### Strategy Performance Measurement Ratios

Contents

## Sharpe Ratio

A return/risk measure developed by William Sharpe. Return (numerator) is defined as the incremental average return of an investment over the risk free rate. Risk (denominator) is defined as the standard deviation of the investment returns. In PerTrac, the user enters the value for the risk free rate.

Where R I = Return for period I

Where M R = Mean of return set R

Where N = Number of Periods

Where SD = Period Standard Deviation

Where R RF = Period Risk Free Return

Annualized Sharpe Ratio

Annualized Sharpe = Monthly Sharpe * ( 12 ) ½

Annualized Sharpe = Quarterly Sharpe * ( 4 ) ½ * Quarterly Data

## Sortino Ratio

This is another return/risk ratio developed by Frank Sortino. Return (numerator) is defined as the incremental compound average period return over a Minimum Acceptable Return (MAR). Risk (denominator) is defined as the Downside Deviation below a Minimum Acceptable Return (MAR). Just as with the Downside Deviation calculation, PerTrac calculates the Sortino using 3 different values for the MAR: 1) a MAR defined by the user under Preferences, 2) the Sharpe ratio risk free rate (also set under Preferences), and 3) zero.

Where R_{I} = Return for period I

Where N = Number of Periods

Where R_{MAR} = Period Minimum Acceptable Return

Where DD_{MAR} = Downside Deviation

Annualized Sortino Ratio

Annualized Sortino = Monthly Sortino * ( 12 ) ½

Annualized Sortino* = Quarterly Sortino * ( 4 ) ½

## Calmar Ratio

It is a return/risk ratio. Return (numerator) is defined as the Compound Annualized Rate of Return over the last 3 years. Risk (denominator) is defined as the Maximum Drawdown over the last 3 years. If three years of data are not available, the available data is used. ABS is the Absolute Value.

Calmar Ratio = Compound Annualized ROR * ABS (Maximum Drawdown )

## Sterling Ratio

It is a return/risk ratio. Return (numerator) is defined as the Compound Annualized Rate of Return over the last 3 years. Risk (denominator) is defined as the Average Yearly Maximum Drawdown over the last 3 years less an arbitrary 10%. To calculate this average yearly drawdown, the latest 3 years (36 months) is divided into 3 separate 12-month periods and the maximum drawdown is calculated for each. Then these 3 drawdowns are averaged to produce the Average Yearly Maximum Drawdown for the 3 year period. If three years of data are not available, the available data is used.

Where D1 = Maximum Drawdown for first 12 months

Where D2 = Maximum Drawdown for next 12 months

Where D3 = Maximum Drawdown for latest 12 months

Average Drawdown = ( D1 + D2 + D3 ) * 3

Sterling Ratio = Compound Annualized ROR * ABS ( (Average Drawdown * 10% ))