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I am of the research is the use of particle swarm optimization (PSO) of currency carry trading portfolio optimization . In this article, I will introduce portfolio optimization and explain its importance. Secondly, I will demonstrate how to apply the PSO portfolio optimization. Third, I will explain arbitrage trading portfolio and summarize my findings.
Portfolio Optimization
Investment portfolio includes assets and investment capital. Portfolio Optimization involves decide how much money should be invested in each asset. With such diverse requirements, the introduction of minimum and maximum constraints asset exposure, transaction costs and foreign exchange costs, I'm using Particle Swarm Optimization (PSO) algorithm.
Portfolio optimization works by predicting the expected portfolio risk and return for each asset. The algorithm accepts these forecasts as input and determine how much capital should be invested in each asset in order to adjust the portfolio risk and maximize return on satisfy the constraints. Predict the expected risk and return of each asset needs as accurately as possible, in order to make the algorithm performed well. There are various methods, in this study, I studied three common ways.
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Normal type of return - In this method, the distribution of assets to create value history and random sampling to obtain the future value of each asset. This method assumes that history and future values are normally distributed.
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Return follow Brownian motion - In this approach, over time, generate random walk each asset representing a daily return. Thereby calculating the overall return of the portfolio. This approach assumes future returns follow a random walk.
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Returns follow a geometric Brownian motion - In this method, again generate random walk, but according to the daily variance and long-term market drift to zoom. This method assumes that future returns follow a random walk scaling.
In my research, I found the third method is the most accurate
Particle Swarm Optimization (PSO)
In the PSO, each particle group represented as a vector. In the context of portfolio optimization, which is a weight vector indicating allocation of capital for each asset. Vector conversion for the location of the multi-dimensional search space. Each particle will remember it personal history best position. PSO for each iteration, find the global optimum position. This is the group best personal best position. Once the world's best place to find each individual particle will be closer to its optimum position and global best position. When performed in multiple iterations, this process produces a good solution to solve this problem, because the particles are converged on the near-optimal solution.
The figure depicts the particle swarm optimization algorithm position relative to the global optimum (blue) and a personal best position (red) How to update the population of each particle.
PSO's performance affected by trade-off. PSO describes the ability to explore the search space to explore different areas. Exploitation describes the ability of PSO focus the search in the search space is a promising area. In order to enhance the exploration and development capabilities of the PSO, the application of the following algorithm enhancements:
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Random polymeric particles reinitialization - Exploration be improved by restarting the particles are particles collected on the global optimum particle. Using the similarity function between the two particles (carrier) measurements converge.
If the particles are particles converge near global optimum, but less suitable for global optimum particle, reinitialize the random search space somewhere. This improves the ability to explore the PSO.
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Best selectively mutated particles - is improved by initializing the world's best neighbor adjacent particles. If a neighbor is better than the world's best particle, the particle is replaced by the world's best neighbors.
For each iteration of the algorithm, to create a neighborhood near the global best particles. If any of these neighbors is superior global optimum particle, the particle is replaced global optimum.
Use Particle Swarm Optimization portfolio optimization
PSO algorithm can be used to optimize the portfolio. In the context of portfolio optimization, group each particle represents a potential capital allocation between asset portfolio. One of the utility function of the relative suitability of these financial portfolio can use a number of balance risk and expected return is determined. I use the Sharpe ratio, because it has become a recognized industry standard benchmark portfolio performance. Consider the following illustration apply to PSO portfolio of assets consisting of three,
Using particle swarm optimization (PSO) portfolio optimization examples. Gray particle being updated. Red particles are particles of personal best position gray, blue particles are the world's best locations.
灰色粒子转换为向量（0.5,0.2,0.3），意味着投资组合资本的50％分配给资产1，20％分配给资产2，30％分配给资产3。该分配的预期夏普比率为0.38，小于个人最佳位置（红色粒子）和全球最佳位置（蓝色粒子）。这样，灰色粒子的位置被更新，使得它更接近全局最佳粒子和个人最佳粒子。
使用粒子群优化（PSO）的投资组合优化的例证。灰色粒子被更新，使其更接近全球最佳，并且是个人最佳的。得到的矢量比以前更好。
灰色粒子已移动，现在转换为矢量（0.3,0.3,0.4），其预期夏普比率为0.48。该值高于之前的个人最佳位置，因此个人最佳位置（红色粒子）将更新为当前位置。
使用粒子群优化（PSO）的投资组合优化的例证。个人最佳位置（红色粒子）现已更新为粒子的当前位置。
使用粒子群优化的真正挑战是确保满足投资组合优化的约束。如前所述，存在许多限制。最常见的限制因素首先是资产之间不再分配和不少于100％的可用资本（即权重向量必须加起来为1.0）。其次，不允许对资产进行负面分配。最后，资本应该分配给投资组合中至少这么多资产。后者是基数约束。两种常用技术用于确保粒子满足约束条件，
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修复不满足约束的粒子 - 对于不满足约束的每个粒子，应用一组规则来改变粒子的位置。
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惩罚不满足约束的粒子的适应性 - 对于不满足约束的每个粒子，惩罚该粒子的夏普比率。
贸易组合
对于我的研究，我将这种技术应用于套利交易组合。套利交易组合包括多个套利交易。 套利交易是一种交易策略，其中交易者卖出利率相对较低的货币，并使用这些资金购买不同的货币，从而产生更高的利率。使用此策略的交易者试图捕捉称为利率差异的利率之间的差异。
通过使多种货币的投资多样化，可以减轻外汇损失的风险，但不能消除。因此，套利交易的投资组合本身风险低于个别套利交易。在套利交易投资组合的背景下，投资组合优化的目标是进一步降低外汇损失的风险，同时提高投资组合实现的投资回报。
Trading portfolio between the yen, the dollar, South African rand and the Brazilian real. Portfolio Optimization goal is to determine how much money should be allocated to each transaction in order to optimize risk-adjusted returns.
In my research, I use particle swarm optimization algorithm to determine the optimal allocation of investment capital among a group of arbitrage trading. Arbitrage trading portfolio My research includes 22 different currencies. Currencies including the Australian dollar, Brazilian real, Canadian dollar, Swiss franc, the RMB, Danish krone, euro, British pound, the rupiah, the new Israeli shekel, the Indian rupee, Mexican peso, Malaysian ringgit, the Norwegian krone, New Zealand dollar, Philippine peso, Russian ruble, Swedish Krona, Thai Baht, Turkish lira and the dollar.
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