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Trading Performance and Statistics |
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The following section provides detailed trading performance statistics, as well as a list of the assumptions used for the particular test.
Many of the statistics listed below deal with risk and return. Appendix I - Risk and Return contains a supplement that discusses these concepts in more detail than is permitted here. If you are new to the world of trading system design, or would like an overview of the concepts underlying the use of risk-adjusted return measurements, please skip ahead to Appendix I - Risk and Return before proceeding with this section.
Summary Performance and Ratios
CAGR% Compounded Annual Growth Rate; this is the annual percentage rate at which an account must continually grow over the period of the study, in order to attain the ending value from the starting value. Synonymous with Geometric Mean Return.
RAR% Regressed Annual Return.Slope of the linear regression of all the points in the equity curve. See page 186 of Way of the Turtle for more information.
Maximum Total Equity Drawdown% Max Total Equity Drawdown (Max DD) is a one-time event that reflects the largest retracement relative to a previous equity high in the entire simulation. It is based on a daily, marked-to-the-market assessment. Expressed as a percentage, this statistic is sampled peak-to-valley, using Total Equity. It conveys the maximum pain an investor would have had to endure over the life of the study in order to achieve the resulting return.
MAR Ratio Often referred to as a pain-to-gain ratio, this risk-adjusted return metric was developed by Managed Accounts Review for ranking Commodity Trading Advisors (CTAs).
MAR Ratio = CAGR / Max Total Equity Drawdown
R-Cubed (R3) Robust Risk/Reward Ratio. uses the RAR% in the numerator and the length-adjusted average maximum draw down in the denominator. The average maximum draw down is computed by taking the five largest draw downs and dividing by 5. The length adjustment is made by taking the average maximum draw down length in days and dividing it by 365 and then multiplying that number by the average maximum draw down. See page 188 of Way of the Turtle for more information.
Modified Sharpe Ratio The Sharpe Ratio is the classic measure of return vs. risk. Developed by Nobel Laureate and (now) Stanford professor William F. Sharpe, it divides excess return by standard deviation to determine reward per unit of risk. (The higher the Sharpe ratio, the better the risk-adjusted performance.) This modified version divides annualized return by annualized standard deviation of returns, using monthly data points. Exclusion of the risk-free-rate in the numerator makes this measure less sensitive to changes in leverage:
Modified Sharpe Ratio = Annualized Return / Annualized Std Dev
Return = 12* Average Monthly Return
Risk Free Rate (excluded)
Annualized Std Dev = Square Root (12) * Std Dev Monthly Returns
Annual Sharpe Ratio This more traditional form of the Sharpe Ratio divides excess annual return by the standard deviation of annual returns to determine reward per unit of risk. Uses actual annual calendar returns:
Annual Sharpe Ratio = (Return - RFR) / Std Dev
Return = Compounded Annual Growth Rate
Risk Free Rate = Computed from the annual risk free rate as set in the TradingBlox.ini file converted to a compounded daily rate times 365.251.
Std Dev = Standard Deviation of Annual Returns
Robust Sharpe Ratio The robust sharpe ratio is RAR% divided by the annualized standard deviation of the monthly returns. See page 189 of Way of the Turtle for more information.
Annual Sortino Ratio Identical in form to the Annual Sharpe Ratio, but uses only downside deviation (negative data points) in its denominator, whereas the Sharpe Ratio uses overall standard deviation (which contains both upside and downside deviation). The Sortino Ratio is typically favored by those who believe that the performance of trend-following CTAs, and others, is unfairly penalized by the Sharpe Ratio's inclusion of upside volatility in its calculation. The higher the Sortino Ratio, the better:
Annual Sortino Ratio = (Return - RFR) / Semi-Deviation
Return = Compounded Annual Growth Rate
Risk Free Rate = Computed from the annual risk free rate as set in the TradingBlox.ini file converted to a compounded daily rate times 365.251.
Semi-Deviation = Std Dev of negative Annual returns
Note: In the calculation of standard deviation for the Sortino Ratio, N equals the number of negative data points, and not the number of data points in the entire population.
Monthly Sharpe Ratio Identical in form to the Annual Sharpe Ratio, but based on monthly data points:
Monthly Sharpe Ratio = (Return - RFR) / Std Dev
Return = Average of the monthly returns.
Risk Free Rate = Converts the annual risk free rate as set in the TradingBlox.ini file to a compounded monthly return.
Std Dev = Standard Deviation of Monthly (calendar) Returns
Daily Sharpe Ratio Identical in form to the Annual Sharpe Ratio, but based on daily data points:
Daily Sharpe Ratio = (Return - RFR) / Std Dev
Return = Average of the daily returns.
Risk Free Rate = Converts the annual risk free rate as set in the TradingBlox.ini file to a compounded daily return.
Std Dev = Standard Deviation of Monthly (calendar) Returns
Daily Geometric Sharpe Ratio Identical in form to the Annual Sharpe Ratio, but based on daily data points:
Daily Sharpe Ratio = (Return - RFR) / Std Dev
Return = Compounded Daily Return.
Risk Free Rate = Converts the annual risk free rate as set in the TradingBlox.ini file to a compounded daily return.
