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 exchange concerns a derivation connecting a stochastic discount factor (SDF) to a one-factor expected-return relation. The setup defines the SDF as one minus a traded tangency-portfolio return, then asks how the no-arbitrage pricing equation yields the…
The document considers an equal-weighted composite of regional equity indexes that have different market holidays. It asks how to handle dates when one region has no observation, noting that simply removing the unavailable index and recalculating the weights…
The document asks whether the information in a large covariance matrix can be represented by a scalar or another compact measure. It points to the matrix’s growth with the number of assets and the resulting dimensionality burden in portfolio analysis. It…
The document asks whether return distributions and models are unaffected when the same observations are reordered. A shuffle preserves the full-sample mean and volatility, but can change serial dependence and the statistics observed in subsets of the sample.…
The document explores how to use an equity alpha signal that sorts stocks into forecast-return groups, where average realized returns rise across the groups and lower-return groups also show lower realized volatility. It asks whether option positions, such…
The discussion explains why low-eigenvalue directions of a covariance matrix can produce low portfolio variance. Expressing weights in the covariance matrix’s eigenbasis makes variance a sum of squared coordinates, each scaled by its eigenvalue. Under a…
Bond duration summarizes how sensitive a bond’s price is to changes in yield. It provides a quick way to compare the interest rate risk of plain fixed-coupon bonds and to estimate price changes without repricing every bond. Modified duration expresses…
The document asks how to calculate monthly returns for a Jegadeesh and Titman style momentum strategy with overlapping portfolios. Each month, a new tranche is formed and held alongside earlier tranches that have not yet reached the end of their holding…
The document explains how to describe performance and risk for a portfolio with equal-sized long and short positions, whose net initial investment is zero. It distinguishes a simplified research convention from an investor-level account that includes the…
The question asks whether monthly portfolio and benchmark returns should be adjusted for differences in month length when estimating annual excess returns, correlations, and CAPM betas. One response suggests normalizing by trading days where possible.…
The document explains that a portfolio’s estimated beta depends on which market return series is used. Regressing the current portfolio holdings against the S&P 500’s realized historical returns measures their relationship to the index as it actually changed…
The document explains two limitations of Value-at-Risk. VaR reports a loss threshold at a chosen confidence level, but it does not describe the size or shape of losses beyond that threshold. For distributions with heavy or long tails, that omission can…
The document outlines a proposed method for constructing a factor-mimicking portfolio whose returns are strongly related to aggregate consumption growth, following the consumption-oriented CAPM literature. It describes calculating quarterly log consumption…
The document asks whether portfolio optimization can avoid using empirical estimates such as historical returns and volatility. Its brief response points to unsupervised learning as a way to investigate relationships among assets, including correlation-like…
The document considers doubling exposure to a diversified permanent-portfolio variant holding equities, long-term government bonds, gold, and real estate. Its proposed construction uses deep in-the-money call options intended to have deltas near one, with…
The discussion explains that Bayesian versions of Fama-French or Carhart factor models can be approached as Bayesian regression. It recommends learning Markov chain Monte Carlo and Gibbs sampling, while noting that Hamiltonian Monte Carlo software can reduce…
The discussion considers how to model a portfolio exposed to several equity indices, including broad-market, small-cap, and financial-sector benchmarks. One reply suggests estimating each stock’s historical correlations to the indices, assigning it to the…
The document asks how to construct a fair buy-and-hold comparison for a strategy that accumulates shares over several days, sells the accumulated position, and later repeats the process with a different trade size. The central challenge is that the…
Value at Risk (VaR) is generally not additive: a portfolio’s VaR cannot usually be found by summing the standalone VaRs of its holdings. For two independent, normally distributed asset returns with zero means, the document derives portfolio risk by adding…
The document surveys how quantitative investors may use machine learning and data, including for estimating fair value, setting trading quotes, and researching stock signals. One response frames high-frequency firms as liquidity providers: models can…
The document explains why a manual portfolio-rebalancing calculation may disagree with a portfolio-return package: weights are dated at the end of a period and apply to the next period's returns. In the example, weights recorded at one month-end are used to…
This document addresses an apparent conflict between the conventional discounted-cash-flow price of a coupon bond and the martingale condition for its price relative to a bank-account numeraire. The key distinction is between the bond’s quoted price and the…
The document explains how to compute a maximum diversification portfolio using only risky assets. Given a nonsingular covariance matrix, the procedure takes its inverse, multiplies it by the vector of asset volatilities, and normalizes the resulting weights…
The document asks how estimated factor exposures can guide weights across a universe of securities. Its answer describes a high-minus-low construction: rank assets on a selected factor, form upper and lower groups, and take opposing positions in those…