Trading Performance and Statistics

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.

Trading Performance and Statistics Sections:

Summary Performance Ratios

Drawdown Statistics

Miscellaneous Performance Statistics

Win/Loss, Profit Factor, and Expectancy

 


Summary Performance Ratios:

Statistic:

Description:

CAGR% ^_Top

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% ^_Top

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% ^_Top

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 ^_Top

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) ^_Top

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 ^_Top

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:

'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Return = 12* Average Monthly Return
 
  Risk Free Rate (excluded)
 
  Annualized Std Dev = Square Root (12) * Std Dev Monthly Returns
 
  Modified Sharpe Ratio = Annualized Return / Annualized Std Dev
'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Annual Sharpe Ratio ^_Top

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:

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

'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Annual Sharpe Ratio = (Return - RFR) / Std Dev
'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Robust Sharpe Ratio ^_Top

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 ^_Top

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:

Risk Free Rate (RFR):

Computed from the annual risk free rate as set in the TradingBlox.ini file converted to a compounded daily rate times 365.251.

Return:

Compounded Annual Growth Rate

Semi-Deviation:

Std Dev of negative Annual returns

'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Annual Sortino Ratio = (Return - RFR) / Semi-Deviation
'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Note:

In the calculation of standard deviation for the Sortino Ratio, "n" equals the entire population and includes zeroes for positive returns.

Monthly Sharpe Ratio ^_Top

Identical in form to the Annual Sharpe Ratio, but based on monthly data points:

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

'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Monthly Sharpe Ratio = (Return - RFR) / Std Dev
'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Daily Sharpe Ratio ^_Top

Identical in form to the Annual Sharpe Ratio, but based on daily data points:

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 Sharpe Ratio = (Return - RFR) / Std Dev
'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Daily Geometric Sharpe Ratio ^_Top

Identical in form to the Annual Sharpe Ratio, but based on daily data points:

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

'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 Daily Sharpe Ratio = (Return - RFR) / Std Dev
'  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Monthly Sortino Ratio ^_Top

Identical in form to the Annual Sortino Ratio, but based on monthly data points:

(See Annual Sortino Ratio )

Calmar Ratio ^_Top

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

Statistic Name:

Description:

Longest Total Equity ^_Top 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% ^_Top

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 (%) ^_Top

The average of the 5 largest percent drawdowns based on total equity.

Average Max Drawdown Length ^_Top

The average of the 5 largest total equity drawdowns by test days, converted to months.

Maximum Closed Equity Drawdown% ^_Top

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% ^_Top

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:

Statistic Name:

Description:

Round Turn per Million ^_Top

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:
At the end of each month, the total round turns for the month are multiplied by 1,000,000 divided by the starting total equity for the month.

The total turns per million is then incremented by this monthly number.

'  -------------------------------------------------------------------------
turnsPerMillion = monthRoundTurns * (ONE_MILLION / monthStartingTotalEquity)
turnsPerMillionTotal = turnsPerMillionTotal + turnsPerMillion
'  -------------------------------------------------------------------------

At the end of the test, the average turns per million is computed as follows:

'  -------------------------------------------------------------------------
averageTurnsPerMillion = ( turnsPerMillionTotal / totalTestingMonths ) * 12
'  -------------------------------------------------------------------------

End Account Balance ^_Top

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 ^_Top

Highest Total Equity achieved at any point during the simulation, using current market prices to value open positions.

Highest Closed Equity ^_Top

Highest Closed Equity achieved at any point during the simulation. (Sometimes referred to as Closed Trade Equity.)

Total Commissions ^_Top

Total commissions paid out for all positions.

Total Slippage ^_Top

The total slippage (in currency) incurred, for all trades. See "Slippage Percent" for definition.

Total Forex Carry ^_Top

The money earned or paid as a result of Forex Carry (see: Forex Carry Calculations for details)

Earned Interest ^_Top

Total amount of interest (in currency), hypothetically earned on cash, or on T-Bill interest in a futures account.

Margin Interest ^_Top

Total amount of interest (in currency), hypothetically paid for money borrowed on margin.

 


Win/Loss, Profit Factor, and Expectancy:

Statistic Name:

Description:

Wins ^_Top

Number of winning trades; also displayed as a percentage of Total Trades.

Losses ^_Top

Number of losing trades; also displayed as a percentage of Total Trades.

Total Trades ^_Top

Total number of trades.

Winning Months ^_Top

Number of profitable months; also displayed as a percentage of total months in the simulation.

Losing Months ^_Top

Number of unprofitable months; also displayed as a percentage of total months in the simulation.

Total Win Dollars ^_Top

The total won on profitable trades, in system wide base currency.

Total Loss Dollars ^_Top

The total lost on unprofitable trades, in system wide base currency.

Profit Factor ^_Top

Total Win Dollars / Total Loss Dollars

Average Risk Percent ^_Top

The average percent of equity risked per trade.

Average Win Percent ^_Top

The average winning trade as a percentage of equity.

Average Loss Percent ^_Top

The average losing trade as a percentage of equity.

Average Trade Percent ^_Top

The average trade as a percentage of equity. This number will be positive for winning systems and negative for losing systems.

Percent Profit Factor ^_Top

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.

 


Edit Time: 9/20/2017 07:56:26 AM


Topic ID#: 4009

 

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