Algorithmic Finance

This article uses Principal Component Analysis to compute and extract the main factors for the financial risk of a portfolio, to determine the most dominating stock for each risk factor and for each portfolio and finally to compute the total risk of the portfolio. Firstly, each dataset is standardized and yields a new datasets. For each obtained dataset a covariance matrix is constructed from which the eigenvalues and eigenvectors are computed. The eigenvectors are linearly independent one to another and span a real vector space where the dimension is equal to the number of the original variables. They are also orthogonal and yield the principal risk components (pcs) also called principal risk axis, principal risk directions or main risk factors for the risk of the portfolios. They capture the maximum variance (risk) of the original dataset. Their number may even be reduced with minimum (negligible) loss of information and they constitute the new system of coordinates. Every principal component is a linear combination of the original variables (stock rate of returns). For each dataset, each financial transaction can be written as a linear combination of the eigenvectors. Since they are mutually orthogonal and linearly independent and that they capture the maximum variance of the original data, the risk of the portfolio is calculated by using the principal components, then they have been used to calculate the total risk of the portfolio which is a weighted sum of the variance explained by the principal components.

Smart Beta Investing has revolutionized investment management field with the ability to offer higher returns with lower costs. The momentum factor in the Smart Beta universe often outperforms other popular factors, besides being well documented in the literature, it is found to be pervasive across different geographies and asset classes. In this paper, we implement a long-only momentum based investment strategy for the Indian equity markets that delivers superior risk-adjusted performance, derived upon comparing multiple strategies across time frames. Based on these tests, we find that the lagged 6-months’ compounded returns indicator with quarterly rebalancing can be used to generate the highest risk-adjusted performance.The paper also tests a related phenomenon called the Accelerated Effect of momentum as documented by Ardila et. al. (2021) for the Indian equity market, and finds that the accelerated momentum effect underperforms the traditional momentum both on an absolute and risk-adjusted basis.

We present an algorithmic trading strategy based upon a graph version of the dynamic mode decomposition (DMD) model. Unlike the traditional DMD model which tries to characterize a stock’s dynamics based on all other stocks in a universe, the proposed model characterizes a stock’s dynamics based only on stocks that are deemed relevant to the stock in question. The relevance between each pair of stocks in a universe is represented as a directed graph and is updated dynamically. The incorporation of a graph model into DMD effects a model reduction that avoids overfitting of data and improves the quality of the trend predictions. We show that, in a practical setting, the precision and recall rate of the proposed model are significantly better than the traditional DMD and the benchmarks. The proposed model yields portfolios that have more stable returns in most of the universes we backtested.

We obtain the bond price formula for the fractional Cox-Ingersoll-Ross model. Then we obtain option price formula for the bond. Finally we apply it to derive option price formula in fractional Heston model.