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Statistic | Description |
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Absolute Risk Measures | |
Annual Mean Return | The Cumulative Mean Return multiplied by the periodicity of returns. |
Annualized Semideviation | Semideviation multiplied by the square root of the number of observations in a year given the periodicity of the returns. For example, if you are using monthly returns, you multiply by the square root of 12. |
Annualized Standard Deviation | Annualized Standard Deviation = |
Count Criteria Matches | Count of the number of matching values in an array of time series data based on your specified target value. |
Count of Returns | Count of the returns over the period. You can use this to detect if there are missing observations. For example, if you sold out of a country and the risk statistics are being calculated at the country level. |
Cumulative Mean Return | The sum of the return observations divided by the count of returns. |
Cumulative Standard Deviation | Standard Deviation = RPi is the fund returns |
Cumulative Variance | Square of standard deviation |
Highest Return | Maximum return observation over the period. |
Kurtosis | Describes the "peakedness" of the distribution, and how far return values are from the mean return value of the distribution to help you understand the distribution of returns around the mean. Defined only when the standard deviation is not equal to 0 and at least 4 observations are present. Where:
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Lowest Return | Minimum return observation over the period. |
Median Return | Middle return observation over the period. |
Mode | Value that appears most often in a set of data. |
Semideviation | Semideviation = Where: |
Semivariance | Square of the Semideviation. |
Skewness | Skewness captures the symmetry of the distribution to help you understand the distribution of returns around the mean. Negative skewness implies that the left "tail" of the distribution is longer and there are more values to the right of the mean in the distribution. Defined only when the standard deviation is not equal to 0 and at least 3 observations are present. = The measure of skewness for portfolio Y (or Benchmark X) over period 1 to n months |
Sum | Sum of the selected observation values over the selected period |
Count Up | Count of observations in the period in which the portfolio's performance is above 0 or any tolerance. |
Count Down | Count of observations in the period in which the portfolio's performance is less than 0 or any tolerance. |
Count Flat | Count of observations in the period in which the portfolio's performance and index performance remains the same. |
Target and Downside Risk Measures | |
Annualized Downside Deviation | Annualized Downside Deviation = Where: |
Downside Beta | Downside Beta = Where:
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Downside Deviation | Downside Deviation = |
Downside Variance | Square of downside deviation |
Expected Downside Value | Expected Downside Value = T is either a constant target return (for example, 0%) or represents the average of the returns for the Target Return Benchmark for the period |
Target Sortino Ratio | Sortino Ratio = Where: |
Omega Ratio | The Omega ratio is a measure of risk of an investment asset, portfolio, or strategy that partitions returns into loss and gain above and below a given threshold. The ratio is calculated as: F is the cumulative distribution function |
Relative Risk Measures | |
Annualized Compound Excess | Annualized Compound Excess Return = Where: GLPR is the Geometrically Linked Portfolio Return |
Annualized Daily/Monthly Downside Capture | Ann Rv / Ann Bv Where: Ann Rv = Annualized fund return over the reporting period that includes only days/months when benchmark return was negative. Ann Bv = Annualized benchmark return over the reporting period that includes only days/months when benchmark return was negative. Annualization will be performed only if the number of down months during the reporting period is greater than twelve for monthly frequency and greater than 365 for daily frequency. |
Annualized Daily/Monthly Upside Capture | Ann R^ / Ann B^ Where: Ann R^ = Annualized fund return over the reporting period that includes only days/months when benchmark return was positive. Ann B^ = Annualized benchmark return over the reporting period that includes only days/months when benchmark return was positive. Annualization will be performed only if the number of up months during the reporting period is greater than twelve for monthly frequency and greater than 365 for daily frequency. |
Annualized Information Ratio | Or, T-statistic. |
Annualized Tracking Risk | Annualized Tracking Risk = Where: P is the periodicity of the returns |
Annualized Value Added | Annualized Value Added = |
Compound Excess Return | Compound Excess Return = Where: |
Covariance | Covariance = Where: |
Information Ratio | Information Ratio = |
M-squared | M2 Return = |
Risk-free Sortino Ratio | Sortino ratio using Risk-free rate as the Target return for each period. |
Sharpe Ratio | Sharpe Ratio = |
Tracking Risk | Tracking Risk = |
Treynor Ratio | Treynor Ratio = |
Value Added | Value Added = |
Count Out Performing | Count of observations in the period in which the portfolio's performance is more than the index performance. |
Count Under Performing | Count of observations in the period in which the portfolio's performance is less than the index performance. |
Count In-Line | Count of observations in the period in which the portfolio's performance is the same as the index Performance or any tolerance. |
Cumulative Daily Upside Capture | A statistical measure of an investment manager's overall performance in positive markets. It is used to evaluate how well the manager performed relative to the market portfolio during periods when the index has risen. Calculated as the Portfolio Cumulative Return divided by Market Cumulative Return, using only days when the market return is positive. |
Cumulative Daily Downside Capture | A statistical measure of an investment manager's overall performance in down markets. It is used to evaluate how well the manager performed relative to the benchmark during periods when the index has dropped. Calculated as the Portfolio Cumulative Return divided by Market Cumulative Return, using only days when the market return is negative. |
Batting Average | A statistical measure used to measure an investment manager's ability to meet or beat an index. It is the number of outperforming days divided by the number of total days. Outperforming days occur when the primary portfolio return is greater than the market return. |
CAPM Measures | |
Jensen's Alpha | Jensen's Alpha = |
Annual Average Alpha | Alpha = |
Beta | CAPM Beta = ERMi and ERPi are the excess returns for each of the i time periods |
Coefficient of Determination | Or R2, Coefficient of Determination = |
Coefficient of Non-Determination | Coefficient of Non-Determination = 1 – R2 |
Correlation Coefficient | Correlation Correlation = |
Std Dev (Random Error) | Std Dev (Random Error) = RPE = Portfolio Excess Returns (RP – RF) |
Standard Error of Alpha | Standard Error of Alpha = |
Standard Error of Beta | Standard Error of Beta = |
Drawdown Risk Measures | |
Calmar Ratio | Annual Mean Return divided by Maximum Drawdown. |
Maximum Drawdown | The largest percentage drawdown that has occurred in an investment data record during the defined time period. |
Shortfall Risk | Shortfall Risk = |
Active Calmar Ratio | This measure calculates the ratio using the portfolio's return relative to a market index. It includes an underlying field for a Market Portfolio return which is then subtracted from the Primary Portfolio return in order to calculate the active return for each observation in the analysis period. The Active Calmar Ratio is then calculated by using the active return in place of the portfolio's return. |
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