Average Up and Down Returns

To calculate this statistic for a given return series r1, ..., rn, the program partitions the series in two parts, one made up of the positive returns, the other of the zero and negative returns. The average up and down returns are the respective averages of these two series.

Average Up Return = 

Average Down Return = 

where

    l = NumUpPeriods
    u1, ..., ul = the positive returns in r1, ..., rn
    m = NumDownPeriods
    d1, ..., dm = the non-positive returns in r1, ..., rn

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