Performance Risk Analysis Field Statistics

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.

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. 

Note: This risk effect requires you to give the returns and the Underlying Weight field as an additional input. For Dynamic Performance models, 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.


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

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: 

T is either a constant target return or represents the average of the returns for the Target Return Benchmark for the period

Downside Beta

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:

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

Annualized Compound Excess Return =  

Where:

GLPR is the Geometrically Linked Portfolio Return
GLMR is the Geometrically Linked Market 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 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

Compound Excess Return =  

Where:
GLPR is the Geometrically Linked Portfolio Return
GLMR is the Geometrically Linked Market Return

Covariance

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

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 =

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

Coefficient of Non-Determination = 1 – R₂

Correlation Coefficient

Correlation Correlation = 

Std Dev (Random Error)

Std Dev (Random Error) = 

Where:

RPE = Portfolio Excess Returns (RP – RF)
RME = Benchmark Excess Returns (RM – 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.
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.

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. 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.