Money Management and Capital Assignment Factors

For re-investing profits or assigning capital to portfolio components, Zorro can determine the optimal capital assignment factors - named OptimalF - for components in a portfolio strategy. For this, it evaluates the component's trade history 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.

Variables

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

OptimalF

OptimalFLong

OptimalFShort

OptimalF factors, combined for long/short and separately for long and short trades of the current strategy component that is selected with the asset and algo functions. For long-only systems, only OptimalFLong is relevant. The margin to be invested per trade can be calculated by multiplying the investment amount with OptimalF. If a component was unprofitable in the training run, its OptimalF factor is zero.

OptimalFRatio

Set this in [Train] mode to generate OptimalF factors with the given ratio of the highest to the lowest factor (default = 0 = no ratio). For instance, at OptimalFRatio = 3 large factors are reduced and small factors are increased so that the highest OptimalF factor is 3 times the lowest factor. The average of all factors remains unchanged. Useful for preventing large component margin differences when using OptimalF factors in portfolio systems.

Remarks

In a portfolio system, OptimalF is separately calculated for any component of a loop, 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 [Train] mode or when the FACTORS flag is not set, the OptimalF factors are 1 unless modified by script. In [Test] and [Trade] mode the OptimalF factors are read from the .fac file in the FIRSTRUN, and are 0 before.
If all trades of a component are won, its OptimalF is 1.0. If the balance curve has so little drawdown that theoretically the full capital can be invested in that component. OptimalF is 0.999 (still, investing the full capital in a component is normally not recommended). Profitable components have a OptimalF between 0.001 and 0.999. If a component is unprofitable, OptimalF is 0.000. Unexpected small OptimalF factors for very profitable components can indicate that either some trades had extreme losses, or that some parameters in the asset list, for instance MarginCost, are wrong.
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 capital for getting the optimal margin.
The OptimalF factors calculation requires a relatively high number of trades per component - ideally more than 100 - for being statistically significant. For this reason, OptimalF factors are normally calculated over the whole backtest 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 training mode can be set to calculate OptimalF factors separately per WFO cycle, albeit in reduced 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 either by the maximum number of simultaneously open trades, or by the square root of components.
OptimalF is not suited for strategies that always invest 100% of the capital, such as portfolio rotation or options trading. Instead use mean-variance optimized or momentum-based weights for portfolio rotation strategies.
OptimalF factors can be alternatively calculated by script with a user-defined algorithm. For this set both FACTORS and NOFACTORS flags, set OptimalFRatio to 0, and set OptimalF, OptimalFLong, OptimalFShort to the script calculated values at the end of the FACTORS training run (if(is(FACCYCLE)) ...).

Examples of different investment methods (see also workshop 6):

// multi-asset system: reinvest the square root of profits separately per component and long / short trades
var AvailableCapital = Capital/sqrt(Number_Of_Components);
Margin = ifelse(For_A_Long_Trade,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);