About Your Personal Rate of Return...
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 calculation methods for
determining your personal rate of return.
Time-Weighted
Rate of Return
Your personal rate of return was calculated using a
"time-weighted rate of return" method. Time-weighted rates of return take into account the amount of time an investor has been
invested in a certain security such as a stock or mutual fund. It measures how
well the investor performed in increasing the dollars that were invested and
provides a truer measurement of how investments have performed. Cash flows such
as contributions moving in and out of the investment(s) do not affect the
time-weighted rate of return. To be exact, your personal rate of return was
calculated using the time-weighted rate of return "Modified Dietz"
method where inflows and outflows are averaged for the entire period (no
monthly chaining).
Modified
Dietz Method Details...
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.
Time-weighted rate of 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.