Optimal f and the Leverage Space Model for Portfolio Money Management
Hi good morning StrategyQuant team
Based on the research I have done so far I would propose the following approaches to be included in StrategyQuant / QuantAnalyzer in regards of Money Management feature employing Optimal f whcih it can be used to compare trading systems and perform portfolio management asset allocation among different markets/trading systems .
1) For individual trading systems we should be able to compare the trading system performance on two-dimensional plane, one axis being the geometric mean, the other being the value for f itself. The higher the geometric mean at the optimal f, the better the system. Also, the lower the optimal f, the better the system. But a recurring criticism with the entgire approach of optimal f is that is too dependant on the biggest losing trade for which I propose applying Monte Carlo simulation to get an emperical more acurate distribution of drawndowns.
2) In order to find the Portfolio Best Fixed Fraction
Optimal f: f value that mathematically maximizes the compounded rate of return. Doesn’t take the drawdown into account.Typically results in very large – and dangerous – f values. Theoretically sound but not practical to trade.
Secure f: f value that maximizes the compounded rate of return subject to a limit on the maximum drawdown; e.g., “what f value gives the greatest rate of return without exceeding 30% drawdown?”Improvement on optimal f. Only problem: the drawdown calculated from the historical sequence of trades is not very reliable.Monte Carlo Simulation: Replaces random variables in a simulation with their probability distributions. Distributions are randomly sampled many times.Output of simulation is a distribution. Can be used to find the “best” fixed fraction by replacing the trade with the distribution of trades. (i.e. PowerPoint presentation page 38)
As a result, I would recommend to emply a combination of Secure F with Monte Carlo Simulation to obtain an empiral distribution of the different scenarios of diffent outcomes that the portfolio of trading systems may take which it should be a more accurate approximation for the real distribution of returns.
Raph Vince (i.e. article attached page 27) proposes the following algorithm:
The exercise employed then, algorithmically, of finding the highest point(s) in the N+1 dimensional landscape of N components, is an iterative one. We have determined the following beforehand:
1. The greatest drawdown we are willing to see (which equals 1-b. Thus, if we are willing to see no more than a 20% drawdown, we would determine b as .8)
2. An acceptable probability of seeing a 1-b drawdown, RD(b), the probability of which shall not be exceeded.
3. The time period we will examine for the points above.
The only thing left then, is to determine those f values (0<= f <=1), of which there are N of them, which result in the highest point in the N+1 dimensional landscape, once the landscape has been pared away by points 1 through 3, above.
The process should be performed using the Genetic Algorithm on candidate f value sets. For each f set, calculate (A) The altitude in the N+1 dimensional landscape, then (B) That point in the landscape compared to the drawdown constraints imposed in points 1 through 3, above. Failing that, a value of 0 is returned for the objective function to the Genetic algorithm for that f set, else, the multiple on the stake for that f set is returned as the objective function value to the Genetic Algorithm3. The process continues until the Genetic Algorithm is satisfied as having completed.
Please let me know if you need any further clarification or explanation
Please let me know by when I can test a java prototype versions of both algorithms in StratetyQuant and QuantAnalyzer
Thank you in advanced for your prompt and flawless support
Regards
Juan Carlos del Carmen Garcia
mobile phone 00 34 616455417
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Votes +2
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Project StrategyQuant X
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Type Feature
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Status Archived
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Priority Normal
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Assignee None
History
Votes: +2
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