Primary
Investment Portfolio Performance Calculation Categories Time
Weighted Rate of Return (TWRR) Time-weighted
returns is a measure of the compound rate of return of a portfolio over a stated
period of time. It requires a set of sub-period returns to be calculated whenever
there is an external cash flow, such as a deposit or withdrawal from the portfolio: - Ignores
the effect of the external cash flows; that is, the cash flows from you.
- Represents
the managers performance.
- Dated
external cash flows; investor initiated dated withdrawals and dated contributions
required.
- Cash
flows may occur at irregular intervals; different combinations of days, weeks,
months and years.
- Requires
Market Value entries for Modified Dietz, geometric linking, large cash flows,
and daily valuation performance calculation methodologies.
Geometric
linking, large cash flows geometric linking, and daily valuation performance calculations
require a set of sub-period returns to be calculated whenever there is an external
cash flow, such as a deposit or withdrawal from the portfolio:
- Closed
form calculation.
- Excel
XIRR will not calculate TWRR correctly for most situations.
Money-Weighted,
Dollar-Weighted Rate of Return (MWRR) Dollar-weighted,
money-weighted rate of return, also called the internal rate of return, is the
interest rate that will make the present value of the cash flows from all the
subperiods in the evaluation period plus the terminal market value of the portfolio
equal to the initial market value of the portfolio. The
calculation of a bond's yield to maturity is an example of money-weighted, dollar-weighted
rate of return (IRR): - Factors
all cash flows; contributions and withdrawals.
- Represents
the portfolio's performance.
-
Requires only beginning and ending valuation and all cash flows.
- Cash
flows must occur at regular intervals; days, weeks, months, or years.
-
Iterative calculation.
It's
important to understand the main limitation of the money-weighted return as a
tool for evaluating managers: - Money-weighted
measure does not treat a portfolio manager fairly.
-
Assuming a money-weighted return is calculated over many periods, the algorithm
will tend to place a greater weight on the performance in periods when the account
size is highest; hence the label money-weighted.
TWRR
Performance Calculation Examples The
following data will be used in each of the investment portfolio performance calculation
methodologies explained below: 12/31/2009
Market Value: $100,000 (Close of Business, 01/01/2010 Start) 01/15/2010
Accrued Income Paid: $1,150 04/14/2010
Market Value (Wednesday Close, Thursday 04/15/2010 Open): $103,000 04/15/2010
Investor Withdrawal: -$5,000 11/19/2010
Market Value (Friday Close, Monday 11/22/2010 Open): $99,000 11/22/2010
Investor Contribution: $25,000 | 12/15/2010
Accrued Interest: $3,500 12/21/2010
Market Value $180,000 12/22/2010
Investor Contribution $50,000 12/27/2010
Advisor Fees Paid (Type 2) $2,300 12/31/2010
Market Value: $192,000 Analysis
Range 12/31/2009 - 12/31/2010 One Year |
Algorithms
Simple
R
 | Midpoint
Dietz
 | Modified
Dietz 
| Geometric
Linking 
|
Simple
'ROI' Total
return formula; no unique/correct calculation of cash flows:
| 'ROI'
Reliability/Quality | Return
Calculation Methodology | Annual
Return | Bad
(Unless
no external cash flows.) |
Simple 'ROI' | 12.94% |
Problems - No
accounting for cash flow dates; composition of BMV composed of initial lump sum
or BMV @ Start and net of contributions/withdrawals regardless of date(s) external
cash flows were added to the portfolio.
- The
issue being how much capital was available to generate 'TWRR' during the analysis
range.
- If all
BMV @ Start, 'TWRR' is correct.
- If
not, 'TWRR' is incorrect
- $100,000
BMV: $100,000 @ Start and the net of -$5,000, + $25,000 + $50,000= +$70,000 @
a later and different dates are treated as being included in BMV in this equation
to calculate 'TWRR'.
- If
BMV of $170,000 was available from the beginning of the period, all of it was
used to generate 'TWRR'; OK.
- If
BMV was actually composed of $100,000 available @ Start then, to the extreme,
a net of $70,000 was deposited on the last day, $100,000 was used to generate
'TWRR', not $170,000; not OK.
- No/incorrect
accounting for advisor fees taken or accruals.
Original
Midpoint Dietz The
Original Midpoint Dietz Method approximates when cash flows are received by assuming
that all cash flows (CF) occur at the midpoint of the period and half-weights
the total flows for the period:
| 'TWRR'
Reliability/Quality | Return
Calculation Methodology | Annual
Return | Poor
(Will
significantly understate or overstate returns; unless, by chance, all external
cash flows, large and small, occur @ midpoint date of analysis range.) |
Midpoint Dietz | 16.25% |
Problems - Does
not calculate 'TWRR' based on actual date of cash flows.
- No/incorrect
accounting for advisor fees taken or accruals.
