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 identifies a suspected comparison error in the Optimal Number of Clusters procedure associated with de Prado and Lewis's work on detecting false investment strategies. The algorithm recursively reclusters groups whose silhouette-based…
This answer derives how many shares to sell after a price change to restore an asset to its initial portfolio weight, assuming sale proceeds remain in cash and no outside capital is added. It writes the starting and ending portfolio values, equates the…
This exchange explains that mean-variance optimization does not inherently require portfolio weights to sum to one. That condition is an added modeling choice, commonly used to represent allocating all available capital to long-only positions, or to require…
This exchange considers whether an asset with negative expected return can still be useful when combined with a portfolio, especially if its returns are negatively correlated or uncorrelated with the portfolio. The answer focuses on expected return relative…
The document asks how to extend mean-variance portfolio optimization with limits on factor exposures and individual positions. The objective is the familiar trade-off between expected return and variance, whose unconstrained solution depends on the inverse…
Market-neutral long–short portfolios can produce positive profit and loss while having little or no net invested capital, making a conventional return denominator unclear. The document presents two ways to define returns for Sharpe ratio analysis: divide…
The document considers a claim whose payoff is the time integral of an asset’s proportional price change. Its main replication argument is direct: hold one unit of the underlying’s inverse price, or equivalently one dollar of stock exposure, so the…
The document explains how CAPM relates to modern portfolio theory and mean-variance optimization. MPT uses expected returns, variances, and covariances to construct an efficient frontier; combining a tangency portfolio with a risk-free asset gives a capital…
The document considers an out-of-sample portfolio process that updates monthly. It uses a rolling 36-month covariance estimate to construct a minimum-variance portfolio, reverse-optimizes those weights into implied returns, combines the estimates with…
The document considers whether a trend-following trader should express a signal on a base currency, such as GBP, through several currency pairs rather than through a single pair. The response argues that a basket of terms currencies may better represent…
The document works through an exam-style question about finding an asset’s covariance with a market portfolio when that portfolio is defined as a weighted combination of two assets. By applying covariance’s linearity, the answer expands the covariance into…
The question concerns a two-period consumption model in which an investor allocates wealth between a risky asset and a zero-coupon bond. The displayed equations appear to let the bond position transfer funds between periods, while the question asks why bond…
The document asks whether a portfolio of two stocks can have both lower volatility and a higher return than either stock, and whether adding more stocks changes the answer. The response gives a mathematical edge case: if two assets have identical volatility…
The document investigates why a global equity portfolio that lagged its benchmark during a short, volatile period could still show a daily regression beta below one. Its main explanation is nonsynchronous trading: markets in different time zones close at…
The document considers whether unknown asset-class returns can be recovered by regressing observed portfolio returns on known allocation weights. It notes a potential identification problem because the weights in each portfolio sum to one, creating a…
The document describes a practitioner’s attempt to extend univariate GARCH risk analysis to a three-series DCC-GARCH model. The workflow fits separate conditional volatility models, combines them through a dynamic conditional correlation specification, and…
The document examines why CAPM assigns an asset with zero market beta an expected return equal to the risk-free rate, even though a single zero-beta asset can still carry substantial risk. It explains diversification using the variance of an equally weighted…
A self-financing portfolio changes value only through changes in the assets it holds, with no external deposits or withdrawals. For holdings phi_i in assets priced S_i, its infinitesimal value change is the sum of each holding multiplied by that asset’s…
The discussion explores whether equal risk contribution portfolios can be built using tail measures such as value at risk or expected shortfall, and what conditions support the approach. It highlights positive homogeneity: for a differentiable risk measure…
The document offers guidance for choosing a short applied mathematics project involving financial data and time-series analysis. It recommends aligning the topic with the supervisor’s research interests and adapting an existing empirical paper into a smaller…
The discussion examines whether principal component analysis of yield curves has practical value beyond describing movements as level, slope, and curvature. One answer argues that PCA may help create a denoised correlation matrix, but questions using…
The post asks whether minimum-risk and minimum-variance portfolios are equivalent, prompted by a paper that distinguishes proposed minimum-risk portfolios from traditional minimum-variance portfolios. The answers explain that the distinction depends on how…
The document frames portfolio construction as minimizing variance, expressed with a covariance matrix and portfolio weights that sum to one. It asks how to add lower and upper limits on the weights when implementing a constrained minimum-variance problem,…
The document considers how to calculate returns for a portfolio combining equities and credit, using an equity index and an investment-grade credit index as examples. It cautions that a credit default swap position does not have a meaningful return from…