Rank Series

The Manager vs. Universe graph and table allow you to present the data as a percentile or ranked series. In both cases, every manager is ranked according to the statistic being shown on the graph or table. The universe is then separated into quartiles according to those ranks.

The rank series plots the rank (0% to 100%)on the vertical axis of the Manager vs. Universe Graph. Each of the universe quartiles are represented by equally sized bands.

Here, we are given:

• a universe of N manager series, each running over t periods:

M1 = M11, M12, ..., M1t
M2 = M21, M22, ..., M2t
...
MN = MN1, MN2, ..., MNt
• a single manager series s1, ..., st running over the same t periods.

We are trying to construct a return series P = p1, p2, ..., pt of percentage ranks such that for each i with 1 <= i <= t, pi is the percentage rank of the manager return si within the set m1i, , mNi of corresponding universe manager returns.

To calculate pi for any i with 1 <= i <= t follow these steps:

1) Order the manager returns m1i, ..., mNi in ascending order, say r0, ..., rN-1.
2) Find the two universe managers that the manager falls between, say:
rk <= si <= rk + 1
3) Interpolate the manager's rank between k and k+1 according the returns:
rank = k + (si - rk) / (rk+1 - rk)
4) Convert rank to a percenage rank with 0% being the top rank and 100% being the
bottom rank:
pi = 100 - (100 * rank / (N - 1)

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