Return Calculations
Cumulative Return
For the fund and benchmark, the cumulative return gives the compounded daily return over the entire valuation period. The precise calculation is as follows:
The cumulative active return is simply
Return Over a Sub-period
It may be useful to have the notion of cumulative returns from the kth period to the lth period during the valuation period. We will denote this by R[k:l]. This is calculated as follows:
Note that R[1:n] is the cumulative return over the valuation period and R[k:k] is the return for period k. It is also convenient at times to define R[1:0] = 0.
Annualized Return
The annualized return gives the return if the cumulative return were compounded over a full year. The calculation is as follows:
The annualized active return is
Cumulative VAMI
The term VAMI is an acronym for Value Added Monthly Index and represents the return on a hypothetical $1,000 investment at the beginning of the valuation period.
where R is the cumulative return over the valuation period (for either the Fund or the Benchmark).
The active VAMI simply gives the difference between the Fund VAMI and the Benchmark VAMI.
Worst X Months
The Worst X Months statistic displays the lowest cumulative return of any X consecutive month period. For example, the worst 3 months is the cumulative return over the 3 consecutive months with the lowest cumulative return.
Best X Months
Defined analogously to Worst X Months.
Worst Month
The Worst Month statistic displays the cumulative return of the month with the lowest return.
Best Month
Defined analogously to Worst Month.
Valley
The valley is the least cumulative return of the portfolio over the valuation period. If looking at a graph of the cumulative return of the fund over the course of the valuation period, the valley would be the lowest point on the graph.
The active valley the difference between the Fund's valley and the Benchmark's valley.
Peak
The peak is the greatest cumulative return of the portfolio over the valuation period. If looking at a graph of the cumulative return of the fund over the course of the valuation period, the peak would be the highest point on the graph.
Batting Average
The batting average is the percentage of days in the valuation period that returns were greater than zero. It is calculated as follows:
