Optimal Trading Portfolio Allocation Enhancement with Maximum Drawdown Using Triple Penance Rule

This study focuses on optimal portfolio trading allocation, using historic trading data to propose an optimal allocation with risk consideration. The risk factors used sequentially in this study are Sharp Ratio (SR) and Maximum Drawdown (MDD). We use the Sequential Least Squares programming (SLSQP) solver to minimise the negative adapted Sharp Ratio for trading profit and loss (PNL) and then we use the Triple Penance Rule assumption for modelling a mathematical formula to represent the relationship between the MDD and the Time under Water (TUW). In this paper, we introduce the risk measure driven by the MDD as the area of the curve during the TUW. The inverse of this area is used to define a proportional weight to the MDD value. The final weight is obtained by applying an algorithm for removing all MDD outliers in the dataset after SLSQP optimization. The final optimal weight is a combination of the calculated proportional PNL weights and the weights from the MDD area. The benchmark is the equal weight portfolio and the maximal return portfolio from Monte Carlo Simulation (MCS). The tested portfolios are two portfolios made from stocks and securities of the Dow Jones Industrial Average (DOJI) and the NASDAQ Composite (COMP). The initial selection is made from only securities that offer at least five years of historical prices. The results show a good compromise in weight allocation between maximising the PNL and minimising MDD and Sharp ratio.