Modified
Dietz The
Modified Dietz Method improves upon the Original Dietz Method by assuming a constant
rate of return on the portfolio during the period, thereby eliminating the need
to know the value of the portfolio on the date of each cash flow. In
an attempt to determine a more accurate return than the Original Dietz Method,
the Modified Dietz Method weights each cash flow by the amount of time each cash
flow is actually held in the portfolio. The
estimate surfers most when a combination of the following conditions exist: (1)
one or more large cash flows occur, (2) cash flows occur during periods of high
market volatility.
| 'TWRR'
Reliability/Quality | Return
Calculation Methodology | Annual
Return | Good
(Noncompliant,
unacceptable in this example because of large 'Investor Contribution' external
cash flows; $25,000
and $50,000) |
Modified Dietz | 21.97% |
To
resolve the 'large cash flows' and 'periods of high market volatility' performance
calculation vulnerabilities of Modified Dietz, beginning January 1, 2010, GIPS
standard require the use of calculation methods that use actual valuation at the
time of large external cash flows. - 'Large'
is not specifically defined by GIPS.
- The
GIPS standards define large cash flow as the level at which the firm determines
that an external cash flow may distort performance if the portfolio is not valued.
Cash
Flows
Modified Dietz Geometric Linking, Large Cash Flows Geometric Linking, and
Daily Valuation Geometric Linking methodologies break the total performance period
into cash flow sub-periods: - Modified
Dietz Geometric Linking: User entered dated Market Values @ user selected time
intervals (Quarters and/or Years, for example), with dated entries for small external
cash flows, advisor fees taken, and accrued cash flows as they occur.
- Modified
Dietz MV1-MV4 and Modified Dietz Geometric Linking MV1-MV2, MV2-MV3, MV3-MV4 performance
calculations my be the same; depending on the size and frequency of small external
cash flows, advisor fees taken, and accruals.
- Large
Cash Flows Geometric Linking: User entered dated Market Values @ user selected
time intervals (Quarters and/or Years, for example) with dated entries for small
external cash flows, advisor fees taken, and accrued cash flows as they occur
and Market Value entry/entries on the date/dates prior to a large external
cash flow(s).
- Daily
Valuation: The actual valuation of the position, account, or portfolio each time
there is an external cash flow; regardless of amount.
- Daily
Valuation can result in generating the most accurate time-weighted rate of return
calculation; however, in most cases performance calculation variances between
Daily and Modified Dietz valuations are so small as to not justify the added input
effort.
Modified
Dietz Geometric Linking, Large Cash Flows Geometric Linking, Daily Valuation Geometric
Linking Sub-period
returns are geometrically linked according to the following formula:
PerfCalc
GIPS 2010 Modified Dietz Geometric Linking, Large Cash Flows Geometric Linking,
Daily Valuation Geometric Linking
The
chief advantage of this method is that Modified Dietz calculates rather than estimates
(as does MWRR) the true time-weighted rate of return. PerfCalc
generates correct, complete, and compliant investment portfolio performance calculations
because Market Values, External Cash Flows, and optional adjustments to profit
(one type of fee and accruals) are better accounted for:
| 'TWRR'
Reliability/Quality | Return
Calculation Methodology | Annual
Return | Better
(Very
reliable performance calculations for most situations.) | Modified
Dietz Geometric Linking and Large Cash Flows Geometric Linking
(GIPS
compliant.) | 25.95% |
Daily
Valuation The
difference between Large Cash Flows Geometric Linking and Daily Valuation Geometric
Linking methodologies is simply one of degrees; Large Cash Flows Geometric Linking;
enter a Market Value @ large external cash flows
only and Daily Valuation Geometric Linking; enter a Market Value @ all external
cash flows: Daily
valuation means valuation, a market value entry, on the date of all external cash
flows — by PerfCalc convention a Market Value on the day prior to an external
cash flow is treated as the starting market value on the day of an external cash
flow. Think
of each methodology from Modified Dietz, to Modified Dietz Geometric Linking,
to Large Cash Flows Geometric Linking, to Daily Valuation Geometric Linking as
zooming in from one Modified Dietz calculation for an analysis range, to a few/many
Modified Dietz geometrically linked Market Value entry analysis ranges, to Modified
Dietz Large Cash Flow Geometric Linking Calculations within the same analysis
range(s), to many geometrically linked Modified Dietz calculations for all external
cash flows within the same analysis range; the more the Modified Dietz calculations
within an analysis range when external cash flows, advisor fees taken, and accruals
occur, the better, the more precise the performance calculation.
| 'TWRR'
Reliability/Quality | Return
Calculation Methodology | Annual
Return | Best
(Most
reliable performance calculations for all situations.) |
Daily Valuation
(GIPS
compliant.) | 25.77% |
In
most cases, entering a market value entry on the date prior to all cash flows
is not worth the added input effort when comparing the results to a Large Cash
Flows Geometric Linking calculation. |
