capital-asset-pricing-model

A comprehensive deep dive into the mathematical bridge between risk management and alpha prediction in algorithmic trading systems. From the Fundamental Law of Active Management to conditional factor models, explore how machine learning transforms static betas into dynamic prediction engines. 📊 Deep Research Topics: quantitative finance, investment analysis, financial education, financial resea…

I'm working with some factor data from a third party company. Their factor model is estimated on a broad universe. I'm trying to re-estimate the model on a smaller subset (my own universe) to construct factor mimicking portfolios. Essentially, I want to find portfolios from within my universe that track their factor most closely. Let's begin with a factor model: $r_{i,t} = X_{i, t-1}^{'} F_t + \e…

Factor models such as Fama-French or the other ones that are partially summarized here work on the cross-section of asset returns. How are the factors built, how are sensitivities/coefficients estimated? In this context Fama-MacBeth regressions are usually mentioned. How does this method work intuitively? Could anyone give a step-by-step manual? EDIT: Links to papers and manuals have been posted…

The following paper (and the references given within) focuses on the practical aspects of implementation of factor-based investing and gives an overarching framework for the more technical answers here: Practical Considerations for Factor-Based Asset Allocation by Kang, X. (Standard & Poor's), Ung, D. (Chartered Alternative Investment Analyst Association (CAIA); Global Association of Risk Profess…

Time Series Factor modelling is a very good and practical manual to building time series factor models. FactorAnalytics is a very good R package that allows you to fit timeseries, fundamental and statistical factor models. A good reference to factor models would be Chapter 15 of this book.

1. Determine Factors Economically, the use of factor models can be either motivated using the ICAPM or the APT . Although there are some theoretical differences between the model, for empirical and practical work these differences are irrelevant. In the end, both models stipulate that returns and expected returns are linear functions of the factors: $$ r_{i,t} = \alpha_i + \sum_j \beta_{i,j} F_{j…

A comprehensive tutorial on factor engineering, signal processing, and performance attribution for quantitative trading. Master the Fundamental Law of Active Management, implementation shortfall, and the reality of backtest overfitting. 📊 Deep Research Topics: quantitative finance, investment analysis, financial education, financial research, market analysis

Master the architecture of modern factor models. Transition from asset-class silos to a surgical, multidimensional understanding of risk drivers. From the Factor Zoo to Generative AI Factors, explore the systematic decomposition of market risk. 📊 Deep Research Topics: quantitative finance, investment analysis, financial education, financial research, market analysis

This thesis develops equilibrium asset pricing models in incomplete markets with a large number of heterogeneous agents using mean field game theory. The market equilibrium is characterized by a novel form of mean field backward stochastic differential equations (BSDEs). First, we propose a theoretical model that endogenously derives the equilibrium risk premium. Agents with exponential preferenc…

Abstract Grossman and Stiglitz (1980) proved that informationally efficient markets are impossible because efficiency destroys the incentive to produce information. Their proof rests on an assumption so foundational that the subsequent literature has never examined it: that trading profit is the sole return to information production. This paper relaxes that assumption. When economic agents can pu…

We analyse the effect of a proportional wealth tax on asset returns, portfolio choice, and asset pricing. The tax is levied annually on the market value of all holdings at a uniform rate. We show that such a tax is economically equivalent to the government acquiring a proportional stake in the investor's portfolio each period, a form of risk sharing in which expected wealth and risk are reduced b…

Abstract This paper investigates whether incorporating daily U.S. fiscal flows improves the explanatory power of traditional asset pricing models. Using data from October 2005 to April 2024, we assess model performance through both classical alpha testing and Bayesian model comparison following the framework of Bryzgalova, Huang, and Julliard (2023). The results show that the inclusion of the fis…

Traditional asset pricing models fail to account for the catastrophic volatility in the current global economic transition. This paper proposes the GIE Framework (P = f + G + E), a non-linear tri-factor model consisting of fundamental credit base (f), geopolitical gradient field (G), and expectational momentum (E). By introducing the Psi (Ψ) Stability Index, we derive a critical state threshold o…

This article's aim is to provide the solution to the equity premium puzzle without using calibrated values. Calibrated values of subjective time discount factor were used in my prior derived models because 4 variables were determined from 3 different equations. Furthermore, calculated values and risk behavior determination of my prior models were compatible with empirical literature. 4 unknown va…

This article proposes a hierarchical framework for structural equity valuation that reorders the main components of modern financial theory. At the foundational level, the Arrow–Debreu framework — developed by Nobel Prize laureates Kenneth Arrow and Gérard Debreu — defines prices as time-dated and state-contingent objects expressed in a common numéraire. Building on this foundation, the PPP–SIRRI…

These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit combining probability theory, statistics, numerical methods, and empirical modeling, with a strong emphasis on implementation in Python. Core topics include ran…

The asset pricing literature emphasizes factor models that minimize pricing errors but overlooks unselected candidate factors that could enhance the performance of test assets. This paper proposes a framework for factor model selection and testing by (i) selecting the optimal model that spans the joint efficient frontier of test assets and all candidate factors, and (ii) testing pricing performan…

We estimate risk premia in the cross-section of cryptocurrency returns using the Giglio-Xiu (2021) three-pass approach, allowing for omitted latent factors alongside observed stock-market and crypto-market factors. Using weekly data on a broad universe of large cryptocurrencies, we find that crypto expected returns load on both crypto-specific factors and selected equity-industry factors associat…