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 considers how to estimate a portfolio’s quarter-end return when valuations for some illiquid private assets have not yet arrived. It frames the task as predicting missing asset values from the returns of assets already marked and the portfolio’s…
The document explains the factor of one half in a mean-variance portfolio objective that subtracts a risk penalty proportional to portfolio variance from expected return. The factor is a mathematical convenience: when differentiating the quadratic variance…
The document discusses adding a penalty proportional to absolute portfolio changes to a mean–variance objective, while retaining constraints such as long-only holdings and fully invested weights. Its central modeling idea is to represent each position change…
The document asks whether two assets with equal return volatility can be combined into a product with greater percentage-return volatility, without simply using cash leverage. It considers a long-only linear combination and derives its variance from the…
Subadditivity says that the risk assigned to a combined position should be no greater than the sum of the risks assigned to its components. The document explains the right-hand side as the separate risks of two positions, whether those positions are held in…
The document explains how to find the global minimum variance portfolio from two risky assets. It represents the portfolio with weights w and one minus w, then expresses portfolio variance using each asset’s variance and their covariance, represented through…
The document investigates when the phrase “Modern Portfolio Theory” entered use, distinguishing the label from the ideas associated with Markowitz. It notes that Markowitz’s early work used different terminology and reports a 1965 article by Herbert Grubel…
The document describes a portfolio-selection problem: individual strategies can be profitable yet generate trades in bursts, leaving gaps in activity and uneven profit growth. The author wants to combine strategies so that trades and returns are distributed…
The document raises a portfolio-construction problem from a life-insurance asset and liability model: whether a large bond portfolio can be represented by a smaller set of zero-coupon bonds with approximately matching cash flows. The motivation is to reduce…
The document works through the variance of a weighted basket when all asset returns have correlation one. For two assets, it writes the usual portfolio variance expression, including the covariance term, and recognizes that the expression becomes the square…
The document explains how risk-free rates affect long-short portfolio returns. If the long and short legs have equal funding amounts, subtracting the risk-free rate from each leg before combining them gives the same result as calculating the long-short…
The document explains CAPM equilibrium as a market-clearing condition: aggregate demand for securities matches their supply. Under the model’s assumptions, investors choose combinations of the risk-free asset and the market portfolio, with their allocation…
The document outlines a rolling-window procedure for comparing portfolios by out-of-sample variance. At each step, returns within a fixed estimation window are used to construct portfolios; the window then advances by one month, dropping the oldest…
The discussion distinguishes introductory portfolio theory from the more advanced subject of portfolio management. It recommends several books associated with portfolio management, while noting that these may be too advanced for a student whose course begins…
The document poses a portfolio performance question involving three assets held at the start, the later sale of one asset, and updated values for the two remaining holdings. It asks how to calculate the portfolio return over the full period, but provides no…
The document addresses why returns computed from MSCI World subindices may not match the published parent-index return when weights are based on each subindex’s index level. The answer states that MSCI indices are market-cap weighted, so a rough…
The document raises a theoretical question about whether a positive equity risk premium could arise from a finite investable asset universe, even without investor risk aversion. It contrasts limited diversification in finite markets with a hypothetical…
The document addresses how to describe one asset’s volatility in relation to a portfolio that contains several correlated assets. The answer identifies the quantity as the asset’s marginal volatility contribution and expresses it as the asset’s own standard…
The document explains why a commonly quoted All Weather allocation may not show equal risk contributions when measured with portfolio software. According to the accepted answer, the weights came from an interview describing an unleveraged sample portfolio…
The document considers whether it is reasonable to average correlation matrices estimated from the same underlying prices but sampled at different return frequencies. Its answer indicates that this practice has been observed in risk modeling, including…
The document examines why annualized volatility estimated from weekly or other lower-frequency returns can exceed an estimate from daily returns. The square-root-of-time scaling rule relies on returns being identically distributed and independent; serial…
The document recommends *Active Portfolio Management* by Richard Grinold and Ronald Kahn as a possible preparation for graduate study in asset pricing and portfolio choice. The original question asks for a book that is accessible to a beginner yet rigorous…
The document considers how to hedge a leveraged liability whose value depends on a basket of two assets and U.S. dollars. It questions whether a hedge based on the assets’ historical correlation is reliable, especially if that relationship changes. The…
For a mean-variance portfolio, the covariance matrix can be separated into asset volatilities and pairwise correlations. Place the estimated standard deviations on the diagonal of a diagonal matrix, then multiply that matrix by the correlation matrix and by…