The following section provides a brief description of each statistic used in PerTrac and gives the formula used to calculate each. PerTrac computes annualized statistics based on monthly data, unless Quarterly data is specified.

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

Average Return (Mean) - This is a simple average return (arithmetic mean) which is calculated by summing the returns for each period and dividing the total by the number of periods. The simple average does not take the compounding effect of investment returns into account.

^{Where N = Number of periods}

Where R _I = Return for period I

_N

Average Return = ( S R _I ) ¸ N

^I=1

Average Gain (Gain Mean) - This is a simple average (arithmetic mean) of the periods with a gain. It is calculated by summing the returns for gain periods (return ³ 0) and then dividing the total by the number of gain periods.

^{Where N = Number of periods}

Where R _I = Return for period I

Where G _I = R _I ( IF R _I ³ 0 ) or 0 ( IF R _I < 0 )

N _G = Number of periods that R _I ³ 0

_N

Average Gain = ( S G _I ) ¸ N _G

^I=1

Average Loss (Loss Mean) - This is a simple average (arithmetic mean) of the periods with a loss. It is calculated by summing the returns for loss periods (return < 0) and then dividing the total by the number of loss periods.

Where N = Number of periods

Where R _I = Return for period I

Where L _I = 0 ( IF R _I ³ 0 ) or R _I ( IF R _I < 0 )

N _L = Number of periods that R _I < 0

_N

Average Loss = ( S L _I ) ¸ N _L

^I=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. In PerTrac, 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

Average Calculation (within the annual returns table) – The average displays a simple average of the displayed statistic; however partial years are considered within the calculation. For example: a fund that has annual returns of 2002 (12.56%), 2003 (2.42%) and a partial 2004 year of 2 months (2.61%) would have an average Annual Return of 8.12%. The result can be achieved by adding (12.56%+2.42%+2.61%) and dividing by 2.167. The denominator of 2.167 was a result of 2 whole years and one sixth of a year (1+1+.1667).

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 = 1}
Annualized Standard Deviation

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

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

* Quarterly Data

Gain Standard Deviation - Similar to standard deviation, except this statistic calculates an average (mean) return for only the periods with a gain and then measures the variation of only the gain periods around this gain mean. This statistic measures the volatility of upside performance.

Where N = Number of Periods

Where R _I = Return for period I

Where M _G = Gain Mean

Where G _I = R _I ( IF R _I ³ 0 ) or 0 ( IF R _I < 0 )

Where GG _I = R _I - M _G ( IF R _I ³ 0 ) or 0 ( IF R _I < 0 )

N _G = Number of periods that R _I ³ 0

_N

M _G = ( S G _I ) ¸ N _G

^I=1

N

Gain Deviation = ( S (GG _I ) ² ¸ (N _G - 1) ) ^½

^I=1

Loss Standard Deviation - Similar to standard deviation, except this statistic calculates an average (mean) return for only the periods with a loss and then measures the variation of only the losing periods around this loss mean. This statistic measures the volatility of downside performance.

Where N = Number of Periods

Where R _I = Return for period I

Where M _L = Loss Mean

Where L _I = R _I ( IF R _I < 0 )or 0 ( IF R _I ³ 0 )

Where LL _I = R _I - M _L ( IF R _I < 0 ) or 0 ( IF R _I ³ 0 )

N _L = Number of periods that R _I < 0

_N

M _L = ( S L _I ) ¸ N _L

^I=1

N

Loss Deviation = ( S ( LL _I) ² ¸ (N _L - 1) ) ^½

^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 is 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). In PerTrac, there are 3 downside deviation calculations, each using a different value for the MAR: 1)Uses a MAR which is defined by the user on the Preferences screen, 2) Uses the Sharpe risk free rate (which can also be defined in Preferences) as the MAR, and 3) uses zero as the MAR.

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 )