Zorro can analyze the performance of its own strategy scripts, as well as of trade lists that are generated by other software and exported as **.csv**
files. A click on [Result] after a test run produces a
chart and a performance report with portfolio analysis.
Chart images and reports are stored in the **Log** folder and
can be displayed with Zorro's image viewer and text editor. Exported charts are
**.png** image files, genersted reports are simple **.txt** files.
This way they can be easily posted to websites or imported in documents.
Additionally, datasets from charts can be exported and further evaluated with third party software, f.i. an R data analysis
package.

During a session, the performance report is available through the report function. In [Trade] mode the chart
and performance report is part of the **.htm** status page. It can be displayed in a web browser and is updated every minute. It also contains a list of all open and pending trades, as well as any specific information that is printed by the script.

This is an example of a performance report:

Walk-Forward Test Z4 portfolio Simulated account AssetsFix.csv (NFA) Bar Period 4 hours (avg 266 min) Simulation period 06.06.2007-02.12.2017 (9483 bars) Test period 10.06.2010-02.12.2017 (6259 bars) WFO test cycles 11 x 569 bars (137 days) WFO training cycles 12 x 3224 bars (111 weeks) Lookback period 700 bars (169 days) Monte Carlo cycles 200 Fill mode Realistic (slippage 5.0 sec) Avg bar 5.1 ticks 470.5 pips range Spread 0.7 pips (roll -0.70/-0.31) Contracts per lot 1.0 Capital invested 5000$ Gross win/loss 60452$ / -43672$ (+16252 pips) Virtual win/loss 60024$ / -44112$ Average profit 4309$/year, 359$/month, 17$/day Max drawdown -2025$ 12% (MAE -2287$ 14%) Total down time 78% (TAE 93%) Max down time 119 days from May 2011 Max open margin 656$ Max open risk 1863$ Trade volume $10164943 (2610626$/year) Transaction costs -637$ spr, -365$ slp, -906$ rol, -1102$ com Capital required $2681 Number of trades 1370 (351/year) Percent winning 44% Max win/loss 810$ / -407$ Avg trade profit 12$ 10.4p (+99.0p / -56.5p) Avg trade slippage -0.27$ 0.2p (+1.1p / -1.4p) Avg trade bars 16 (+23 / -10) Max trade bars 141 (34 days) Time in market 355% Max open trades 14 Max loss streak 17 (uncorrelated 13) Annual return 161% Profit factor 1.38 (PRR 1.28) Sharpe ratio 1.94 Kelly criterion 0.63 Ulcer index 12% Cycle performance 1.39 1.40 1.31 1.33 1.37 1.38 Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total 2010 -2 20 -16 20 -13 22 10 -8 8 +38 2011 -1 15 15 -9 26 -1 -1 13 6 28 1 1 +135 2012 2 -9 21 1 3 -2 -0 3 1 0 7 13 +51 2013 6 13 -7 -4 9 6 -8 -4 0 1 -2 -8 -3 2014 6 3 0 -0 4 -2 3 -6 8 12 -9 5 +23 2015 5 -7 8 13 -1 0 0 1 3 -1 -5 -12 +17 2016 19 1 6 9 6 -10 10 3 1 -1 6 -2 +30 2017 -1 -7 6 -5 0 -0 -1 2 1 -5 -1 7 -6 Confidence level AR DDMax Capital 10% 236% 1440$ 1390$ 20% 227% 1550$ 1470$ 30% 218% 1680$ 1570$ 40% 209% 1830$ 1680$ 50% 202% 1940$ 1760$ 60% 193% 2140$ 1900$ 70% 186% 2340$ 2040$ 80% 174% 2730$ 2320$ 90% 166% 3080$ 2580$ 95% 146% 4010$ 3580$ 100% 104% 5640$ 4710$ Portfolio analysis OptF ProF Win/Loss Wgt% Cycles AUD/USD avg .014 1.36 281/475 11.4 XXXXXXXXXX/ EUR/USD avg .006 1.41 91/115 6.2 XXXXXX\XXXX GER30 avg .030 1.33 34/45 2.5 X/X/\.