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 compares two ways to set portfolio weights to a target ex-ante volatility. Mean-variance optimization uses the inverse covariance matrix to adjust the signal and chooses a risk-aversion parameter to reach the target. Direct risk scaling instead…
The document raises a portfolio risk management problem: how a fund investing in both public markets and private assets can measure active risk and establish acceptable limits. It identifies private equity, private credit, infrastructure, and real estate as…
The document asks what calculations and holdings ETF issuers must publish, especially for US funds. Its answer does not resolve the US reporting question; instead, it outlines the European Union framework for Key Information Documents (KIDs) and related…
This document describes ways to select a small stock basket that tracks a broad index, framing the limit on the number of holdings as a cardinality constraint. A mixed-integer quadratic program directly handles that constraint, while a genetic algorithm is…
The document raises an index-construction problem using stocks with roughly similar market capitalizations but very different share prices. It calculates an average weighted by each stock’s market-cap share, then replaces the high-priced constituent with a…
The document asks how to simulate daily prices for a ten-asset stock portfolio over a long horizon when each asset has an expected return and volatility, and cross-asset correlations are initially assumed to be zero. The response suggests drawing a random…
The document discusses limiting turnover when optimizing a bond portfolio for option-adjusted spread (OAS) subject to duration and other constraints. Given current weights, the accepted approach expresses a turnover cap as a bound on the sum of absolute…
The document presents a proposed way to compare bundles of peer-to-peer consumer loans that have not matured. The available data include borrower characteristics recorded at origination and payment histories observed to date. The questioner seeks a valuation…
The document derives the decline in stocks that would move a portfolio away from its target stock allocation far enough to trigger a rebalance. It assumes stocks begin at allocation X₀, bonds remain unchanged, and the trigger occurs when the stock share of…
The discussion asks how to combine two uncorrelated strategies, each with a Sharpe ratio of one. For an equally weighted portfolio, it derives the Sharpe ratio as the sum of the strategies’ volatilities divided by the square root of the sum of their…
The document considers how to represent major currency pairs together as a connected data structure, rather than analyzing each pair as an isolated time series. The proposed “pentahedron” concept is reframed as a weighted graph: currencies are nodes and…
The document discusses how to choose return frequency, historical estimation window, and benchmark when estimating an asset's beta through linear regression. It frames those choices around the intended use: estimating returns with CAPM for mean-variance…
The document asks how to add a tactical forecasting layer to a plain risk parity allocation. Its example is anticipating a shift in fixed income from a bullish to a bearish trend and reducing duration to hedge the portfolio. It also asks about forecasting…
The document addresses the meaning and selection of the tau parameter in the Black-Litterman portfolio model. Although tau is often described as controlling the weight assigned to investor views, the responses indicate that its interpretation and calibration…
The document asks whether Markowitz optimization reduces unsystematic risk while leaving systematic risk unchanged, and whether systematic exposure can be reduced. The response describes the framework as finding minimum-variance portfolios for specified…
The document raises a concern that portfolio optimization can be circular when a portfolio manager supplies expected returns and covariances based on views that already shaped the current portfolio, and a risk manager then uses those same inputs to judge its…
The document gives a general method for assigning portfolio variance to individual assets from a covariance matrix and weight vector. Total variance is the quadratic form of weights and covariance. For each asset, its variance contribution is its weight…
The document compares common Sharpe ratio formulas and explains the distinction between forward-looking and realized measures. Both relate excess return to volatility, but an ex-ante ratio uses expected future returns and risk, while an ex-post ratio uses…
The document considers whether monthly investment returns can be expanded into daily observations for factor regressions and portfolio weight analysis. Its main proposal is stochastic backfilling: model the lower frequency asset’s return distribution,…
The document discusses covariance estimation when equity return histories start at different times or contain gaps, such as holidays. For unequal starting dates, one approach begins with the longest available histories, estimates their relationships, and…
The document considers how to summarize the pairwise correlations among assets. It questions whether Fisher’s z transformation is the right way to average sample correlations and discusses bias in the sample correlation estimator. It presents an Olkin–Pratt…
The document explains how equality and inequality constraints serve different purposes in mean-variance portfolio optimization. The budget condition that portfolio weights sum to one is naturally an equality. Other common constraints, such as long-only…
The document compares the Sharpe ratio and information ratio through their return-over-risk definitions. It explains that the traditional Sharpe ratio measures excess return relative to a risk-free rate, while the information ratio measures active return…
The document presents an attempted Lagrangian formulation for finding a minimal martingale measure among equivalent martingale measures. It defines an option payoff, a terminal self-financing portfolio value, a candidate density process, and a constraint…