: IRR METHOD
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.
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Calculation Assumptions for Annualized Returns...
ANNUALIZING RETURNS
Investors often need to see returns for multi-year periods reflected on an annualized
basis. Annualized returns for such periods show the equivalent yearly return for
each of the years within the multi-year period that that would have been needed
to achieve the overall period return.
dailyVest's FOM performance calculation engine readily calculates returns for each
of the individual years (and partial years) within the overall period, but since
returns fluctuate from year-to-year, investors may want to know what single rate
of return would have needed to be achieved each year within the overall period to
arrive at the overall period return.
…where Rmultiyear is the overall period return for the multi-year period expressed
as a decimal and “n” is the number of years in the multi-year period.
EXAMPLE: ANNUALIZED RETURNS FOR WHOLE YEAR PERIODS
Assume a 5-year period return of 31.54% and assume the following sub-period
returns were actually achieved: Year 1 = 3.75%, Year 2 = 6.21%, Year 3 = 4.83%,
Year 4 = 8.45%, Year 5 = 5.01% As can be seen, each year’s return varies between
a minimum of 3.75% and maximum of 8.45%. What equivalent return (i.e., “annualized
return”) would be required to achieve a 31.55% return for the overall 5-year period?
Using the formula above, the “Rannualized” = 5.6359%. So, it can be said that
the 31.55% return for the 5-year period could also have been achieved had we had
annual returns of 5.63% for each of the 5 years. This can be proved by geometrically
linking the 5-year returns of 5.63%.
EXAMPLE: ANNUALIZED RETURNS FOR FRACTIONAL YEARS
Investors may want to see an annualized return for a period which includes a fractional
year. dailyVest software handles scenarios like this using the same method above.
Assume an investor wants to know the annualized return since account inception,
which in this case is assumed to be 18 months (1½ years). If the period return since
inception is 21.39%, then the annualized return is computed as 13.74%, or...
While this example was done for illustration mainly, dailyVest software uses days
instead of months when calculating the nth root. This is more accurate since not
all months have the same number of days. dailyVest DOES NOT annualize returns for
periods less than one year. Doing so would be inaccurate, since the period is too
short to attempt to derive a return for a year from it. This is also a standard
industry practice.
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Comparison of Dollar-Weighted and Time-Weighted Methodologies...
| Time-Weighted Rate of Returns (“TWRR”) |
Dollar-Weighted Rate of Returns (“DWRR”) |
DEFINITION:
The return produced over time by a fund independent of contributions or withdrawals.
Measures a fund’s compounded rate of growth over a specified time period.
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DEFINITION:
IRR is the discount rate that equates the cost of an investment with the cash
generated by that investment. IRR tracks the performance of actual dollars invested
over time.
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MAJOR DIFFERENCES:
1.) Time-weighted returns are not affected by the size
of interim cash inflows or outflows. The return for
each period is calculated based on the amount of money
in the portfolio at the start of each period.
2.) Time-weighted returns split up the time for which
a return is going to be calculated into equal sub-periods. Time-weighted returns
also tie these sub-period returns together to form the final rate of return using
geometric linking. By geometrically linking the returns from each sub-period a time-weighted
return eliminates any skewing of returns that will be calculated when large cash
flows move though an investment.
Note: TWRR is used to measure the performance of public fund managers, according
to GIPS® recommendations because it eliminates the impact of the timing of fund
cash flows and isolates the portion of a portfolio’s return that is attributable
solely to the manager’s actions. It is used by public fund managers because they
normally do not control cash flowing into or out of their funds. (This recommendation
of course does not exclude use of this method by individual investors.)
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MAJOR DIFFERENCES:
1.) Dollar-weighted returns do reflect cash inflows and outflows, as well as the
investment performance of the funds chosen by the investor. Dollar-weighted
returns can be heavily changed depending on if and when large cash flows in
and/or out of an investment occur.
2.) IRR does not split up the time period into equal sub-periods;
instead it searches for a constant rate of return for one entire time period.
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About the Global Investment Performance Standards (GIPS®)...
ADHERENCE TO RECOMMENDATIONS
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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