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 asks how to extend mean-variance optimization to a Fama-French factor framework. It describes returns as factor exposures multiplied by factor returns, plus asset-specific returns, and asks how to represent portfolio risk when several factors…
The discussion considers whether growth in passive and index investing could weaken price discovery by reducing the capital devoted to researching securities and trading on mispricing. It distinguishes low-cost passive investing from exact index replication,…
The document explains how to calculate the price-to-earnings ratio of an equal-weighted equity index from the constituent stocks' P/E ratios. Its answer gives the harmonic mean: take the number of stocks and divide by the sum of the reciprocal constituent…
The document poses a portfolio allocation problem for two assets with stated expected returns and equal volatility, asking how the choice might change when their correlation is positive one, zero, or negative one. It raises the idea that when correlation is…
The document considers how to optimize a portfolio of foreign-currency equities when returns and risk are measured in an investor’s home currency. Its central suggestion is to model the investment as carrying both equity risk and currency risk, rather than…
The document frames how to evaluate a portfolio policy that combines slow structural regime classification with faster detection of tactical instability. Its actions are Allocate, Reduce, and Abstain, with persistence rules intended to prevent short-lived…
The document examines how to represent portfolio returns when combining several assets over multiple periods. It contrasts ordinary returns with log returns, using portfolio weights and interval returns to show why each is convenient along one dimension but…
The document describes an aftcast as evaluating portfolio paths from many historical start dates, using a long return history to examine retirement withdrawals. The questioner adjusts returns for inflation, compounds daily portfolio value, and subtracts a…
The document considers how to project future profit and loss and drawdowns for trading strategies and portfolios. It raises several possible approaches: extrapolating a backtest, resampling its empirical returns, forecasting time-varying variance with GARCH…
The document explains why portfolios optimized for variance and expected shortfall can have different weights, even when expected returns are equal. It decomposes a portfolio return distribution at a lower-tail quantile into tail and non-tail regions.…
The document explains two ways to represent equity risk when validating value-at-risk for a stock portfolio. One approach models shocks for each individual stock and applies them directly. Another models shocks to shared factors, such as a market or…
The document considers what investors should review before investing in a fund, pushing back on the idea that one metric—such as fees, turnover, or recent benchmark performance—can settle the decision. It highlights sources of downside risk including…
The discussion asks whether an asset pricing model can explain observed stock market anomalies and receive broad empirical support. The response does not provide a tested pricing model or a comparative review of empirical results. Instead, it outlines a…
The document discusses fitting a Marchenko–Pastur (MP) eigenvalue distribution to a sample correlation matrix built from S&P 500 stock returns. It notes that a smoothed density plot can make the empirical and theoretical peak heights appear quite different…
The document addresses a Markowitz portfolio optimization problem with lower and upper bounds on each asset weight. It explains that ordinary componentwise upper and lower limits are linear constraints, so they can be included through Kuhn–Tucker conditions…
The discussion considers how to combine long/short momentum and mean-reversion strategies. It notes that simply normalizing each strategy’s signal and adding them is one possible approach, then emphasizes that momentum and reversion are relative to the asset…
The document asks how to combine a momentum signal whose strongest predictive power is at a three-month horizon with a valuation signal that works best over one year. It proposes scaling the valuation signal by dividing it by four when using both in a…
The document asks how to decompose an asset’s marginal contribution to portfolio Mahalanobis distance into volatility and correlation parts. It presents a contribution formula based on each asset’s return and the corresponding row of the inverse covariance…
The document discusses how to calculate a Sharpe ratio when assets have different numbers of trading days or show repeated zero returns. Its answer recommends excluding days when the asset did not trade or the strategy had no position, then scaling the…
The document considers how to allocate portfolio gains when investors contribute capital at different times and one partner later withdraws. Its example uses ETF purchases at different prices, raising the question of whether an early investor’s redemption…
The document addresses why a researcher’s value-weighted CRSP returns may exceed a published market return. Its main diagnosis is a timing error in portfolio weights: monthly returns from the prior month-end to the current month-end must be weighted using…
The document describes a proposed way to estimate investment home bias by comparing the share of a country's investors' equity capital invested domestically with that country's share of the global equity market. The questioner seeks annual investor…
The document explains why a portfolio variance or tracking-error variance calculated as a quadratic form can be negative: the input covariance matrix may fail to be positive semidefinite, so it is not a valid covariance matrix. A valid covariance matrix must…
The document explores how an investor’s risk aversion relates to preferences for skewness and kurtosis in portfolio choice. It points toward lower partial moments and conditional value at risk as frameworks that emphasize downside outcomes, and contrasts…