## Minimize AIC

This is the : The Akaike Information Criterion. In this model, the utility function is given by:

AIC = m * log( Var(e) / m ) + 2 * n

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

Again, StyleADVISOR chooses the subset of indices where the utility function assumes its minimal value.

## Mean

The mean, or average, of the return series is the sum of the returns divided by their number.

Avg(r1, ..., rn) =

where r1, ..., rn is a return series, i.e., a sequence of returns for n time periods.

## Maximum Drawdown

This is the maximum loss (compounded, not annualized) that the manager ever incurred during any subperiod of the entire time period. Conceptually, the calculation looks at all subperiods of the time period in question and calculates the compound return of the manager over that period. The maximum drawdown is the minimum of zero and all these compound returns.

To view our quick tip video on Maximum Drawdown, click the following link:  http://www.styleadvisor.com/sites/default/files/quick_tip_video/max_draw....

In this model, the utility function is the adjusted R2, i.e., StyleADVISOR chooses the subset of indices that gives the highest adjusted R2. Recall that the adjusted R2 is defined as follows:

Adjusted R2 = 1 - ((m - 1) / (m - n)) * (Var(e) / Var(M))
where
Var(M) = variance of manager returns
Var(e) = variance of excess return of manager over benchmark, using current subset

## Market Line

The Market Line can be plotted on the Manager Risk/Return graph. The capital market line is a straight line that can be drawn in any coordinate system where risk is the x-axis and return is the y-axis. The capital market line is the straight line that connects the point for the cash equivalent and the point for the Market Benchmark in this coordinate system. Any point on this line corresponds to a portfolio consisting of part cash equivalent (possibly shorted) and part Market Benchmark.

## Market Beta: No Limit

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.

## Market Benchmark: Adjust for Beta

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.

Some people feel that calculating any statistic of a manager vs. a Market Benchmark is inherently unfair because in all likelihood, the risk characteristics of the manager and the benchmark are different. Adjusting the Market Benchmark for beta is one possible way to eliminate this unfairness.

## Manager Style Graph Style Points

To understand how StyleADVISOR calculates style points as shown in the style map, it is necessary to understand the concept of a Style Basis. A style basis consists of a set of indices, each of which is assigned to a point in a coordinate system, the so-called Manager Style Graph, or Style Map. The example below shows StyleADVISOR’s default style basis. Here, the Style Basis is the Russell Generic Corners, so each of the four Russell style indices are assigned to points in the style map as indicated.

## Kurtosis

Kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution.

Kurtosis(r1, ..., rn) =

## In-Sample vs. Out-of-Sample

The difference between an in-sample analysis and an out-of-sample analysis lies in the way that the rolling window Style Benchmark is calculated. In the one window case, the Style Benchmark is simply the composite series

S = x1C1 + x2C2 + ... + xNCN

where C1, ... , CN are the index series and x1, ... , xN is set of corresponding style weights.

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