In finance, rate of return (ROR),
or sometimes just return, is the ratio of
money gained or lost on an investment
relative to the amount of money invested. The money invested may be referred to
as the asset, capital, principal, or the cost basis of the investment.

For purposes of measuring ROR, the initial
value V_{i}and
finalvalueV_{f}
must be clearly stated.

Rate of Return (ROR)

In mathematical terms, the Rate of Return (ROR)
is defined as the following:

where V_{i}
is the initial investment value andV_{f}
is the final investment value.

Annual and Annualized Rate of
Return

An Annual Rate of Return is the return on
an investment over a one-year period, such as from January 1, 2006 through
December 31, 2006. An Annualized Rate of Return is the return on an investment
calculated from the return over a period other than one year (such as a month, or two years),
using one of the methods described below, to give a comparable one-year return.

Compound Rate of
Return

In financial
economics, the term compoundROR indicates a
rate of return that is based on compounding,
reinvestment, or the changing market value
of an account. Compound ROR indicates that the
value of the investment increases or decreases
during the investment period. To calculate the
compound rate of return, the investor includes
the reinvested profits in the total investment.
The return depends on the frequency of
compounding/reinvesting. The table below shows
the difference in annual return without/with
monthly profit reinvesting. Over a one year
period, the difference is small if the annual
return is <20%. However, over a multi year
period, compounding can make a big difference -
please try this calculator.

Annual
Rate of Return

Without monthly profit
reinvesting (i.e. without monthly change of the
nominal account size for notionally funded accounts)

With monthly profit
reinvesting (the nominal account size is changed
monthly to reflect the accumulated profit/loss )

1%

1.005%

5%

5.116%

10%

10.471%

15%

16.075%

20%

21.939%

30%

34.489%

40%

48.213%

50%

63.209%

Calculating Annualized Rates
of Return

There are two common ways returns
are calculated over multiple periods of time:

Average Return, or Arithmetic Annualized ROR, or ROR on
fixed capital(which can be
used if the profit is NOT reinvested), and

Compound Return or Geometric Annualized ROR (should be
used if profit is reinvested); also known as
Compound Annual Growth Rate (CAGR). The compound monthly
ROR is required by CFTC Regulation
4.35(a)(6)(i)(F)
for
reporting purposes.

Value Added Monthly Index (VAMI) - Hypothetical Growth
of $1,000

The Value Added Monthly Index (VAMI) is an index
that tracks the monthly performance of a hypothetical $1,000 investment using
monthly compounding (profit reinvestment) method. The calculation for the
n-th month's VAMI is:

where ROR_{n}is the monthly ROR
for the n-th month and VAMI_{n} is the VAMI index at the
end of the n-th month. VAMI is
initialized at 1,000.