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Portfolio Optimization. Random Matrix Approach to Estimating Covariance Matrix
Estimating covariance matrix is one of the biggest challenges in portfolio optimization. Sample covariance matrices tend to be very noisy and it gets substantially worse as the number of stocks in the dataset increases. In this article I will describe and implement a method for estimating covariance matrix based on Random Matrix Theory (RMT). It…
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Portfolio Optimization with Weighted Mean and Covariance Estimators
One of the assumptions of Modern Portfolio Theory (MPT) is that the mean and covariance matrix of returns are known. Clearly that is not the case and we have to use some estimates. The accuracy of the estimates used has a big effect on the resulting portfolio. In the previous article I used sample mean and covariance…
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Introduction to Portfolio Optimization and Modern Portfolio Theory
Portfolio optimization is an important area of quantitative finance. It was introduced by Harry Markowitz in 1952 in his paper ‘Portfolio Selection’ and was further developed into a whole research field. Now there exists a lot of different portfolio optimization frameworks and new papers on the topic are being published almost every day. The main…
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Modeling stock prices with ARMA model
In this article I will investigate the idea of using autoregressive-moving-average (ARMA) models to predict stock prices. It is based on a paper ‘Stock Price Prediction Using the ARIMA Model’ (Ariyo et al. 2014). In my previous articles I mostly used more advanced methods of modeling and I realized that I never really tried working with…
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Pairs trading with wavelet transform
This article is based on paper ‘Pairs Trading with Wavelet Transform’ (Eroglu et al. 2022). Authors claim that using wavelet transform to remove noise from stocks price series leads to significant improvements in profitability of different pairs trading strategies. I am going to test several different strategies and see how using wavelet transform affects their performance. I…
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Pairs trading with partial cointegration
This article is based on the paper ‘Pairs trading with partial cointegration’ (Clegg & Krauss, 2016). I am going to describe Partial Cointegration (PCI) model presented in the paper, explain how to estimate its parameters and implement a trading strategy based on it. I will backtest the strategy both on synthetic and real data and compare its performance…