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
A positive and statistically significant intercept in a Carhart regression can coexist with a large portfolio loss. The intercept measures performance relative to the model’s factor exposures, not whether the portfolio made money in absolute terms. A…
The document describes a scenario-based approach to estimating Conditional Value at Risk for a portfolio. Rather than simulate each security in isolation, define scenarios for the risk factors that drive asset prices, reprice the entire portfolio under each…
This exchange considers how to estimate annualized tracking error from a series of monthly relative returns. It identifies multiplying the monthly dispersion by the square root of twelve as the usual annualization step, reflecting aggregation across twelve…
The discussion considers how to express a relative return belief such as one asset outperforming another without specifying a fixed return spread. A standard Black-Litterman view can encode a specified difference between expected returns, but the proposed…
The document asks how to simulate multiple stock paths with stochastic volatility while representing dependence between assets. It explains why a basic stochastic volatility model may be unsuitable for pricing: its marginal distributions may not match traded…
The document clarifies how PortfolioAnalytics interprets the `training_period` and `rolling_window` settings in rebalancing optimization. Both are integer counts of observations, measured in the same time units as the returns series. Thus, their effective…
The document investigates why posterior expected returns calculated from two equivalent Black–Litterman formulas differ from published results. It compares calculations based on equilibrium returns, asset covariance, investor views and view uncertainty with…
The document raises questions about constructing an equal-volatility portfolio from daily stock returns and measuring its Sharpe ratio. The investor describes calculating log returns, scaling each stock’s returns using a rolling volatility estimate, and…
The document explains how to translate a Markowitz allocation into stock purchases. Multiply the available capital by each asset’s portfolio weight to obtain target dollar allocations, then buy the closest feasible number of shares. If a broker does not…
The document asks how the sample length used to estimate portfolio volatility affects the result, and whether recent returns can receive greater weight. Portfolio volatility is computed from asset weights and a covariance matrix, so changing the return…
The document outlines how to find the weights of two risky assets in a portfolio when their expected returns, standard deviations, and correlation are known. It expresses portfolio excess return as the weighted asset returns less the risk-free rate, and…
The note considers a Markowitz portfolio setup in which the risk-free rate exceeds the expected return of the minimum-variance risky portfolio. Under the stated assumptions, the tangency portfolio lies on the inefficient part of the risky frontier, implying…
The note gives an intuitive finite-scenario argument for why expected shortfall is subadditive, a property that supports recognizing diversification in portfolio risk. It describes expected shortfall as the average loss in the worst tail of outcomes, using a…
The document distinguishes an optimization model from the numerical method used to solve it. For an unconstrained linear regression objective such as minimizing mean squared residuals, standard least-squares methods and properly implemented heuristics should…
The document describes ways to rank stocks using historical returns. It distinguishes a return-based measure of value, such as the mean of log returns, from risk measures such as return volatility or maximum drawdown. Stocks can be compared on both…
The example considers a deterministic market with a constant asset priced at one and a second asset whose value rises over time. With no uncertainty, the market is complete in the stated one-period setup because any terminal payoff can be obtained by holding…
The document describes ways to estimate correlations that give more weight to recent observations. One method applies exponential weighting directly to the products of paired returns to estimate covariance, then normalizes by the corresponding standard…
The document examines the relationship between a square-root market-impact model and the three-halves power often used for trading-cost penalties in portfolio optimization. The initial question is whether the higher exponent comes from integrating an…
The document asks how to judge whether a market or tangency portfolio built from a set of stocks is desirable for long-term investment. The response proposes two initial checks: compare the portfolio’s risk-adjusted return, such as its Sharpe ratio, with…
The document asks how to incorporate cross-sectional scores, such as recent momentum or price-to-book ratios, into a minimum-variance portfolio. The proposed idea is to balance portfolio variance against a reward for holding assets with stronger scores. It…
The document examines whether loan principal repayments belong in a project's net present value calculation. It exposes a common comparison error: subtracting repayments from operating cash flows while omitting the initial loan proceeds makes the financed…
The discussion surveys approaches to investment analysis and portfolio construction rather than identifying a single accepted industry standard. It covers fundamental value analysis, mean-variance and factor models, risk measures such as value at risk,…
The answer explains shrinkage as a way to improve estimation by pulling noisy estimates toward a shared target. It connects this intuition to Bayesian priors and Stein’s results: information across a group of estimates can help estimate each individual…
The document compares two proposed ways to choose weights for a long–short portfolio of S&P 500 stocks while minimizing estimated volatility. One approach estimates a covariance matrix from historical returns and minimizes the quadratic portfolio variance.…