| Several of the statistics can be calculated using either an arithmetic or geometric linking method used to derive the fund, benchmark and risk free returns used in the risk statistics. |
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The statistics using either an arithmetic or geometric linking method are described in the following table.
Measure | Arithmetic Linking | Geometric Linking |
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Value Added | Sum of the Excess Returns (Rpi–Rmi) divided by the Count of Returns. | (Single Period Geometrically Linked Portfolio Return–Single Period Geometrically Linked Market Return). |
Annualized Value Added | (Arithmetic Value Added) * nObsPerYear. | (Annualized Period Geometrically Linked Portfolio Return–Annualized Period Geometrically Linked Market Return). |
Information Ratio | (Arithmetic Value Added) divided by Standard Deviation of Excess Returns (Tracking Risk). | (Geometric Value Added) divided by Standard Deviation of Excess Returns (Tracking Risk). |
Annualized Information Ratio | (Arithmetic Annualized Value Added) divided by (Annualized Tracking Risk). | (Geometric Annualized Value Added) divided by (Annualized Tracking Risk). |
Sharpe Ratio | (Annual Mean Portfolio Return–Annual Mean Risk Free Rate) divided by Annualized Standard Deviation of Portfolio Return. | (Annualized Geometrically Linked Portfolio Return–Annualized Geometrically Linked Target Return) divided by Annualized Standard Deviation of Portfolio Return. |
Treynor Ratio | (Annual Mean Portfolio Return–Annual Mean Risk Free Rate) divided by the Portfolio Beta. | (Annualized Geometrically Linked Portfolio Return–Annualized Geometrically Linked Target Return) divided by the Portfolio Beta. |
Sortino Ratio | (Annual Mean Portfolio Return–Annual Mean Risk Free Return) divided by the Annualized Downside Deviation. | (Annualized Geometrically Linked Portfolio Return–Annualized Geometrically Linked Target Return) divided by the Annualized Downside Deviation. |
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When Daily Data Frequency is chosen you must specify the number of Days in the year to annualize. The default is 252.
There are some subtleties involving different data frequencies and annualized risk statistics. Daily annualized return values can differ slightly from monthly or quarterly annualized returns. For example, consider 2 years of monthly data. For annualized returns, the cumulative returns for two years are raised to (12 / 24) in the case of monthly frequency and (4 / 8) for quarterly frequency. The annualized values are the same.
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- 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,
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The Drawdown Measures Type option includes 10 drawdown risk measures. A drawdown is any losing period during an investment record. Drawdown is defined as the percent retrenchment from a peak to a valley. A drawdown is from the time a retrenchment begins until a new high is reached.
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- Active Max Drawdown Date
- Active Max Drawdown Duration Period Count
- Active Max Drawdown Duration Start and End
- Active Max Drawdown Period Count
- Active Max Drawdown Recovery Date
- Active Max Drawdown Recovery Period Count
- Active Max Drawdown Start Date
- Active Maximum Drawdown
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You can use benchmark returns as target returns when you define certain risk measures. This applies to Annualized Downside Deviation, Downside Deviation, Downside Variance, Expected Downside Value, Target Sortino Ratio, and Shortfall Risk.
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Otherwise, if you define these measures using a Target Return field set to Constant, the risk calculations use a fixed numeric value you specify as the target return value for all funds and time periods.
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M-Squared Ratio is the risk adjusted return measure named for Modigliani and Modigliani.
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