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STATISTICS USED IN PERFORMANCE ANALYSIS

The following provides a brief description of each statistic used in our analysis and gives the formula used to calculate each. Annualized statistics are based on monthly data, unless Quarterly data is specified.

VAMI Sortino Ratio
Compound Average Return Calmar Ratio
Standard Deviation Sterling Ratio
Downside Deviation Drawdown
Sharpe Ratio Maximum Drawdown

Value Added Monthly Index (VAMI) - This index reflects the growth of a hypothetical $1,000 in a given investment over time. The index is equal to $1,000 at inception. Subsequent month-end values are calculated by multiplying the previous month’s VAMI index by 1 plus the current month rate of return.

Where Vami 0=1000 and
Where R N=Return for period N

Vami N=( 1 + R N ) ´ Vami N-1


Compound (Geometric) Average Return - The geometric mean is the monthly average return that assumes the same rate of return every period to arrive at the equivalent compound growth rate reflected in the actual return data. In other words, the geometric mean is the monthly average return that, if applied each period, would give you a final Vami (growth) index that is equivalent to the actual final Vami index for the return stream you are considering. Annualized compound quarterly and annualized returns are calculated using the compound monthly return as a base.

Where N=Number of periods

Where Vami 0=1000

Compound Monthly ROR=( Vami N ¸ Vami 0 ) 1/ N - 1

Compound Quarterly ROR=( 1 + Compound Monthly ROR ) 3 - 1

Compound Annualized ROR=( 1 + Compound Monthly ROR ) 12 - 1


Standard Deviation - Standard Deviation measures the dispersal or uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be. For this reason, standard deviation is often used as a measure of investment risk.

Where R I=Return for period I

Where M R=Mean of return set R

Where N=Number of Periods

N

M R =( S R I ) ¸ N

I=1

N

Standard Deviation=( S ( R I - M R ) 2 ¸ (N - 1) ) ½

I=

Annualized Standard Deviation

Annualized Standard Deviation=Monthly Standard Deviation ´ ( 12 ) ½

Annualized Standard Deviation * =Quarterly Standard Deviation ´ ( 4 ) ½

* Quarterly Data

M G = ( S G I ) ¸ N G

I=1


Downside Deviation - Similar to the loss standard deviation except the downside deviation considers only returns that fall below a defined Minimum Acceptable Return (MAR) rather then the arithmetic mean. For example, if the MAR were assumed to be 10%, the downside deviation would measure the variation of each period that falls below 10%. (The loss standard deviation, on the other hand, would take only losing periods, calculate an average return for the losing periods, and then measure the variation between each losing return and the losing return average).

Where R I=Return for period I

Where N=Number of Periods

Where R MAR=Period Minimum Acceptable Return

Where L I=R I - R MAR ( IF R I - R MAR < 0 )or 0 ( IF R I - R MAR ³ 0 )

N

Downside Deviation=( (S ( L I ) 2 ) ¸ N ) ½

I=1

Downside Deviation = ( (S ( L I ) 2 ) ¸ N ) ½

I

Where NL=Number of Periods where R I - M < 0

N


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.

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

N

M R =( S R I ) ¸ N

I=1

N

SD=( S ( R I - M R ) 2 ¸ (N - 1) ) ½

I=1

Sharpe Ratio=( M R - R RF ) ¸ SD

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).

Where R I=Return for period I

Where N=Number of Periods

Where R MAR=Period Minimum Acceptable Return

Where DD MAR=Downside Deviation

Where L I=R I - R MAR ( IF R I - R MAR < 0 )or 0 ( IF R I - R MAR ³ 0 )

N

DD MAR=( (S ( L I ) 2 ) ¸ N ) ½

I=1

Sortino Ratio=( Compound Period Return - R MAR ) ¸ DD MAR

Annualized Sortino Ratio

Annualized Sortino=Monthly Sortino ´ ( 12 ) ½

Annualized Sortino* =Quarterly Sortino ´ ( 4 ) ½

* Quarterly Data


Calmar Ratio - This 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.


Sterling Ratio - This 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 Calmar Ratio = Compound Annualized ROR ¸ ABS (Maximum Drawdown)

= 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% ))


Drawdown - Drawdown is any losing period during an investment record. It is defined as the percent retrenchment from an equity peak to an equity valley. A Drawdown is in effect from the time an equity retrenchment begins until a new equity high is reached. (i.e. In terms of time, a drawdown encompasses both the period from equity peak to equity valley (Length) and the time from the equity valley to a new equity high (Recovery).

Maximum Drawdown is simply the largest percentage drawdown that has occurred in any investment data record.

 

 

 

 

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