Calculation
The initial value of an investment, Vi, does not always have a clearly defined monetary value, but for purposes of measuring ROI, the initial value must be clearly stated along with the rationale for this initial value. The final value of an investment, Vf, also does not always have a clearly defined monetary value, but for purposes of measuring ROI, the final value must be clearly stated along with the rationale for this final value.
The rate of return can be calculated over a single period, or expressed as an average over multiple periods.
Single-period
Arithmetic return
The arithmetic return is defined as the following:
If the final investment value excludes capital gains, then rarith is sometimes referred to as the yield. See also: effective interest rate, effective annual rate (EAR) or annual percentage yield (APY).
If the final investment value includes both capital gains and intermediate income such as dividends, then rarith is the holding period return.
Logarithmic or continuously compounded return
The logarithmic return or continuously compounded return, also known as force of interest, is defined as:
.
It is the reciprocal of the e-folding time.
Multiperiod average returns
Arithmetic average rate of return
The arithmetic average rate of return over n periods is defined as:
Geometric average rate of return
The geometric average rate of return, also known as the time-weighted rate of return, over n periods is defined as:
The geometric average rate of return calculated over n years is also known as the annualized return.
color laser cartridge
没有评论:
发表评论