For re-investing profits or assigning capital to portfolio components, Zorro can
determine the optimal capital allocation factor - named **OptimalF** - for every component in a portfolio strategy.
For this, it evaluates the component's balance curve for calculating the
investment amount that generates the maximum end profit while avoiding a negative balance. For instance, if **OptimalF** is **0.05**, then the
suggested invested margin is 5% of the available capital. The margin can be
smaller - for reasons mentioned in workshop 6, only
the square root of gains should be reinvested - but it must not be higher. The
**OptimalF** algorithm was developed by **Ralph Vince** and described in
several publications (see books).

**OptimalF** factors can also be used for allocating the capital
to the components of a multi-asset system under certain conditions. The total
allocated margin must be at any time small compared to the total invested
capital. This is normally the case for trading systems with independent assets
on leveraged accounts, where the capital is mostly needed for buffering
drawdowns. The suggested margin of a trade is then the available capital
multiplied with **OptimalF**. There are several methods to
determine the available capital of a portfolio component; a method on the
conservative side is dividing the initial total capital by the square root of
components and multiplying it with the square root of gains (see example).
Systems that don't fulfil the requirements, for instance portfolio rebalancing
systems that are always in the market with 100% capital, normally use other algorithms such as
mean_variance or momentum-based weights
for distributing the capital.

For generating **OptimalF** factors, set the FACTORS flag.
The factors are then calculated in a special test run at the end of the [Train] process, and stored in a file **Data\*.fac**. It's a simple text file that looks like this:

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 EUR/USD:VO .027 2.20 24/23 3.3 EUR/USD:VO:L .027 1.58 12/11 0.9 EUR/USD:VO:S .032 2.90 12/12 2.5 NAS100:ES .114 1.42 63/90 4.6 NAS100:ES:L .101 1.39 33/44 2.1 NAS100:ES:S .128 1.46 30/46 2.5 USD/CAD:BB .030 1.41 19/25 1.3 USD/CAD:BB:L .030 1.41 19/25 1.3 USD/CAD:BB:S .000 ---- 0/0 0.0 USD/CAD:HU .012 1.74 48/36 3.3 USD/CAD:HU:L .066 1.42 24/20 0.2 USD/CAD:HU:S .012 1.79 24/16 3.1 USD/CHF:CT .104 1.60 16/17 0.6 USD/CHF:CT:L .104 1.60 16/17 0.6 USD/CHF:CT:S .000 ---- 0/0 0.0 USD/CHF:CY .025 1.10 21/24 0.1 USD/CHF:CY:L .025 1.10 21/24 0.1 USD/CHF:CY:S .000 ---- 0/0 0.0 USD/CHF:HP .025 1.45 31/48 3.2 USD/CHF:HP:L .000 ---- 0/0 0.0 USD/CHF:HP:S .025 1.45 31/48 3.2 USD/CHF:VO .011 3.93 17/8 7.6 USD/CHF:VO:L .011 3.93 17/8 7.6 USD/CHF:VO:S .000 ---- 0/0 0.0

The first column identifies the component; it consists of the asset name and the algorithm identifier. "**S**" or "**L**" are separate statistics for short or long trades. The second column contains the **OptimalF** factors for that component.
The higher the factor, the more capital should be invested in the strategy
component. Since calculated separately for any component, the factors do not sum
up to 1. A **0** indicates that this component should not be
traded. The further columns contain the profit factor, the number of winning and losing trades, and the weight of the component.

As the factors are stored in a simple text file, they can be edited anytime with a text editor, even while live trading. Zorro detects if factors have been changed, and automatically reloads them. If the factors are evaluated in the strategy, as in some of the Z strategies, a component can be excluded from further trading by setting its factor to zero, or by placing a minus sign in front of it for making it negative.

When **OptimalF** factors have been generated, they can be
accessed or modified with the following variables:

- In a portfolio system,
**OptimalF**is separately calculated for any component, and is not affected by the other components. Every algo and asset call switches the**OptimalF**variable to the factors belonging to the new component. - In Ralph Vince's publications,
**OptimalF**is defined in a slightly different way, requiring a formula containing the maximum loss for calculating the number of lots of a trade. Zorro's**OptimalF**factors are already adjusted by the maximum loss, and thus can be directly multiplied with the earned capital for getting the optimal margin. - The
**OptimalF**factors calculation requires a large number of trades per component - ideally more than 100 - for being statistically significant. For this reason,**OptimalF**factors are normally calculated over the whole test period even when WFO is enabled. This violates the out-of-sample test philosophy, so the backtest performance can be slightly on the optimistic side. For enforcing a totally out-of-sample test, the**ALLCYCLES**flag can be set to calculate**OptimalF**factors separately per WFO cycle, albeit in low quality due to the smaller number of trades. **OptimalF**is affected by maximum losses in the trade history, and thus tends to decrease when the test period increases. The reason is the same as the drawdown dependency on the test period discussed under performance.- The
**OptimalF**calculation assumes that one trade is executed after the other. If the strategy opens several trades simultaneously, as in a portfolio system, divide the investment by the maximum number of simultaneously open trades. Alternatively, divide it by the square root of components. - If the balance curve has little drawdown, theoretically the full capital can be invested in that component for maximum profit.
**OptimalF**is then set to**0.999**. Investing the full capital is not recommended in real trading, as the balance curve is not guaranteed to continue this way in the future. If a component is unprofitable, OptimalF is set to**0.000**. **OptimalF**is not for strategies that always invest 100% of the capital, such as portfolio rotation. Use mean-variance optimized or momentum-based weights for those strategies.- Factors can be alternatively caclulated by script with a user-defined
algorithm. For this set the SETFACTORS flag, set
**OptimalFRatio**to 0, and set**OptimalF**,**OptimalFLong**,**OptimalFShort**to the script calculated values at the end of the**FACTORS**training run (**if(is(FACTORS)) ...**).

// multi-asset system: reinvest the square root of profits separately per component and long / short tradesvar AvailableCapital = Capital/sqrt(NumComponents); Margin = ifelse(ForLongTrade,OptimalFLong,OptimalFShort)*AvailableCapital*sqrt(1+(WinLong-LossLong)/AvailableCapital);// single-asset system: reinvest the square root of your total profitsMargin = OptimalF * Capital * sqrt(1 + (WinTotal-LossTotal)/Capital);

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