Dynamic portfolio optimization

Abstract

We consider the problem of dynamic portfolio optimization as a discrete-time, finite-horizon setting. Our model assigns weights to different stocks to represent the stock’s proportion in the optimum portfolio. The objective function of our model is chosen to be to maximize Sharpe Ratio. Our model also incorporates Transaction costs, and suggest the change in portfolio, considering a fixed transaction cost for every transaction. The simulation is also done in MATLAB that uses genetic algorithm to find a portfolio with minimum number of stocks and minimum MSE with the market.Portfolio optimization is choosing appropriate proportions of assets such that highest return is achieved for a given risk preference of the portfolio holder under borrowing, lending and transaction cost constraints. Dynamic portfolio optimization seeks to alter the portfolio composition at regular intervals as the market fluctuates so as to realign it to its long term return target.We started with literature review, learning about the current process and history of portfolio optimizations. We went through a lot of models including the Merton Model the Markowitz Model and the CAPM Model. Following the literature review, we went through a MATLAB code to simulate the optimization of portfolio using genetic algorithm. We also did Excel analysis to optimize out portfolio based on the Sharpe Ratio and the risk. We also did a parallel excel analysis to account for the transaction cost and to see how it impacts our solution.We were able to construct a portfolio in MATLAB, and we find out am optimal portfolio that minimizes the MSE with the market, while holding the minimum number of stocks. We were also able to successfully find out an optimum portfolio based on different objective functions for a sample of 30 stocks