\XXXX SPX500 avg .077 1.75 96/162 16.4 XXXXXXXXXXX USD/JPY avg .006 1.69 130/175 8.7 XXXXXXXXXX/ XAG/USD avg .008 1.35 113/152 5.3 \\XXXXXXXX/ BB avg .010 1.29 82/111 2.6 X/\XXX/\XXX CT avg .019 1.38 106/126 7.6 XXXX\XXXXXX CY avg .017 1.83 60/66 5.6 /XXX\/XXX/X ES avg .025 1.34 163/275 7.4 XXXXX/XXXXX HP avg .017 1.34 332/440 19.2 XXXXXXXXXXX LP avg .009 1.54 106/219 11.3 \XXXXXXXXXX VO avg .014 1.71 217/288 24.2 /XXXXXXXXXX AUD/USD:ES .036 1.14 45/87 0.1 \\/\\//\\// AUD/USD:ES:L .036 1.14 45/87 0.1 \\/\\//\\// AUD/USD:ES:S .000 ---- 0/0 0.0 ........... AUD/USD:HP .024 1.18 76/102 2.2 X/\XX\/XX\/ AUD/USD:HP:L .024 1.13 47/68 1.2 //./\\///\/ AUD/USD:HP:S .043 1.35 29/34 1.0 \/\\/./\\\/ AUD/USD:LP .029 1.66 75/149 7.5 \/X///X\/X/ AUD/USD:LP:L .029 1.80 42/71 6.8 \//////\/\/ AUD/USD:LP:S .058 1.23 33/78 0.6 \/\///\\/// EUR/USD:CT .009 1.11 22/33 0.5 X/\X\X\X/XX EUR/USD:CT:L .027 1.22 10/19 0.7 \/\/\\\\.// EUR/USD:CT:S .000 0.91 12/14 -0.2 /.\\\/\//\\ EUR/USD:HP .036 1.32 45/59 2.4 \///\/\\\/\ EUR/USD:HP:L .036 1.32 45/59 2.4 \///\/\\\/\ EUR/USD:HP:S .000 ---- 0/0 0.0 ........... EUR/USD:VO .027 2.20 24/23 3.3 .X.//.\X/XX EUR/USD:VO:L .027 1.58 12/11 0.9 ././...//\\ EUR/USD:VO:S .032 2.90 12/12 2.5 .\../.\\.// GER30:BB .038 1.03 2/4 0.0 /......\\/\ GER30:BB:L .038 1.03 2/4 0.0 /......\\/\ GER30:BB:S .000 ---- 0/0 0.0 ........... GER30:CT .256 1.92 3/2 0.6 \/./...\/.. GER30:CT:L .256 1.92 3/2 0.6 \/./...\/.. GER30:CT:S .000 ---- 0/0 0.0 ........... GER30:ES .267 1.82 2/3 0.2 ..\/\../..\ GER30:ES:L .000 ---- 0/0 0.0 ........... GER30:ES:S .267 1.82 2/3 0.2 ..\/\../..\ GER30:VO .051 1.31 27/36 1.7 ////\.\\/\/ GER30:VO:L .051 1.31 27/36 1.7 ////\.\\/\/ GER30:VO:S .000 ---- 0/0 0.0 ........... SPX500:ES .110 1.44 17/21 1.3 //\/\///\\\ SPX500:ES:L .110 1.44 17/21 1.3 //\/\///\\\ SPX500:ES:S .000 ---- 0/0 0.0 ........... SPX500:LP .006 1.04 17/55 0.2 \\/\\\\\//\ SPX500:LP:L .006 1.04 17/55 0.2 \\/\\\\\//\ SPX500:LP:S .000 ---- 0/0 0.0 ........... USD/JPY:BB .057 1.51 24/36 0.6 \/\\/\/.\./ USD/JPY:BB:L .000 ---- 0/0 0.0 ........... USD/JPY:BB:S .057 1.51 24/36 0.6 \/\\/\/.\./ USD/JPY:CT .016 1.46 16/19 2.0 \./..\/.\// USD/JPY:CT:L .016 1.46 16/19 2.0 \./..\/.\// USD/JPY:CT:S .000 ---- 0/0 0.0 ........... USD/JPY:HP .024 2.24 34/29 6.4 .XX/\/\/.\/ USD/JPY:HP:L .024 1.22 9/13 0.3 .\//\/\..\/ USD/JPY:HP:S .028 2.65 25/16 6.0 ./\/.../.\/ XAG/USD:CT .038 1.87 13/13 0.6 ....\///\\/ XAG/USD:CT:L .000 ---- 0/0 0.0 ........... XAG/USD:CT:S .038 1.87 13/13 0.6 ....\///\\/ XAG/USD:HP .018 1.43 44/46 1.1 \\/X/\//X// XAG/USD:HP:L .105 4.16 6/3 0.3 .\./....\/. XAG/USD:HP:S .014 1.33 38/43 0.8 \\/\/\///// XAG/USD:VO .011 1.39 40/62 3.0 .\/\//\\\// XAG/USD:VO:L .000 ---- 0/0 0.0 ........... XAG/USD:VO:S .011 1.39 40/62 3.0 .\/\//\\\//

