Performance Risk Analysis Field Statistics
This section describes the risk and risk adjusted return statistics you can calculate using the Performance Risk Analysis Field and the options you can choose for those statistics.
Risk Return Statistics
The following table lists the risk and risk adjusted return statistics you can calculate using the Performance Risk Analysis Field. The statistics are grouped by type.
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:
|
Lowest Return | Minimum return observation over the period. |
Marginal Contribution to Volatility | The appropriate risk measure for portfolios managed on an absolute basis is the standard deviation. The Marginal Contribution to Volatility helps in decomposing and finding out how each stock/ sector in the portfolio has contributed to the overall portfolio volatility. The variables that get into the calculation of Marginal Contribution are the standard deviation of the asset’s return contribution, and the correlation of that asset’s contribution with the Portfolio’s return. This effect is currently supported only for the dynamic performance models. NOTE: This risk effect requires you to give the returns and the Underlying Weight field as an additional input. The dynamic Abal mapped to the returns field and the new weight field input should be the same for this effect to compute. |
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:
|
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. |
Risk Return Statistic Options
This section describes the options you can configure when you create a Performance Risk Analysis field. A field example is shown in the following figure.
Each statistic has several options, as described in the following table.
Option | Description |
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Precision | PACE uses all the decimal places in the database to calculate the statistic. This setting only impacts the display of the result. |
Frequency | You can calculate risk statistics using monthly, daily and quarterly return frequency. |
Use | Options include:
|
No. of Days in a Year for Annualization | When Daily Data Frequency is chosen you must specify the number of Days in a year to be used to annualize. The default is 252. |
Type | For a description of types and corresponding sub types, refer to "Performance Risk Analysis Field Statistics." |
Sub Type | For a description of types and corresponding sub types, refer to "Performance Risk Analysis Field Statistics." |
Standard Deviation Method | This choice is active for statistics that can be calculated assuming the data represents the full population or is calculated with appropriate degree of freedom reduction, assuming the data represents a sample of the full population. |
Target Return | Active for Target Risk statistics, with the exception of Downside Beta, and for Shortfall Risk. Options for these measures include:
|
Method of Averaging | Method to derive the average returns. The next section has more on this. |
Period Options | Similar to those used for Performance Link Analysis fields, for example 1year, inception-to-date. |
Analyze up to termination date | You can select this check box and a corresponding entity termination date field to prevent the analysis period from extending beyond the termination date for the entity. If the entity has a termination date that falls within the requested period, the analysis period ends at the termination date. For risk fields that require data for more than one entity, the system uses the termination date for the fund entity (primary portfolio). If you plan to select the Use Business Calendar option, selecting this option allows you to use the business calendar for entities that terminate within the reporting period. Otherwise, the number of observations for the terminated entity does not match the business days in the period, and the business calendar check fails for those entities. |
Use Business Calendar | Determines whether to use the business calendar to ensure there are no missing returns. Select this check box to use the entity's business calendar to confirm the expected number of daily and monthly records for each period. If there are any returns missing from the period selected, Eagle Performance returns the field as null. |
Entities and Fields | This section allows you to select the entities and return fields necessary for the calculation. Depending on the risk calculation, you may indicate from one to three entities in the Portfolio/Selection column. For example, you may need to specify a Primary Portfolio, a Market Portfolio, and/or a Target Benchmark. The Underlying field is the return field upon which you are calculating the risk. The Underlying fields are fields from the PERF_SEC_RETURNS table in the PERFORM database. |