## R-Squared

Generally speaking, the R-Squared (R2) of a manager versus a benchmark is a measure of how closely related the variance of the manager returns and the variance of the benchmark returns are. If the benchmark is a Style Benchmark, this can be rephrased by saying: The R2 is a measure of how well the variance of the Style Benchmark explains the variance of the manager.

## Relative Cumulative Excess Return

The relative cumulative excess return is the ordinary cumulative excess return as a percentage of the benchmark's return.

CumRtn(r1, ..., rn) - CumRtn(s1, ..., sn)
CumRtn(s1, ..., sn)

## 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:

## Percentile 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 percentile series plots the actual statistic (return, i.e.) on the vertical axis of the Manager vs. Universe Graph. The universe is represented by colored bands that represent the span of returns for each quartile of the universe.

Here, we are given:

## Pain Ratio

The pain ratio is the analogue to the Sharpe Ratio, with the pain index used instead of the standard deviation:

Pain Ratio = (AnnRtn(r1,...,rn) - AnnRtn(c1,...,cn)) / PainIndex(r1,...,rn)

where:

r1,...,rn = manager return series
c1,...,cn = cash equivalent return series

## Pain Index

There are two ways of describing the definition of the pain index:

## Number of Up & Down Periods

The number of up periods for a given return series r1, ..., rn, is the number of positive returns in the series. Similarly, the number of down periods is the number of zero and negative returns in the series.

## Model Selection

The Advanced Parameters tab in the Edit Analysis Parameters dialog allows the user to set a number of parameters that modify the way the calculations are made.

StyleADVISOR allows the user to modify the mathematical calculation used to analyze a manager's style. This is done on the Advanced Parameter tab in the Edit Analysis Parameters dialog under Model Selection. Changing the model will affect all style weights and style bases, i.e., it will affect the Manager Style and Asset Allocation graphs, as well as everything that involves a Style Benchmark.

## Minimize SC

This is the : .Schwarz Criterion. In this model, the utility function is given by:

SC = m * log( Var(e) / m ) + n * log(m)

where

Var(e) = variance of excess return of manager over benchmark, using current subset
n = number of indices in current subset
m = number of returns

In this model, StyleADVISOR chooses the subset of indices where SC assumes its minimal value.

## Minimize Cp

This is also known as : Mallow's Cp-criterion. In this model, the utility function is given by:

Cp - n = (m - nt) * Var(e) + (n - m) * Var(et)

where

Var(et) = variance of excess return of manager over benchmark, using all indices
Var(e) = variance of excess return of manager over benchmark, using current subset
n = number of indices in current subset

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