You can use all the symbols available in the Symbols section to create your objective function.

Consider for instance the expression in the screenshot above,

portfolio_nav(portfolio, to_date)

In the Objective box, this works just fine, since the expression in the Objective box is computed only after the system has finished executing and the portfolio has been updated accordingly. But if you had defined a symbol

_final_nav = portfolio_nav(portfolio, to_date)

in the Symbols grid, it would have been computed at the beginning of the run and then never again, since both arguments (portfolio, to_date) remain the same throughout system execution. Using _final_nav as your objective function would therefore have yielded misleading results!

Also note that final portfolio NAV may not be the most adequate performance measure, since it doesn't take into account how much risk was incurred to achieve that NAV. Two popular risk-adjusted performance measures which address this problem are the Sharpe ratio and the Treynor ratio:

where the "risk-free" return is typically taken to be the return on US Treasury bills, a money market account or similar "safe" asset.

While it's possible to compute average returns using the XIRR function, it is not necessary to do so for the purpose of optimization. Instead, define symbols

_initial_nav = portfolio_nav(portfolio, from_date)

_rfdc = asset_quotes(riskfree, "c", from_date, to_date)

_rfdc_n = rows(array(_rfdc))

_risk_free_return = index(array(_rfdc), _rfdc_n, 2) / index(array(_rfdc), 1, 2)

(where riskfree stands for the asset symbol of your risk-free asset; substitute the appropriate actual symbol) and then compute the numerator (in the Objective box - see notes above!) as

portfolio_nav(portfolio, to_date) - _initial_nav * _risk_free_return

The standard deviation of (daily) portfolio returns can be computed as

stdev(subarray(roc(portfolio_quotes(portfolio, "c", from_date, to_date), 1), 1, 0, 2, 0))

while the portfolio's Beta is given by

ba(asset_quotes(market, "c", from_date, to_date), portfolio_quotes(portfolio, from_date, to_date))

where market stands for the asset symbol of a market proxy (typically an index like the S&P 500 or the Russell 3000).

The optimal portfolio according to the Sharpe measure can therefore be found by maximizing the objective function

(portfolio_nav(portfolio, to_date) - _initial_nav * _risk_free_return) / stdev(subarray(roc(portfolio_quotes(portfolio, from_date, to_date), 1), 1, 0, 2, 0))

while the optimal portfolio according to the Treynor measure can be found by maximizing the objective function

(portfolio_nav(portfolio, to_date) - _initial_nav * _risk_free_return) / ba(asset_quotes(market, "c", from_date, to_date), portfolio_quotes(portfolio, from_date, to_date))

The rationale for having two separate sets of date range controls is that sound trading system development always involves the use of at least two non-overlapping date (and data) ranges: one used for optimization, the other for verification of the optimized system. The system should display similar behaviour (number of transactions per time unit, average portfolio return, drawdown, distribution of gains and losses) over both date ranges. Without such verification there is an overwhelming risk of over-fitting, i.e. of creating a system that performs perfectly over the optimization range, but lousy at all other times.

When Shuffle is checked, the optimizer does not use quotes in the selected date range "as is". Instead, before the system is executed, the quotes in the selected range are converted to daily relative moves which are then randomly reshuffled and converted back to quotes. The result is a set of quotes which, while fictitious, have the same distribution of daily moves, the same starting point and the same end point (and therefore the same overall trend) as the original quotes. All assets and currency quotes are reshuffled together (i.e. all asset and currency moves from day X are relocated to the same day Y) so as to also preserve any cross-correlations between quotes.

Quotes are reshuffled every time the optimizer takes a new step through parameter space, i.e. every time a parameter value is updated. If a value > 1 has been set in the "x" (times) box,

reshuffling and system execution are also iterated the specified number of times for each set of parameter values, whereafter the set's "official" objective function value is computed from the "x" individual results, using the method specified to the right of the "x" box:

The purpose of all this tribulation is to avoid the common trap of overfitting the system to a particular sequence of market events which are not likely to ever repeat again in the same order.

It should be noted that while random shuffling is close in spirit to Monte Carlo optimization, it skips a crucial step necessary to qualify as such. In Monte Carlo methods, a postulated distribution of price moves (e.g. a log-normal distribution) is fitted to the historical quotes, whereafter the fictitious prices are obtained from the fitted distribution rather than directly from the historical data. This extra step can be argued to make Monte Carlo methods more "general" in nature, by better insulating the fictitious quotes from peculiarities of the available historical data; but this insulation is achieved at the cost of postulating a particular underlying distribution, essentially as a matter of faith.

Generally speaking, the more historical data you have at your disposal, the better it will reflect the actual distribution, whatever its nature. On the other hand, old data may have been collected under market conditions so different from current ones as to have limited predictive value.

Once clicked, the Execute button stays grayed out until all parameter values in the specified range have been stepped through or Stop (6) is clicked. Execution progress and estimated time left (ETA = hours:minutes:seconds left) are displayed next to the button (5); extrema and the latest parameter set evaluated so far are displayed in the result grid below the button (7).

The top data row displays the largest (Max), smallest (Min) and latest (Last) objective function value ("<OBJECTIVE>") found during the latest optimization run. The rows below it display the corresponding parameter values.

For instance, in the screenshot below,

To transfer a set of parameter values (whether Max, Min or Last) from the result grid to the corresponding Value fields in the System view's Parameters grid, select a cell in the desired column, then click OK (12).

If Log is checked, every point in parameter space reported under Last in the result grid (7) during the optimization run will also be written to the CSV (Comma Separated Value) file specified in the log file box (9). Any data previously in the file will be overwritten. The file path can be typed into the box, or you can click to use a standard Save File dialog.

Symbolic directory names can be used in the file path (e.g. "<TEMP>", as in the screenshot above) and will be automatically substituted for actual directory paths wherever possible.

The first row in the CSV file created by the optimizer is a header describing the contents of each column (<OBJECTIVE> value in the first column, symbol names in the rest). Each subsequent row describes a point in parameter space. All values are written in general floating point format (using a decimal period) and can be read using common spreadsheets and charting software.

Click to close the optimizer window without transferring any values to the Parameters grid.