The following table shows the meaning of the values. Most of the calculated values are only valid for a profitable report (**Gross Win > Gross Loss**); they are meaningless when the profit is negative. Indicated values with a "**$**" suffix are in units of the account currency (not necessarily US-$), indicated values with a "**p**" or "**pips**" suffix are in pips.

Bar period |
Bar period in seconds, minutes, or hours, and average bar duration in minutes. Variations in bar duration are caused by weekends, holidays, or special bars. |

Simulation period |
Time of the WFO run (usually 4..5 years) and the number of bars, without the preceding lookback period. |

Test period |
Time and bar number of the test; simulation period without training and lookback. |

WFO test cycles |
Number and length of the WFO test cycles (this is also the recommended re-training period). |

WFO train cycles |
Number and length of the WFO training cycles. |

Lookback period |
Amount of data to be collected before test or training begins. |

Monte Carlo cycles / Confidence |
Number of Monte Carlo simulation cycles, and selected confidence level (if any) for the following performance figures. |

Fill mode |
Simulated fill mode (Naive or Realistic) and Slippage. |

Avg bar |
Average number of price ticks and average high-low difference per bar in the simulation; for single asset strategies. |

Spread |
Spread in pips, and long/short rollover fee in account currency units; for single asset strategies. |

Commission |
Roundturn commission in account currency units; for single asset strategies. |

Contracts per lot |
Lot size; for single asset strategies. |

Gross win / loss |
Sums of all wins and all losses in currency units, and the overall volume-neutral result in pips. Note that there can be a negative pip result and a positive gross win (or vice versa) due to different assets pip costs and different trade volumes. |

Virtual win / loss |
Sums of all wins and all losses of phantom trades in currency units, for virtual hedging. Normally worse than the gross win / loss due to higher transaction costs. |

Average profit |
Annual, monthly, and daily profit (workdays only); simply the difference between start and end balance divided by the number of periods. |

Max drawdown / MAE |
Maximum drawdown during the test period, in account currency units and in percent from the gross profit. The drawdown is the difference between a balance peak and the lowest subsequent equity valley (balance = account value, equity = balance plus value of the all open trades). MAE (maximum adverse excursion) is the difference between an equity peak and the lowest subsequent equity valley.
Drawdown is dangerous, MAE is normally not (see remarks below). |

Total down time
/ TAE |
Percentage of time when the current equity is below a preceding balance peak.
TAE (time in adverse excursion) is the time when trades are
open and the
current equity is below a preceding equity peak. Strategies often have up to 90% down time,
but can be still profitable. |

