Geometrically Linked Versions of Risk Statistics

Daily Risk Statistics

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.

However, for daily frequency the cumulative returns are raised to (365 / actual number of days found in 2 years). The denominator varies depending on how many returns are available in the PERF_SEC_RETURNS table during those 2 years.

Additionally, enabling the business calendar on option has an effect on this. It is not necessarily twice of 365, for example, 730. Even if returns are available for all the calendar days, the denominator can be 731, if one of the years is a leap year.
Hence, the daily annualized return value can differ from the monthly or quarterly annualized return value.

Downside Beta

The Capital Asset Pricing Model treats risk equally across both down and up markets. However, finance literature suggests that at least a portion of investors place more importance on losses compared to gains. Such loss aversion causes these investors to expect to receive a return premium for holding assets with greater downside risk. This leads to the specification and implementation of measures that can be used to assess investor exposure to one sided downside risk.

Beta, the CAPM measure of risk, is the covariance between excess stock returns and the excess market return divided by the variance of the excess market return.

where:
= covariance of a portfolio's returns to the excess market returns.
= variance of the excess market returns

The problem with beta is it treats gains the same as losses, yet investors like gains while only perceiving the losses as risk. A high-beta can be the result of the portfolio gaining more than the market when the market goes up even though the portfolio does not lose more than the market when the market goes down.

The downside beta, , is defined as:

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,   .

Drawdown Risk Measures

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.

Maximum Drawdown is the largest percentage drawdown that has occurred in an investment data record during a defined time period (any length).

The Calmar ratio is calculated by taking the Compound Annualized Rate of Return (the Eagle Performance Annual Mean Return statistic) over the last three Years and dividing by the value of the Maximum Drawdown over the last 3 years (default time period). It measures the return in comparison to the greatest amount of risk over the period.

The Shortfall Risk statistic is part of the Drawdown Measures Type option.

There are also seven Max Drawdown measures available for the period that provided the Max Drawdown or the Max Drawdown Duration. These are two different drawdown periods. Max Drawdown identifies the period associated with the largest percentage drop in return and recovery. Max Drawdown Duration identifies the longest drawdown period and recovery regardless of the percentage drop in return.

The five measures for Max Drawdown period are:

• Max Drawdown Start Date
• Max Drawdown Date
• Max Drawdown Recovery Date
• Max Drawdown Period Count
• Max Drawdown Recovery Period Count

The two measures for Max Drawdown Duration period are:

• Max Drawdown Duration Start and End
• Max Drawdown Duration Period Count

In addition, there are eight Active Drawdown risk measures that measures portfolio drawdown relative to a market index rather than calculating an absolute drawdown.

These eight active measures are configured and calculated similarly to the absolute measures. The active configuration includes an underlying field for a Market Portfolio return which is subtracted from the Primary Portfolio return in order to calculate the active return for each observation in the analysis period. The drawdown calculations are then run using the active return in place of the portfolio's return.

The eight Active Drawdown risk measures are:

• 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

Use Benchmark Returns as Target Returns for Target Downside Measures

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.

When you create the Performance Risk Analysis fields for these measures, you can define 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. You can assign a:

• Constant target return for all entities using the same target return benchmark. The benchmark assigned for that relationship can be a market return or target return that changes over time. All funds assigned to this benchmark use the same target return which changes based on the average return for the analysis period. When you define the risk field, you set the Target Return field to Average Target Benchmark. Then in the Entities and Fields area, you identify the target benchmark relationship.

An example follows where you select a target benchmark relationship. The benchmark assigned for that relationship is named 1percent and has the same 1% return value for all observations at the expected frequency and for the expected date range. In this case all funds with the 1 percent benchmark assigned to the relationship have the same target return. You can assign a second benchmark for that relationship named 2percent. All funds compared to that benchmark have a target return of 2%. In this way, the same field attribute is used but it has different constant target returns based on the benchmark assigned for the fund being analyzed.

• Dynamic target return. The assigned benchmark can be a market return or target return that changes over time. All funds assigned to this benchmark use the same target return which changes based on the average return for the analysis period. When you define the risk field, you set the Target Return field to Average Target Benchmark. Then in the Entities and Fields area, you identify the target benchmark portfolio or the target benchmark relationship.

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.

Geometric M-Squared Ratio

M-Squared Ratio is the risk adjusted return measure named for Modigliani and Modigliani.

Unlike the Sharpe Ratio, the M-Squared Ratio attempts to measure the return result as if the portfolio had taken on the same level of risk (standard deviation) as the market. This return is the expected rate of return that would be earned by the portfolio if it was levered up or down so that its standard deviation was equal to that of the benchmark. Eagle Performance implements a full geometric variant of M-squared.

 Click the thumbnail to preview an example of the Geometric M-Squared Ratio. Once in preview mode, you can download to view the full file.