### Averages for Performance Measurement

The 5 kinds of averages used for performance measurement are given below:

## Average Return (Mean)

It is calculated by summing the returns for each period and dividing the total by the number of periods.  The Average Return does not take the compounding effect of investment returns into account.

Where N = Number of periods
Where R I = Return for period I

## Average Gain (Gain Mean)

It 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.  Example: when calculating Average Gain for 36 months, we will average only the monthly returns which are positive.

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

## Average Loss (Loss Mean)

It 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.  Example: when calculating Average Gain for 36 months, we will average only the monthly returns which are negative.

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

## Compound (Geometric) Average Return

It 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 Final Equity which is same as that arrived by actual trades. Generally, the compound quarterly and annualized returns are calculated using the compound monthly return as a base.

Where N = Number of periods

Bal(0) =  100000 (Initial account balance)

Bal(N) =                 (balance after N trades)

Compound Monthly Return =  ( Bal N  ¸ Bal 0 ) 1/ N  – 1

Compound Quarterly Return = ( 1 + Compound Monthly ROR ) 3 – 1

Compound Annualized Return = ( 1 + Compound Monthly ROR ) 12 – 1

## Average Holding Time

Average holding time of a trade is measured by dividing the total exposure time of all trades by number of trades. If two strategies which have same Net Profit but different holding time, the strategy with less average holding time is preferable.

Also, for trend following strategies, the average holding time of winning trades should be more than average holding time of losing trades.