Max down time |
Longest drawdown duration, i.e. maximum time from a balance peak to the lowest subsequent equity valley. The BALANCE flag can be used for identifying the balance peaks in the profit curve. |

Max open margin |
Maximum total margin allocated during the backtest period. |

Max open risk |
Maximum loss when all open trades hit their initial Stop at the worst possible moment.
Dependent on the stop distances and the likeliness of such an event, the
Max open risk can far exceed the Capital required.
This parameter has no meaning for virtual hedging
strategies or for strategies that use no stop loss for some trades. |

Trade volume |
Total and annualized value of all assets bought and sold, in units of the account currency (see remarks). |

Transaction costs |
Total costs of spread (Spr), slippage (Slp), swap/rollover/margin
interest (Rol) and commission (Com) for all trades. Slippage and rollover can increase the profit in some cases; costs are then positive. In test mode the simulated costs are displayed, in trade mode the real costs
when available through the broker API.
Slippage cost in trade mode is calculated from the difference of price at
order time and fill price. |

Capital required |
Required initial capital for trading the strategy; equivalent to the maximum margin on non-leveraged accounts, and the sum of maximum margin and normalized maximum drawdown or MAE on leveraged accounts. This amount would be required when the strategy is entered at the worst possible moment of the simulation, for instance directly at a balance peak preceding a drawdown. For strategies that reinvest profits (Capital variable), the displayed value is multiplied with the ratio of initial and final balance, and thus can be much smaller than the maximum drawdown or open margin. |

Number of trades |
Number of trades in the backtest period. Only real trades are counted, not phantom or pending trades. |

Percent winning |
Percentage of winning trades. |

Max win / loss |
Maximum win and loss of all trades. |

Avg trade profit |
Average return of a trade in account currency units and in volume-neutral pips; separately listed for winning (+) and losing (-) trades. Robust strategies should return a multiple of the spread. Avoid systems that generate either many trades with small average returns, or few trades with very large average returns. |

Avg trade slippage |
Average slippage cost of a trade in account currency units and in pips; separately listed for positive (+) and negative (-) slippage. In test mode it's the simulated slippage, in trade mode the real slippage. |

Avg trade bars |
Average number of bars of a trade; separately for winning (+) and losing (-) trades. |

Max trade bars |
Maximum time a trade was open. |

Time in market |
Total time of all trades compared to the backtest time. This can be more than 100% when several trades are open at the same time. The smaller the time in market, the less exposed is the capital to the market risk. |

Max open trades |
Maximum number of simultaneously open trades. |

Max loss streak /uncorrelated |
Maximum number of consecutive losses during the test, and the theoretical number under the assumption of uncorrelated returns, i.e. equally distributed wins and losses. If the real number is noticeably higher, wins and losses tend to cluster with this strategy, and an equity curve trading algorithm could improve the performance. |

Annual return (AR) |
Annualized profit divided by the required initial capital; main performance parameter for systems that don't reinvest profits. Depends on drawdown and can thus be subject to random fluctuations (see remarks). |

Return on investment (ROI) |
Annualized profit divided by maximum required margin. For accounts with no leverage, where the investment is determined by margin and not by drawdown, |

Annual growth rate (CAGR) |
Compound annual growth rate of the investment; the nth root of the total equity growth, where n
is the number of years in the test period. Displayed for strategies that
reinvest profits. |

Profit factor / PRR |
Gross win divided by gross loss. The pessimistic return ratio (PRR) is the profit factor
multiplied by (1-1/sqrt(W))/(1+1/sqrt(L)); it gives a worse result when the number of trades is low. |

Sharpe ratio |
Annualized ratio of mean and standard deviation of the bar returns when the system is in the market; bars with no trades do not contribute. The Sharpe ratio is a popular performance gauge (see remarks) and should be > 1 for good strategies. |

