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, you should use the square root rule for reinvesting - 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:
// multi-asset system: reinvest the square root of profits separately per component and long / short trades var 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 profits Margin = OptimalF * Capital * sqrt(1 + (WinTotal-LossTotal)/Capital);
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