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
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 = Where: P is the periodicity (or number of return observations in a year) If you are using monthly returns, multiply by the square root of 12.
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 = Where: RPi is the fund returns RP is the average fund return N is the count of returns –- is the average
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: = The measure of kurtosis for portfolio Y (or Benchmark X) over period 1 to n months = The return for the parameter in question (portfolio or benchmark) for month i = The mean (average) for the parameter in question (portfolio or benchmark) over the period 1 to n months s = The standard deviation for the parameter in question (portfolio or benchmark) over the period 1 to n months n = Number of months in period
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. M3=nn-1n-2i-1nxi-xs3 Where: = The measure of skewness for portfolio Y (or Benchmark X) over period 1 to n months = The return for the parameter in question (portfolio or benchmark) for month i = The mean (average) for the parameter in question (portfolio or benchmark) over the period 1 to n months s = The standard deviation for the parameter in question (portfolio or benchmark) over the period 1 to n months n = Number of months in period
Sum	Sum of the selected observation values over the selected period
Count Up	Manager's performance is above 0 or any tolerance.
Count Down	Manager's performance is less than 0 or any tolerance.
Count Flat	Manager's performance and index performance remains the same.
Target and Downside Risk Measures
Annualized Downside Deviation	Annualized Downside Deviation = Where: T is either a constant target return or represents the average of the returns for the Target Return Benchmark for the period
Downside Beta	Where: = Return of the portfolio at time t = Return of the market portfolio at time t = Target return for the portfolio = Target return for the market portfolio The target returns and are adjustable. They can be set as: The average portfolio return, and the average market return, The average risk free return Any other constant target such as 0 Time varying risk free returns For more information, refer to Downside Beta.
Downside Deviation	Downside Deviation = Where: T is either a constant target return or represents the average of the returns for the Target Return Benchmark for the period
Downside Variance	Square of downside deviation
Expected Downside Value	Expected Downside Value = where Where: 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: T is either a constant target return or represents the average of the returns for the Target Return Benchmark for the period. Arithmetic linking: (Annual Mean Portfolio Return–Annual Mean Target Return) divided by the Annualized Downside Deviation. Geometric linking: (Annualized Geometrically Linked Portfolio Return–Annualized Geometrically Linked Target Return) divided by the Annualized Downside Deviation.
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: Where: F is the cumulative distribution function r is the threshold defining the gain versus the loss a,b are the investment intervals
Relative Risk Measures
Annualized Compound Excess Return	Where: GLPR is the Geometrically Linked Portfolio Return GLMR is the Geometrically Linked Market Return
Annualized Information Ratio	Or, T-statistic. Annualized Information Ratio =
Annualized Tracking Risk	Annualized Tracking Risk = Where: P is the periodicity of the returns
Annualized Value Added	Annualized Value Added =
Compound Excess Return	Where: GLPR is the Geometrically Linked Portfolio Return GLMR is the Geometrically Linked Market Return
Covariance	Where: _p is the average of the portfolio returns (Rp_j) _b is the average of the benchmark returns (Rb_j)
Information Ratio	Information Ratio =
M-squared	M² Return = For more information, refer to Geometric M-Squared Ratio.
Risk-free Sortino Ratio	Sortino ratio using Risk-free rate as the Target return for each period. The T in the Target Sortino Ratio formula numerator is replaced by the Risk-free rate and the T in the denominator is replaced by the Target Return in the Field Attribute definition.
Sharpe Ratio	Sharpe Ratio = Where: RF is the risk-free returns
Tracking Risk	Tracking Risk = Where: D is the difference between the fund and benchmark returns
Treynor Ratio	Treynor Ratio =
Value Added	Value Added = Where: RM is the benchmark returns
Count Out Performing	Manager's performance is more than the index performance.
Count Under Performing	Manager's performance less than the index performance.
Count In-Line	Manager'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 = Where: ERMi and ERPi are the excess returns for each of the i time periods ERM is the average excess return of the market (RM – RF) ERP is the average excess return of the portfolio (RP – RF)
Coefficient of Determination	Or R₂, Coefficient of Determination =
Coefficient of Non-Determination	1 – R₂
Correlation Coefficient	Correlation =
Std Dev (Random Error)	Where: RPE = Portfolio Excess Returns (RP – RF) RME = Benchmark Excess Returns (RM – RF)
Standard Error of Alpha
Standard Error of Beta
Drawdown Risk Measures
Calmar Ratio	Annual Mean Return divided by Maximum Drawdown. For more information, refer to Drawdown Risk Measures in Chapter 3 of this book.
Maximum Drawdown	The largest percentage drawdown that has occurred in an investment data record during the defined time period. For more information, refer to Drawdown Risk Measures
Shortfall Risk	Shortfall Risk = Where: TargetReturns is either a constant target return or represents the average of the returns for the Target Return Benchmark for the period For more information, refer to Drawdown Risk Measures.
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
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: Preliminary Returns. All the returns, both Final and Preliminary, are retrieved when calculating the statistic. Final Returns. Only the returns that have been marked as Final in the PERFORM database are retrieved when calculating the statistic.
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: Average Target Benchmark. Defines the target return as the average return of a specified entity or type of benchmark over the specified analysis period. The target return value can vary based on the fund being analyzed. If you select this option, you must select Target Benchmark values in the Entities and Fields section of this dialog box to specify a target benchmark portfolio or relationship. For more information, see "Using Benchmark Returns as Target Returns in Target Downside Measures." Constant. (Default) Allows you to specify a static value for the target return. Calculations use this target return value for all funds and time periods. If you select this option, you must specify a corresponding numeric value in the adjacent field. The default numeric value is 0. Active for CAPM risk statistics. Options for CAPM measures include: Average Risk Free. The mean of the risk free observations is calculated internally and is used for the risk free rate. Risk Free. The legacy value for CAPM Measures. Constant. Provides a constant value risk free rate. Allows you to specify a fixed rate of return for the Risk Free Return Rate (for example, a constant 5%) rather than having to provide a full time series of risk free returns specified for an entity.
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. For more information, refer to "Performance Link Analysis Field Options."
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. Options include: 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 specified, Eagle Performance returns the field as NULL. Leave the check box cleared to prevent use of the business calendar. The risk calculation runs for the returns that are in the database for the specified period.
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.