Kelly criterion |
Ratio of mean and variance of the bar returns when the system is in the market; bars with no trades do not contribute. The kelly criterion is the optimal investment factor for a single-asset, single-algo, single-trade per bar strategy to maximize the profit. |

R2 coefficient |
Coefficient of determination; the similarity of the equity curve with a straight line ending up at the same profit. The closer R2 is to 1, the steadier are the profits and the better they will be possibly reproduced in real trading (see remarks). |

Ulcer index |
Mean drawdown percentage; a measure of length and depth of drawdowns (see remarks). The higher the ulcer index, the stronger your stomach must be for trading the script. The ulcer index should be < 10% for preventing ulcer. |

Cycle performance |
Separate profit factors of the oversampling cycles. High profit differences between cycles are a sign of an unstable strategy. |

Year |
Annual and monthly returns in percent, either in relation to the required capital for non-reinvesting strategies, or to the previous period for reinvesting strategies with nonzero Capital. |

Monte Carlo analysis |
Performance analysis (see Monte Carlo Method; non-reinvesting strategies only) by evaluating many possible equity curves with different distributions of trades and returns. A strong serial correlation of trade returns can cause Monte Carlo results higher than the result from the real equity curve. |

Confidence level |
Confidence level of the following performance parameters. F.i. at 95% confidence level, 95% of all simulations generated the same or better results, and 5% generated worse results. |

AR |
Annual return at the given confidence level. |

DDMax |
Maximum drawdown (not normalized) at the given confidence level. |

Capital |
Capital requirement at the given confidence level. |

Portfolio analysis |
Performance analysis per asset, per algorithm, and per component. Only components with trades are listed. The figures are taken from the last oversampling cycle; when the ALLCYCLES flag is set, they are taken from all cycles. |

OptF |
OptimalF factors for portfolio components (see Money Management;
non-reinvesting strategies only). When 0, the component was unprofitable in the test.
When Capital is set, a reinvesting strategy is
assumed and no factors are displayed. |

ProF |
Profit factor (gross win divided by gross loss, including phantom trades). A '++++' in the column indicates that there were only winners, '----' indicates that there were no winners. |

Win / Loss |
Number of winning and losing trades, including phantom trades. |

Wgt% |
Weight of the component in percent; component profit divided by total profit. Indicates the contribution of the component to the whole strategy. The weight can be negative, f.i. with a losing component and a positive overall result. |

Result |
Current profit or loss of the component in live trading. |

Cycles |
Profit separated by WFO cycles. '/' is a winning cycle, '\' a losing cycle, 'X' is a cycle with both winning and losing components, and '.' is a cycle without trades. |

Additionally, the performance can be evaluated by user criteria or stored for further evaluation with the user-supplied evaluate function.

