## Statistic

## Omega

Omega compares the count and scale of individual return points above a minimum accepted return threshold (MAR) against the count and scale of individual return points below the MAR threshold.

## K-Ratio

The Zephyr K-Ratio quantifies two things: the appreciation of wealth and the consistency of that wealth creation.

Like many statistical ratios, the K-Ratio is a return-vs.-risk tradeoff metric, with the numerator being an expression of return and the denominator a measure of risk. The numerator, the measure of return, is the slope of a best-fit regression line superimposed over a cumulative return series. The steeper the slope, the larger the number, the faster the rate of appreciation of wealth.

## Expected Cumulative Return

The Expected Cumulative Return is the Expected Return compounded over *T* periods.

where:

Expected Cumulative Return

Expected Return

* T* = number of periods

## Expected Risk (Standard Deviation)

The Expected Risk is the standard deviation of the Expected Return. As the time horizon increases, the Expected Risk moves towards zero.

where:

Expected Risk

Expected Return

* E*[R] = Portfolio Return

## Expected Return (Annualized)

The Expected Return (Annualized) is the annual Portfolio Return adjusted for variance drain over T periods. For periods longer than one year, the Expected Return is less than the annual Portfolio Return.

where:

Expected Return

*E*[*R*] = Portfolio Return

*V* = variance of portfolio

*T* = number of periods

## Turnover

Turnover shows the total one-way turnover to move from the current portfolio to the efficient portfolio. That is, the proportion of the current portfolio that must be sold.

## Tracking Error

Tracking Error (also known as 'active risk') is the annualized standard deviation of excess return to the benchmark. Like R-Squared, Tracking Error is calculated using the common date range of the benchmark and the weighted portfolio return series.

where:

Tracking Error

*std* = standard deviation

## R-Squared

The R-Squared is the correlation squared of the benchmark to a weighted portfolio return series. Correlation Squared is the classical statistical method for measuring how closely related the variances of two series are. R-Squared is calculated using the common date range of the benchmark and the weighted portfolio return series.

where:

*R*^{2} = R-Squared

## Portfolio Risk

This is the one year standard deviation of the portfolio.

where:

Portfolio Risk

w* _{i}* = weight of asset

*i*

w

*= weight of asset*

_{j}*j*

correlation of asset

*i*with asset

*j*

## Portfolio Return

This is a one year portfolio return.

where:

*E*[*R*] = Portfolio Return

w_{i} = weight of asset *i*

*E*[*R _{i}*] = Forcast Return of asset

*i*

*n*= number of assets