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:

R2 = R-Squared

Portfolio Risk

This is the one year standard deviation of the portfolio.



where:

Portfolio Risk
wi = weight of asset i
wj = weight of asset j
correlation of asset i with asset j

Portfolio Return

This is a one year portfolio return.



where:

    E[R] = Portfolio Return
    wi = weight of asset i
    E[Ri] = Forcast Return of asset i
    n = number of assets

 
 

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