Std Dev = Standard Deviation of Monthly (calendar) Returns
Monthly Sortino Ratio Identical in form to the Annual Sortino Ratio, but based on monthly data points:
Monthly Sortino Ratio = (Return - RFR) / Semi-Deviation
Return = Average of the monthly returns.
Risk Free Rate = Converts the annual risk free rate as set in the TradingBlox.ini file to a compounded monthly return.
Semi-Deviation = Std Dev of negative Monthly data points
Calmar Ratio Another gain-to- pain ratio, used to determine return relative to drawdown (downside) risk. The higher the Calmar ratio, the better: The Calmar Ratio is identical to the MAR Ratio with the exception of their denominators. MAR uses the Max DD over the life of the simulation, based on a daily, marked-to-the-market assessment. While the Calmar's denominator uses the Max DD over the life of the simulation, it is based on the worst month-end to month-end Total Equity data points. Note: Unlike some forms of the Calmar Ratio, which consider only the last 3 years of returns, Trading Blox uses the entire duration of the simulation.
Calmar Ratio = CAGR / Max Drawdown (monthly data points)
Drawdown Statistics
Longest Total Equity Drawdown A one time event that reflects the longest duration drawdown in Total Equity over the life of the simulation. It is measured from previous equity peak to new equity peak, and expressed in months.
Maximum Monthly Total Equity DD% Like Maximum Drawdown, this is a one-time event that reflects the largest retracement relative to a previous equity high in the entire simulation. It is based on a month-end to month-end, marked-to-the-market assessment. Expressed as a percentage, this statistic is calculated peak-to-valley using Total Equity.
Average Max Drawdown (%) The average of the 5 largest percent drawdowns based on total equity.
Average Max Drawdown Length The average of the 5 largest total equity drawdowns by test days, converted to months.
Maximum Closed Equity Drawdown% A one-time event that reflects the largest retracement relative to a previous equity high in the entire simulation. It is based on a daily, marked-to-the-market assessment. Expressed as a percentage, this statistic is calculated peak-to-valley using Closed Equity.
Average Closed Equity Drawdown% The average of all Closed Equity drawdowns. If Monday is a Closed Equity peak, Tuesday shows a 2% retracement, and new peak is hit on Wednesday, then this one-day, 2% drawdown is stored, and averaged with all other drawdowns. This is significantly different from the way the other drawdown statistics are calculated.
Miscellaneous Performance Statistics
Round Turn per Million The number of contracts traded per million currency on average. This number takes the average number of contracts traded divided by the average equity in millions. Trading Blox computes the round turns per million as follows:
End Account Balance The ending balance after all trades are closed out at the end of the simulation (at this point Closed Equity and Total Equity are equal).
Highest Total Equity Highest Total Equity achieved at any point during the simulation, using current market prices to value open positions.
Highest Closed Equity Highest Closed Equity achieved at any point during the simulation. (Sometimes referred to as Closed Trade Equity.)
Total Commissions Total commissions paid out for all positions.
Total Slippage The total slippage (in currency) incurred, for all trades. See "Slippage Percent" for definition.
Total Forex Carry The money earned or paid as a result of Forex Carry (see: Forex Carry Calculations for details)
Earned Interest Total amount of interest (in currency), hypothetically earned on cash, or on T-Bill interest in a futures account.
Margin Interest Total amount of interest (in currency), hypothetically paid for money borrowed on margin.
Win/Loss, Profit Factor, and Expectancy
Wins Number of winning trades; also displayed as a percentage of Total Trades.
Losses Number of losing trades; also displayed as a percentage of Total Trades.
Total Trades Total number of trades.
Winning Months Number of profitable months; also displayed as a percentage of total months in the simulation.
Losing Months Number of unprofitable months; also displayed as a percentage of total months in the simulation.
Total Win Dollars The total won on profitable trades, in system wide base currency.
Total Loss Dollars The total lost on unprofitable trades, in system wide base currency.
Profit Factor Total Win Dollars / Total Loss Dollars
Average Risk Percent The average percent of equity risked per trade.
Average Win Percent The average winning trade as a percentage of equity.
Average Loss Percent The average losing trade as a percentage of equity.
Average Trade Percent The average trade as a percentage of equity. This number will be positive for winning systems and negative for losing systems.
Percent Profit Factor Total Wins in Percent / Total Losses in Percent - This is a more useful statistic than Profit Factor since it does not weight later trades more heavily than earlier trades like Profit Factor does. To compute Total Wins in Percent, we add up the percentage won for each trade that is a winning trade as a percentage of the account equity at the time the trade was initiated. To compute Total Losses in Percent, we add up the percentage lost for each trade that is a losing trade as a percentage of the account equity at the time the trade was initiated.
Expectation Sometimes known as Expectancy, this statistic shows how much one expects to gain for every amount bet or risked on a given trade. Numbers greater than 0.0 are winning systems, less than 0.0 are losing systems.
Average Gain of All Trades / Average Risk of All Trades, or,
( TotalWinPercent - TotalLossPercent ) / TotalRiskPercent
Margin to Equity Ratio
The summary margin to equity ratio is the MarginEquityTotal / TotalTradingDays, where the MarginEquityTotal is a sum of each day's margin to equity percent. The equity used for this is system total equity. So this number is the average margin to equity percent over the course of the test, using the system total equity as the equity basis. |