- When developing a strategy, don't look only into the performance report. Especially when results are unexpected or affected by parameters in strange ways, look into the log file and follow the single trades. This is often more informative than the performance summary.
- Additional performance figures of any kind can be added to the report with a
**print(TO_REPORT, ...)**command. All trades are stored and can be enumerated in a (**for(all_trades)**) loop in the evaluate function. The daily equity or balance curve is available in the ResultsDaily array for further calculations. Graphical presentations of performance parameters can be produced with plotBar statements. Examples can be found in the include\profile.c file. If you need a certain performance parameter that can not be easily generated by script, please ask for it on the Zorro user forum. - All performance parameters above are calculated under the assumption that the result is positive. A neutral or negative result will invalidate most performance parameters.
- Setting the Capital variable and reinvesting profits will invalidate performance parameters that are derived from maximum drawdown, such as required capital, annual return, and Monte Carlo analysis.
- In backtest and training, performance is normally calculated under the assumption of constant spread, commission, slippage, rollover, and account currency exchange rate, which are taken from the asset list. Theoretically the performance could be adapted to variations in those parameters as in the example under PipCost. This is however only recommended in special cases, because the resulting differences are normally irrelevant for the strategy performance, but would add artifacts to the test and training process.
- When the backtest runs over several sample cycles, the price curve in the chart only shows the trades of the last cycle, but the performance report and the equity curve are calculated from all cycles. If some cycles win and others lose, the summing up can generate results that appear inconsistent, for instance a small positive
**Sharpe ratio**, but a small negative**Annual return**. - The
**Maximum Adverse Excursion**(**MAE**) can be substantially higher than**Maximum Drawdown**, especially when trades stay open a long time. Example: A single trade first goes up to $3000 profit, then falls down to -$1000 loss, then goes up again and is closed at $500 profit. This trade has a MAE of -$4000, but only a drawdown of -$1000. You need a capital of at least $1000 plus the position margin for avoiding a margin call. Unlike the drawdown, the MAE is therefore not dangerous (except for your nerves) and does not affect the capital requirement (except when you use excess equity for buying more assets). But when you observe a high difference between MAE and maximum drawdown, try improving the trade exit algorithms. **Maximum drawdown**and**MAE**depend on the test period; longer periods cause higher maximum drawdown. On a break-even system the maximum drawdown is proportional to the square root of the test period*. For this reason, drawdown dependent performance figures such as**Annual return**and**Capital required**are calculated from a**normalized drawdown**, which adjusts the drawdown to 3 years. For this, the drawdown is multiplied with the square root of 3 years divided by the test period. This results in performance figures that are largely independent on the test period.**Maximum drawdown**and**MAE**are a result of the random win/loss pattern of trades. They can change greatly with minor changes to the strategy or test period; therefore all performance parameters calculated from the original equity curve are subject to randomness. For better accuracy, use Monte Carlo Simulation.- The
**Capital required**is a statistical parameter calculated from the simulation. It is unrelated to the**Risk**displayed by Zorro for single trades, which is the maximum loss when hitting the initial stop. The**Max open risk**parameter and even an individual trade**Risk**can be higher than the required capital. Do not take the**Capital required**parameter as a guaranteed loss limit! - The
**Ulcer index**is traditionally calculated from the drawdown percentages in relation to their preceding equity peaks. This gives a misleading result, as the equity peaks normally rise during the trade period, causing the ulcer index to be affected mostly from the begin of the equity curve where the peaks are lower and the percentages higher. For this reason, Zorro calculates a modified ulcer index that uses a percentage of the maximum equity peak instead of the preceding equity peak. - The
**Sharpe ratio**takes risk into account; it is supposed to compare the strategy performance with a risk-free return as from a savings account. A Sharpe ratio of 1.5 would be equivalent to a savings account with 50% risk-free interest. Traditionally, 4% are subtracted from the Sharpe ratio for obtaining the difference to the usual 4% interest of risk-free investment returns; this would make no sense for comparing trade strategies, thus nothing is subtracted here. - The
**R2**coefficient is a measure of the upwards tendency of the equity curve. The equity curve is compared with a steady slope, i.e. a line through its start and end points (not with its own regression line as in some applications, as this could feign a high linearity even with a falling equity curve). R2 is the squared correlation coefficient of real curve and straight slope. A equity curve with no upwards tendency at all produces a R2 coefficient of zero. - The per-asset and per-algo figures in the portfolio analysis are a simple non-weighted average of the single components. Thus, low-volume components contribute overproportionally and the weights won't add up to 100%.

Keep in mind that that all those performance figures are derived from historical data (even when it's out-of-sample data). The future is unknown, so there is no guarantee to achieve the same performance in live trading. Many figures - f.i. Sharpe ratio, Monte Carlo analysis, drawdown extrapolation, R2 coefficient - are based on mathematical models that assume a Gaussian distribution of returns. However there is no guarantee that real returns always follow a Gaussian distribution. For those reasons, don't interpret too much into performance figures. Even a system with excellent theoretical performance can cause real loss of money.

* See Malik Magdon-Ismail / Amir Atiya, "Maximum Drawdown", 2004.