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It is widely known that the common risk-factors derived from PCA beyond the first eigenportfolio are generally difficult to interpret and thus to use in practical portfolio management. We explore a alternative approach (HPCA) which makes strong use of the partition of the market into sectors. We show that this approach leads to no loss of information with respect to PCA in the case of equities (constituents of the S&…
Embedding value investment in portfolio optimization models has always been a challenge. In this paper, we attempt to incorporate it by employing principal component analysis to filter out dominant financial ratios from each sector and thereafter, use the portfolio optimization model incorporating second-order stochastic dominance criteria to derive an optimal investment. We consider a total of $11$ financial ratios …
Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show that this market factor is the index resulting from the daily compounding of a weighted average of …
We study the construction of SPX--VIX (multi\textendash product) option surfaces that are simultaneously free of static arbitrage and dynamically chain\textendash consistent across maturities. Our method unifies \emph{constructive} PCA--Smolyak approximation and a \emph{chain\textendash consistent} diffusion model with a tri\textendash marginal, martingale\textendash constrained entropic OT (c\textendash EMOT) bridge…
The capital market plays a vital role in marketing operations for aerospace industry. However, due to the uncertainty and complexity of the stock market and many cyclical factors, the stock prices of listed aerospace companies fluctuate significantly. This makes the share price prediction challengeable. To improve the prediction of share price for aerospace industry sector and well understand the impact of various in…
We introduce a unified framework for rapid, large-scale portfolio optimization that incorporates both shrinkage and regularization techniques. This framework addresses multiple objectives, including minimum variance, mean-variance, and the maximum Sharpe ratio, and also adapts to various portfolio weight constraints. For each optimization scenario, we detail the translation into the corresponding quadratic programmin…
This research introduces a novel quantitative methodology tailored for quantitative finance applications, enabling banks, stockbrokers, and investors to predict economic regimes and market signals in emerging markets, specifically Sri Lankan stock indices (S&P SL20 and ASPI) by integrating Environmental, Social, and Governance (ESG) sentiment analysis with macroeconomic indicators and advanced time-series forecasting…
According to The Exchange Act, 1934 unlawful insider trading is the abuse of access to privileged corporate information. While a blurred line between "routine" the "opportunistic" insider trading exists, detection of strategies that insiders mold to maneuver fair market prices to their advantage is an uphill battle for hand-engineered approaches. In the context of detailed high-dimensional financial and trade data th…
We propose a portfolio allocation method based on risk factor budgeting using convex Nonnegative Matrix Factorization (NMF). Unlike classical factor analysis, PCA, or ICA, NMF ensures positive factor loadings to obtain interpretable long-only portfolios. As the NMF factors represent separate sources of risk, they have a quasi-diagonal correlation matrix, promoting diversified portfolio allocations. We evaluate our me…
Financial trading aims to build profitable strategies to make wise investment decisions in the financial market. It has attracted interests in the machine learning community for a long time. This paper proposes to trade financial assets automatically using feature preprocessing skills and Recurrent Reinforcement Learning (RRL) algorithm. The strategy starts from technical indicators extracted from assets' market info…
This paper compares different methods for forecasting the term structure of U.S. and European zero-coupon government bonds using both traditional econometric and Machine Learning (ML) approaches. We compare classical models (e.g., Dynamic Nelson-Siegel (DNS) and Principal Component Analysis (PCA)) with different Neural Network (NN) architectures, including those inspired by the classical models, on the U.S. Treasury …
This paper analyses the Chinese Sovereign bond yield to find out the principal factors affecting the term structure of interest rate changes. We apply Principal Component Analysis (PCA) on our data consisting of the Chinese Sovereign bond from January 2002 till May 2018 with the different yield to maturity. Then we will discuss the multi-factor immunization model (method on hedging market risk) on a bond portfolio.
This paper develops a three-currency Heath-Jarrow-Morton framework in which corporate credit is treated as a separate economy, connected to the nominal and real economies through synthetic inflation and credit exchange rates. The framework produces a testable identity. Under joint no-arbitrage, the credit spread of an issuer expressed over the inflation-rateindexed risk-free curve equals the same issuer's credit spre…
Classical correlation and rolling PCA summarize market dependence through covariance spectra, but they do not provide a unified operator representation for entropy, purity-based mixing, and standardized structural deviations built from rolling multi-feature trajectories. We propose the Quantum Network of Assets (QNA), a quantum-inspired but non-physical density-operator framework in which normalized asset-level state…
Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, …
An eigenvalue λ of A satisfies A v = λ v. In risk, eigenvalues of the covariance matrix are the variances of the principal components — they tell you how many true factors you have.
PCA finds orthogonal directions of maximum variance in a covariance (or correlation) matrix — the yield-curve level/slope/butterfly and many equity ‘statistical factors’ are PCA.
SVD factors any matrix A = U Σ V' into orthogonal rotations and a diagonal of singular values — the workhorse behind PCA, low-rank approximation, and many recommenders.
PCA finds orthogonal directions of maximum variance in a covariance (or correlation) matrix — the yield-curve level/slope/butterfly and many equity ‘statistical factors’ are PCA.
SVD factors any matrix A = U Σ V' into orthogonal rotations and a diagonal of singular values — the workhorse behind PCA, low-rank approximation, and many recommenders.