Overview of Back Test Outputs
Total Number of Trades
Total number of trades including buy, sell, and exit trades.
Average Number of Trades per Month
Average number of trades per month, including buy sell, and exit trades.
Number of Profitable Trades
Total number of profitable trades since the beginning of the back test.
Number of Loosing Trades
Total number of un-profitable trades since the beginning of the back test.
Total Profit
Total profit since the beginning of the back test.
Total Loss
Total loss since the beginning of the back test.
Percent Profit
Percentage of profitable trades in since the beginning of the back test.
Largest Profit
Largest single-trade profit.
Largest Loss
Largest single-trade loss.
Maximum Drawdown
The maximum account drawdown, defined as the percent retrenchment from equity peak to equity valley. A drawdown is in effect from the time an equity retrenchment begins until a new equity high is reached.
Maximum Drawdown (Monte Carlo)
Same as Maximum Drawdown, except the test is repeated 5,000 times, with each test introducing a small random slippage. Preferred over regular drawdown.
Value Added Monthly Index (VAMI)
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 ) X Vami N-1
Compound Monthly ROR
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.
Standard Deviation
Measure 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.
Where R I=Return for period I
Where M R=Mean of return set R
Where N=Number of Periods
M R = (Σ R I) ÷ N
I=1
(Σ (R I - M R) 2 ÷ (N - 1)) ½
Annualized Standard Deviation
Standard Deviation X (12) ½
Downside Deviation (MAR = 10%)
Similar to the standard deviation above except the downside deviation considers only returns that fall below a defined Minimum Acceptable Return (MAR) rather than 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 )
((S (L I) 2) ¸ N) ½
I=1
Downside Deviation = ((S (L I ) 2 ) ¸ N ) ½
Where NL=Number of Periods where R I - M < 0
Sharpe Ratio
A measure developed by William Sharpe that 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
M R = (Σ R I) ÷ N
I=1
SD= (Σ(R I - M R) 2 ÷ (N - 1)) ½
I=1
Sharpe Ratio= (M R - R RF) ÷ SD
Sortino Ratio (MAR = 5%)
A 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 ≥ 0 )
DD MAR= ((Σ( L I ) 2 ) ÷ N ) ½
I=1
Sortino Ratio = (Compound Period Return - R MAR) ÷ DD MAR
Annualized Sortino ratio (MAR = 5%)
Annualized Sortino=Monthly Sortino X (12) ½
Calmar Ratio
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.
Sterling Ratio (MAR = 5%)
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. These 3 drawdowns are averaged to produce the Average Yearly Maximum Drawdown for the
3-year period.
Where D1 Calmar Ratio = Average Annual ROR /Worst 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% ))
