Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
4,194 documents
This question sets up a two risky-asset example for learning the Black–Litterman portfolio model. It starts with CAPM estimates for the assets, including a market return, asset betas, residual volatility inputs, and a risk-free rate, then asks how to derive…
The document asks how to obtain and calculate Fama–French three- and five-factor inputs for a selected group of large technology stocks. It distinguishes ordinary market data such as daily high, low, close, volume, and adjusted price from the portfolio…
The document clarifies what “market beta” means in the Fama–French (1992) cross-section of expected returns. It describes the model as a generalization of CAPM: the framework uses three factor exposures, and the market beta is the exposure to the market…
The document asks how to examine historical idiosyncratic volatility for individual stocks at daily frequency, without converting residuals to monthly observations or forecasting. The suggested approach is to estimate factor-model residual variance for each…
The document discusses how to distinguish a broad test of a positive risk–return relationship from a more specific test of the CAPM. It presents a cross-sectional return model with beta, squared beta, and residual risk as explanatory terms, and identifies…
The document explains how to assess a portfolio or return series against Fama–French risk factors. The main approach is a time-series regression of excess portfolio returns on factor returns, with the intercept interpreted as Jensen’s alpha: performance not…
The document addresses how “orthogonal” is used when discussing alpha, risk sources, and portfolio factors. Its answer gives an intuitive interpretation: two return streams move independently, so one’s direction does not determine whether the other rises,…
The document sketches an early timeline for formal portfolio selection theory. It identifies Harry Markowitz’s 1952 work on mean-variance portfolio selection as a foundation of modern portfolio theory, emphasizing how diversification affects portfolio…
The document outlines the two stages of Fama–MacBeth regression for testing whether factor exposures explain stock returns. First, time-series regressions estimate each security’s factor loadings. Then monthly cross-sectional regressions use those estimated…
The document explains why separate factor regressions for two portfolios do not establish that one has a higher alpha than the other. Each regression tests its own alpha against zero; comparing the estimates requires a statistical model that explicitly links…
The document outlines how to assess whether an ESG score behaves like a priced equity factor. It cautions that correlating ESG scores with established characteristics such as size or value does not establish a risk premium. Instead, it proposes sorting…
The document raises an estimation concern about the prediction matrix in Bryan Kelly’s Principal Portfolios framework. The matrix links each asset’s next-period return to signals associated with other assets, and the cited estimator averages return–signal…
The document discusses how to interpret principal component analysis when many pharmaceutical-company characteristics are analyzed together. The example reports component variance shares and loadings, and retains five components because their cumulative…
The note explains a dimension-counting point in the generalized method of moments formulation of the single-factor CAPM. The time-series conditions include one residual mean and one residual-factor product expectation for each of N assets, giving 2N…
The document explains why a multi-factor equity model might use market-cap-weighted means when converting factor values into Z-scores. In a universe with many small companies and a few very large ones, an unweighted cross-sectional regression can let the…
The document considers whether adding Bitcoin to a stock-market proxy improves a CAPM test. The questioner reports applying a GRS test to ten industry portfolios and finding jointly significant alphas with a stock-based market proxy. Adding Bitcoin at a 2.1%…
The document explains the joint-test problem in empirical tests of market efficiency. A researcher does not observe market efficiency directly; instead, the test evaluates whether returns contain statistically significant abnormal performance relative to an…
The document explains how SMB is constructed differently across the Fama–French three-factor and five-factor models. In the five-factor framework, SMB combines size spreads from portfolios sorted on book-to-market, operating profitability, and investment.…
The document addresses how to summarize valuation data when companies, especially young firms, have negative earnings or negligible sales. It explains why price-to-earnings ratios become difficult to interpret in this setting: a negative ratio sorts below…
The document asks whether CAPM implies zero alpha for every asset and presents both the theoretical restriction and the empirical testing issue. Under the model, expected excess return is explained by market beta, so alpha is zero as a population…
The document raises questions about interpreting CAPM, Fama–French three- and five-factor, and Carhart regressions for an actively managed emerging markets fund. The fund shows a negative SMB coefficient against broad emerging markets data, but the…
The document describes a proposed way to adapt long-horizon simulated stock returns to alternative climate scenarios. The author plans to use shocks for factors such as temperature and carbon prices. For temperature, the question cites existing literature…
The document asks whether forward-looking volatility estimates can improve an estimate of an asset’s CAPM beta for the coming month. The proposed approach replaces historical market variance with VIX-implied volatility and historical asset volatility with…
The document considers which size factor to use when estimating three-, four-, and five-factor performance regressions: the SMB series associated with the three-factor model or the version used in the five-factor model. It describes the regressions as…