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, ..., M_1t
  M₂ = M₂₁, M₂₂, ..., M_2t
  ...
  M_N = M_N1, M_N2, ..., M_Nt

•   a single manager series s₁, ..., s_t running over the same t periods.

We are trying to construct a return series P = p₁, p₂, ..., p_t of percentage ranks such that for each i with 1 <= i <= t, p_i is the percentage rank of the manager return s_i within the set m_1i, , m_Ni of corresponding universe manager returns.

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

1) Order the manager returns m_1i, ..., m_Ni in ascending order, say r₀, ..., r_N-1.
2) Find the two universe managers that the manager falls between, say:
    r_k <= s_i <= r_{k + 1}
3) Interpolate the manager's rank between k and k+1 according the returns:
    rank = k + (s_i - r_k) / (r_k+1 - r_k)
4) Convert rank to a percenage rank with 0% being the top rank and 100% being the
    bottom rank:
    p_i = 100 - (100 * rank / (N - 1)

Related Statistics:
Percentile Series
Volatility of Rank