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.
5,922 documents
The document describes a question about measuring volatility for five equal-weighted portfolios drawn from S&P 500 constituents and grouped by ESG ratings. Constituents are updated monthly as index membership changes, while ESG group assignments are…
The document formulates a wealth-management problem in which an investor chooses a consumption stream and risky-asset holdings while also deciding when to stop. Wealth earns the risk-free return, receives a Brownian-driven risky investment component, and is…
The document explains why a daily correlation matrix should not be multiplied by the number of trading days when annualizing covariance. Correlation is dimensionless: it is covariance divided by the product of the two assets’ standard deviations. If…
The document discusses how to weight a small set of stocks to track the S&P 500. One approach is to estimate weights from historical returns, seeking strong correlation with the index or low tracking error. Regression, principal component methods, and…
The document addresses how to calculate average monthly percent excess returns for portfolios formed while replicating the Fama–French five-factor model. Its suggested workflow is to obtain historical portfolio prices or returns and a Treasury bill rate or…
The document derives the familiar H-model stock valuation expression as an approximation to a two-stage dividend discount model. In the underlying model, dividends grow initially at a higher rate and later settle to a lower perpetual rate. The derivation…
The document introduces utility frameworks that distinguish aversion to ordinary investment risk from aversion to uncertainty about the probabilities themselves, often called ambiguity. It points readers to work on asset pricing under Knightian uncertainty…
The document raises practical questions for researching and backtesting crypto or forex strategies when exchange pairs use different quote currencies. It asks how to value holdings in a common currency, such as USD, whether to use a direct market or a chain…
The document formulates the minimum-variance portfolio problem for a universe of stocks. It assumes the portfolio is fully invested, represents asset risk through a covariance matrix, and seeks weights that minimize portfolio variance while requiring the…
The note surveys ways to approximate a hedge fund’s return stream using a different, potentially passive strategy. It groups prior research into linear factor models, nonlinear or less transparent models, and work emphasizing the difficulty of reliable…
The question asks whether Markowitz minimum-variance optimization can choose weights for a basket of call options on different stocks, given fixed strikes, a covariance matrix, and weights summing to one. The answer distinguishes minimizing expected payout…
The note explains why combining two trading strategies does not guarantee a higher Sharpe ratio. It treats strategy return streams as assets in a mean-variance portfolio and shows that the achievable Sharpe depends on their expected returns, volatilities,…
The note explains how to infer an investor’s risk-aversion coefficient for a portfolio on an efficient frontier, provided the investor follows mean-variance preferences. It starts with utility equal to expected portfolio return minus a risk penalty…
The discussion examines why the CAPM security market line is straight despite a portfolio-return expression that includes a leverage-related quadratic term when returns are framed as exponential growth rates. The accepted response explains that the efficient…
The discussion clarifies how to calculate expected utility when utility is the logarithm of wealth. If wealth is certain and remains at its initial value, utility is a constant, so its expectation is simply the logarithm of that wealth. An initial wealth…
The discussion explains that VaR and CVaR can be calculated repeatedly to track portfolio risk over time. It distinguishes the risk measure itself, which is computed from a return or loss distribution, from time-series methods that may be used to estimate…
The document compares estimating portfolio value at risk from a multivariate normal model with using historical returns or a copula. Historical simulation applies the observed joint return series directly, so it can reflect cross-asset dependence and…
The question asks whether to use close-to-close percentage changes or logarithmic price differences for minute-level EUR/USD data, and whether the choice matters more when combining multiple currency pairs. The reply draws on a standard distinction:…
The post considers how to allocate capital across more than fifty backtested strategies that trade ETFs, mostly equities, with daily signals and next-day open execution. The strategies are mainly short-horizon mean-reversion systems, with different trading…
The document explains that adjusted historical prices incorporate corporate actions that occur after each observation date. Because later dividends and other events are applied cumulatively, older adjusted closes can differ increasingly from the raw closes…
The document asks how to measure monthly returns for two S&P 500 equity portfolios formed from the highest- and lowest-scoring ESG companies. The proposed portfolios are reconstituted annually using the prior year’s ESG scores, and the author wants to…
The document describes estimating incremental value at risk by calculating portfolio VaR from simulated scenario returns, removing one position’s scenario returns, and recalculating VaR. Incremental VaR is the difference between the original and reduced…
The document discusses PCA for equity risk modeling when the number of stocks exceeds the available return observations. With fewer observations than assets, the estimated covariance or correlation matrix has limited rank; components beyond that rank have…
The document surveys alternatives to the sample covariance matrix used in Markowitz mean-variance portfolio construction. It names RiskMetrics exponentially weighted moving average estimators from 1996 and 2006, multivariate DCC-GARCH, and Ledoit-Wolf…